{
 "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": "iVBORw0KGgoAAAANSUhEUgAAARQAAAD8CAYAAAC2EFsiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nbOXYZAsoW9nKVo5N/i8Y+dfQSqsaLgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105c90f28>"
      ]
     },
     "metadata": {},
     "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 0x1295daa90>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAD8CAYAAABpcuN4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nVGCKMACnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1295daac8>"
      ]
     },
     "metadata": {},
     "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": [
       "0.99999999999999956"
      ]
     },
     "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 0x12dc58e80>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYoAAAD8CAYAAABpcuN4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDcaR1kKuhCtEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1296df7b8>"
      ]
     },
     "metadata": {},
     "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": {
    "collapsed": true
   },
   "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": [
      "0.0 212.1\n",
      "10.0 212.1\n",
      "20.0 212.1\n",
      "30.0 212.1\n",
      "40.0 212.1\n",
      "50.0 212.1\n",
      "60.0 212.1\n",
      "70.0 212.1\n",
      "80.0 212.1\n",
      "90.0 212.1\n",
      "100.0 212.1\n",
      "110.0 212.1\n",
      "120.0 212.1\n",
      "130.0 212.1\n",
      "140.0 212.1\n",
      "150.0 212.1\n",
      "160.0 212.1\n",
      "170.0 212.1\n",
      "180.0 212.1\n",
      "190.0 212.1\n",
      "200.0 212.1\n",
      "210.0 212.1\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 0x12dd3cf98>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEKCAYAAAAfGVI8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8FPX9x/HXJyEhCbccyn0JKIhECVRFBEQUQUHwQAsI\n1pZa71bqUW09Wqz9tWqr9aKVioqCIIqoeICCIoIQ5EYERCGKcgkYziT7/f0xEwiQhAWyO7vZ9/Px\nyGN3Zmdn3jss89m5vl9zziEiIokrKegAIiISLBUCEZEEp0IgIpLgVAhERBKcCoGISIJTIRARSXAq\nBCIiCU6FQEQkwakQiIgkuApBBwhHrVq1XJMmTYKOISISV7Kzszc552ofbrq4KARNmjRh3rx5QccQ\nEYkrZvZNONPp0JCISIJTIRARSXAqBCIiCS4uzhEUJy8vj5ycHHbv3h10FClGWloaDRo0ICUlJego\nInIYcVsIcnJyqFKlCk2aNMHMgo4jRTjn2Lx5Mzk5OTRt2jToOCJyGHF7aGj37t3UrFlTRSAGmRk1\na9bU3ppInIjbQgCoCMQw/duIxI+4PTQkIhJ3nIO8nbBzC+z6EXb5j3m7IX83FOz1HvP3QigPXAh+\n9huoVDOisVQIjkFycjJt27YlPz+fk08+mdGjR5ORkcGIESN46aWXSE5OJikpiWeeeYaf/exndO3a\nlfXr15Oeng7APffcw2WXXRbwpxCRMrPrR9i6Fraug23r/Ed/+Kf13usFe49ghgZtr1AhiGXp6eks\nWLAAgIEDB/L0009z5pln8uabbzJ//nwqVqzIpk2b2Lt3/z/8mDFjyMrKCiqyiJSF3dtgwxewYRls\nWO49bvwCdmw8cLqUDKjWEKo3hBPaQkZNSK8BGcd5j4V/KelQIQ2SK0KFiv7z6G2eVQjKSOfOnVm0\naBFNmjShVq1aVKxYEYBatWoFnExEjklBHny/CNbNhZzPvMdta/e/nlIJ6pwMLXtC7VZQvZH3V62R\nt8GPg/Nl5aIQ3D95Kcu+216m82xdryr3XtwmrGnz8/OZMmUKPXv25Pzzz+eBBx6gZcuWnHfeeQwY\nMIAuXbrsm3bgwIH7Dg1NmzaNmjUju8snIkdo7w74ZhZ8PRPWfQbffQ75u7zXqtaHBh0g6xqo09or\nANUaQlJcX3dTPgpBUHbt2kVmZibg7RFce+21pKamkp2dzccff8yHH37IgAEDeOihhxg6dCigQ0Mi\nMScUgh8Ww+oPvL+1s73j+EkpUPdUb6PfoAM07AjVGgSdNiLKRSEI95d7WSt6jqCo5ORkunbtSteu\nXWnbti2jR4/eVwhEJAbk74E1H8HyN2DFlP3H9uu0gY7DoPm50Pgs79h9AigXhSCWrFixgqSkJFq0\naAHAggULaNy4ccCpRIS83bDyPVg2Cb58F/b+BKmVocX50KIHNOsGVesGnTIQKgRlLDc3l5tuuomt\nW7dSoUIFTjzxREaOHBl0LJHEFArB2lmwaBwsnQR7tnlX7rS5BE6+GJp2gZS0oFMGToXgGOTm5h4y\nrn379syaNavY6adPnx7hRCICwLYcmP88fD4Gtud4V/acfDGceoW38Y/ipZnxQGtDRMqHUMg72Ttv\nFHw5xbuLt/m50ON+aHUhpFYKOmHMUiEQkfi2cwvMHw3z/gdbv4FKtaHTrdB+CNRoEnS6uKBCICLx\n6cevYfZTMP8FyNsBTTrDeffCSRdDhdSg08UVFQIRiS8/LIOP/wFLXwNLgraXw1k3wfHBXEZeHqgQ\niEh8+GEpzPg/WPa6d9nnmTd4LXNWqx90srinQiAisW3zapj2gF8AqsA5v4czrvfa8ZEyEbEGMsxs\nlJltMLMlRcYdZ2bvm9lK/7FGpJYfDTk5OfTt25cWLVrQvHlzbrnlln0tjT733HPceOONASc8VOXK\nlYsdn5ycTGZmJqeccgqXX345O3fuBGDEiBG0adOGU089lczMTObMmQNA165dadWqFZmZmWRmZjJh\nwoSofQZJELkb4a3h8ERHWDUVzrkdbl0E596jIlDGItlS0nNAz4PG3QlMc861AKb5w3HJOUf//v25\n5JJLWLlyJV9++SW5ubncfffdEVtmfn5+xOZd2FzGkiVLSE1N5emnn+bTTz/d16T2okWLmDp1Kg0b\nNtz3njFjxrBgwQIWLFigfhWk7OzdATP+Do9lepeCth8KN38O596tAhAhESsEzrmPgC0Hje4LjPaf\njwYuidTyI+2DDz4gLS2Na665BvB+UT/66KOMGjVq36/pdevW0bNnT1q1asX9998PwI4dO+jduzft\n2rXjlFNOYdy4cQBkZ2fTpUsX2rdvzwUXXMD69esB75f3H/7wB7p06cKIESNo0qQJoVAIgJ07d9Kw\nYUPy8vJYvXo1PXv2pH379nTu3JkvvvgCgDVr1nDmmWfSoUMH/vjHP4b12Tp37syqVatYv379IU1q\n16tXr4zWoMhBnIOlr8PjWfDhX6BZV7hhDvR+GCrXCTpduRbtcwTHO+fWAzjn1ptZif+6ZjYMGAbQ\nqFGj0uc65U74fnEZxsTrROLCh0p8eenSpbRv3/6AcVWrVqVRo0asWrUKgM8++4wlS5aQkZFBhw4d\n6N27N9988w316tXjrbfeAmDbtm3k5eVx0003MWnSJGrXrs24ceO4++67GTVqFABbt25lxowZAMyf\nP58ZM2bQrVs3Jk+ezAUXXEBKSgrDhg3j6aefpkWLFsyZM4frr7+eDz74gFtuuYXf/OY3XH311Tzx\nxBOH/dhqUlsCseUrePv33iGgE9rCZaOg8ZlBp0oYMXuy2Dk3EhgJkJWV5QKOcwjnXLEdtBcd36NH\nj30bx/79+zNz5kx69erF8OHDueOOO7jooovo3LkzS5YsYcmSJfTo0QOAgoIC6tbd3/jVgAEDDng+\nbtw4unXrxtixY7n++uvJzc1l1qxZXH755fum27NnDwCffPIJr776KgCDBw/mjjvuKPbzqEltCUT+\nHpj5T/j4YUhOhZ4PQYdfqQmIKIv22v7BzOr6ewN1gQ1lMtdSfrlHSps2bfZtYAtt376ddevW0bx5\nc7Kzsw8pFGZGy5Ytyc7O5u233+auu+7i/PPPp1+/frRp04ZPP/202GVVqrT/1vg+ffpw1113sWXL\nFrKzszn33HPZsWMH1atXL7ZJ7MLlHo6a1Jao+2YWTLoRtqyGNv3hggcTtvXPoEW7W503gCH+8yHA\npCgvv8x0796dnTt38vzzzwPer/jbbruNoUOHkpGRAcD777/Pli1b2LVrF6+//jqdOnXiu+++IyMj\ng0GDBjF8+HDmz59Pq1at2Lhx475CkJeXx9KlS4tdbuXKlenYsSO33HILF110EcnJyVStWpWmTZsy\nfvx4wNsrWbhwIQCdOnVi7NixgPcL/kisWLGClStX7htWk9pSJvJ2wbt3w/96gSuAQRPh8v+pCAQo\nkpePvgx8CrQysxwzuxZ4COhhZiuBHv5wXDIzXnvtNcaPH0+LFi1o2bIlaWlpPPjgg/umOfvssxk8\neDCZmZlceumlZGVlsXjxYjp27EhmZiYjRozgnnvuITU1lQkTJnDHHXfQrl07MjMzS2zBFLzDQy++\n+OIBh4zGjBnDs88+S7t27WjTpg2TJnk19l//+hdPPPEEHTp0YNu2bUf0GXNzcxkyZAitW7fm1FNP\nZdmyZdx3331HtqJEivp2PjzTBT79N3S4Fq77BE7sHnSqhGfOxdzh90NkZWW5efPmHTBu+fLlnHzy\nyQElknDo30j2CRXAx4/A9L9ClROgz+MqAFFgZtnOucOeyNMZGRGJrNwNMPFX8NV0r12gXv+A9OpB\np5IiVAhEJHK+muEVgd3boM+/4bRBEMbFCxJdcV0ISrqEU4IXD4ccJYKcg1mPwdT7oOaJMPg1tQ4a\nw+K2EKSlpbF582Zq1qypYhBjnHNs3ryZtDT1BZuQ8nbDm7fCwpehdV/o+yRULL6NK4kNcVsIGjRo\nQE5ODhs3bgw6ihQjLS2NBg0aBB1Dou2nH2DcQMiZC13/AF1u16GgOBC3hSAlJYWmTZsGHUNECm1c\nAS/0h11b4Irnvb0BiQtxWwhEJIbkZMOYyyCpAlwzBeplBp1IjkC07ywWkfJm9Qcw+mJIqwrXvqsi\nEIe0RyAiR+/rmfDSAKjVEga96t0sJnFHhUBEjs6G5TD251CjKQyZrE5j4pgODYnIkdv+Hbx4KVRI\nh0ETVATinPYIROTI7N4GL14Gu7fDNW9D9cN0HCUxT4VARMKXvxfGDYJNK2DgeKh7atCJpAyoEIhI\neEIhmHQ9rPkI+j0Dzc8NOpGUEZ0jEJHwTLsPFo+H7n+CdlcGnUbKkAqBiBzenJHwyb8g61o4+3dB\np5EypkIgIqVbPhmm3A6tekOvv6vtoHJIhUBESrZ2Drz6S2iQBZf+F5KSg04kEaBCICLF27QSXh4A\nVevDVeMgNSPoRBIhKgQicqiffvBuGEuq4DUdUalm0IkkgnT5qIgcaE8uvHQF7NgIQ9+E49Tce3mn\nQiAi+xXkw/ih8P0iuGos1G8fdCKJAhUCEfE4B2/9Fla9Dxf9E1peEHQiiRKdIxARz0d/h/nPwzm/\nh6xrgk4jUaRCICLw+Rj4cAS0uwq63R10GokyFQKRRLdqKky+GZp1g4sf0w1jCUiFQCSRfZsNrwyB\n2id7Hc5XSA06kQQgkEJgZr81s6VmtsTMXjaztCByiCS0TSthzOVepzIDx3t9DktCinohMLP6wM1A\nlnPuFCAZUFOGItG0/Tt4oT9gMPh1qFo36EQSoKAuH60ApJtZHpABfBdQDpHEs3OLVwR2/ejdMFaz\nedCJJGBR3yNwzn0L/ANYC6wHtjnn3jt4OjMbZmbzzGzexo0box1TpHzauxNevhK2rIYrx0C9zKAT\nSQwI4tBQDaAv0BSoB1Qys0EHT+ecG+mcy3LOZdWuXTvaMUXKn4I8767hdZ9B//9Asy5BJ5IYEcTJ\n4vOANc65jc65PGAicFYAOUQSRygEk26Ele9C74ehzSVBJ5IYEkQhWAucYWYZZmZAd2B5ADlEEoNz\nXscyi8ZCt3ugw7VBJ5IYE8Q5gjnABGA+sNjPMDLaOUQSxgd/hrn/gbNugnOGB51GYlAgVw055+4F\n7g1i2SIJZeY/4eOHof1Q6PFn3TUsxdKdxSLl1dxnYeq9cMql0PsRFQEpkQqBSHm0aDy8dRu07An9\nnlFfw1IqFQKR8mb5ZHjt19DkbLj8OUhOCTqRxDgVApHyZMUUGH+N17PYVS9DSnrQiSQOqBCIlBcr\np8IrV8MJbWHQBKhYJehEEidUCETKg9UfwtifQ+2TYPBESKsWdCKJI4ctBGbWuphxXSOSRkSO3JqP\n4eWroOaJcPUkSK8RdCKJM+HsEbxiZneYJ93MHgf+GulgIhKGbz6FlwZAjcZeEcg4LuhEEofCKQQ/\nAxoCs4C5eE1Gd4pkKBEJw7q5XscyVevC1W9AZTXOKEcnnEKQB+wC0oE0vAbjQhFNJSKl+3Y+vHgp\nVKoFQyZDleODTiRxLJxCMBevEHQAzgauMrMJEU0lIiVbvwhe6Afp1bwiULVe0IkkzoXT1tC1zrl5\n/vPvgb5mNjiCmUSkJN8vhuf7QmplrwhUbxh0IikHwikEG8ys0UHjZkQijIiU4rsF8MIlkJIBQ96A\nGk2CTiTlRDiF4C3AAYZ3jqApsAJoE8FcIlJUTja82A8qVoOhk1UEpEwdthA459oWHTaz04FfRyyR\niBxo7Wx48TKoVNM/HHTwDrrIsTniO4udc/PxThyLSKR9/Qm80B8q14Ghb6sISEQcdo/AzH5XZDAJ\nOB3YGLFEIuL5ajq8dKV3QnjIZKhyQtCJpJwK5xxB0Zar8vHOGbwamTgiAsCqqTB2IBzXzLtjuHKd\noBNJORbOOYL7oxFERHwr3oFXBkPtVjB4knduQCSCSiwEZjYZ72qhYjnn+kQkkUgiW/4mjB8KJ5wC\ngyaq7SCJitL2CP4RtRQiAotegdeug/qnw6BX1ZS0RE1pheBPzrnuZvY359wdUUskkojmPANTbocm\nneHKlyCtatCJJIGUVgjqmlkXoI+ZjcW7oWwf/zJSETkWzsGMv8H0v0Kr3nDZKEhJCzqVJJhS9wiA\nO4EGwMMcWAgccG4Ec4mUf6EQvHsXzHkaMgfCxY9BcjgX8omUrRK/dc65CcAEM/ujc+7PUcwkUv4V\n5MGkG2DRODjjBjj/L5CknmMlGOFcPqoiIFKW8nbB+Gvgyylw7j3QeTiYHf59IhESyE8QM6tuZhPM\n7AszW25mZwaRQyTqdm/zOpT58h3o/TCc83sVAQlcUAck/wW845y7zMxSgYyAcohEz08/wJjLYMMy\nuPS/0PayoBOJAKXfUFbqnSzOuS1Hs0AzqwqcAwz157MX2Hs08xKJG5tWwov9YccmuGostOgRdCKR\nfUrbI8hmfz8EjYAf/efVgbV4/RIcjWZ4jdb9z8za+cu5xTm34yjnJxLb1n0GLw0AS4Khb0L99kEn\nEjlAiecInHNNnXPNgHeBi51ztZxzNYGLgInHsMwKeC2YPuWcOw3YgXeZ6gHMbJiZzTOzeRs3qrFT\niVNfvAWjL4b06vDL91UEJCaFc7K4g3Pu7cIB59wUoMsxLDMHyHHOzfGHJ+AVhgM450Y657Kcc1m1\na9c+hsWJBGTuszBuEBzfBq5932tJVCQGhVMINpnZPWbWxMwam9ndwOajXaBz7ntgnZm18kd1B5Yd\n7fxEYo5zMO3P8Nbv4MQeXl8ClWoFnUqkROFcNXQVcC/wGt45g4/8ccfiJmCMf8XQV8A1xzg/kdhQ\nkAdv3AwLX4LTh0DvR3S3sMS8cG4o2wLcYmaVnXO5ZbFQ59wCIKss5iUSM3Zv95qQXj0Nuv4Butyu\newQkLhz20JCZnWVmy/AP35hZOzN7MuLJROLJj9/AqAu87iX7PA5d71ARkLgRzj7ro8AFwBsAzrmF\nZnZORFOJxJN1n8HYn0P+Xq8fgebdgk4kckTCamLCObfuoFEFEcgiEn8WT4DnLoLUyvDLqSoCEpfC\n2SNYZ2ZnAc4/uXszsDyysURinHMw/SGY8RA0OgsGvKi+hSVuhVMIrsNrG6g+3j0A7wE3RDKUSEzL\n2+U1Ib3kVWj3c7j4n1ChYtCpRI5aOFcNbQIGRiGLSOzbvt67SezbedD9Xjj7tzopLHGvtEbnHse7\nb6BYzrmbI5JIJFat+8wrAnt+gitegNZ9gk4kUiZK2yOYF7UUIrEu+zl4azhUqw+DX/OajRApJ0rr\nqnJ0NIOIxKT8vTDldsj+HzQ/Fy59FjJKbaFdJO6Ec0PZ+2ZWvchwDTN7N7KxRGLAT9/D6Iu8ItDp\nVhg4QUVAyqVwrhqq7ZzbWjjgnPvRzOpEMJNI8NbNhVcGe11LXjYKTrk06EQiERPODWUFZtaocMDM\nGlPKSWSRuDf/eXiuFySnes1HqwhIORfOHsHdwEwzm+EPnwMMi1wkkYDk74V374K5/4Vm3bw9AR0K\nkgRQaiEwMwOW4nUccwZeV5W/9e8tECk/tq71Wg79NhvOugm636fmoyVhlPpNd845M3vdOdceeDNK\nmUSia8U78NqvwYXgiuehdd+gE4lEVTjnCGabWYeIJxGJtoI8eO+P8PIAqN4Ifj1DRUASUjj7vt2A\nX5vZN3gdzRvezsKpEU0mEknbvoUJv4B1syHrF3DBXyElLehUIoEIpxBcGPEUItG0ahpM/BXk7fZu\nEGt7WdCJRAJVWltDVZ1z24GfophHJHJCBV7T0R/9HeqcDJePhtotg04lErjS9gheAi4CsvHuGyja\nxKIDmkUwl0jZ2pYDr10HX38MmYOg198hNSPoVCIxobS2hi7yH5tGL45IBCx5Fd78LRTkQ98n4TS1\nqi5SVDhtDfUzs2pFhqub2SWRjSVSBnZvg4m/9k4K12oJv5mpIiBSjHAuH73XObetcMBvd+jeyEUS\nKQPffApPnQ2Lx0PXu+Cad+A4Hc0UKU44Vw0VVyx0y6XEpoI8mP5XmPmod2/AL96Bhh2DTiUS08LZ\noM8zs0eAJ/BOEt+EdwJZJLZsWuldFvrd53DaIOj5EFSsEnQqkZgXzqGhm4C9wDhgPLAbdV4vsSQU\ngtlPw9Od4cevvW4k+z6hIiASpnA6r98B3BmFLCJHbstXMOlG+OYTaHE+XPwYVK0bdCqRuHLYQmBm\nLYHhQJOi0zvnzj2WBZtZMl6/yN8WXqoqErZQCOb+B6beB0kp3mWhmT8Hs8O+VUQOFM45gvHA08B/\ngYIyXPYtwHKgahnOUxLBljX+XsBMOLEH9HkMqtYLOpVI3AqnEOQ7554qy4WaWQOgNzAC+F1ZzlvK\nsVDI6zRm6r2QVME7D5A5UHsBIsconEIw2cyuB14D9hSOdM5tOYbl/hO4HdDZPAnPljXwxk1eExEn\nnuedC6hWP+hUIuVCOIVgiP/4+yLjjrqtITO7CNjgnMs2s66lTDcMv0vMRo0alTSZlHcFeTD7Ke/e\ngKQK0Off3qWh2gsQKTPhXDVU1m0NdQL6mFkvIA2oamYvOucGHbTckcBIgKysLFfGGSQerPvMayPo\nhyXQqpfXUFy1BkGnEil3SryPwMxuL/L88oNee/BoF+icu8s518A51wS4Evjg4CIgCW7XjzD5Fni2\nB+zaCle+BFe9rCIgEiGl3VB2ZZHndx30Ws8IZJFE5xwsegX+3QHmvwBn3gg3zIGTegedTKRcK+3Q\nkJXwvLjho+Kcmw5ML4t5SZz7fgm8c6d3Mrh+exg0EeqqN1SRaCitELgSnhc3LHJ0dmyGD/8C2c9B\nWnXo/Qi0HwpJyUEnE0kYpRWCdma2He/Xf7r/HH9YvXzLsSnIg3mj4MMRsCcXOg6DrndCeo2gk4kk\nnNJ6KNNPMomM1R96h4E2fgHNunqthNY5OehUIglL/QpI9GxZA+/dA1+8CdUbw4Ax3olg3RMgEigV\nAom8XVu9jmJmP+k1EHfuH70rglJ0hFEkFqgQSOTk74V5z8KM/4NdW+DUK+G8e9VAnEiMUSGQsucc\nLJ0I0x7wOopp2gXO/zPUbRd0MhEphgqBlK2vP/HOA3w3H+q0gUGvQvPuOg8gEsNUCKRsrJ0N0x+C\nrz6EKvW8JqLbXaX7AUTigAqBHJuvP4EZD8GajyCjFvR4ADr8ClIzgk4mImFSIZCjs+ZjmPE3r0mI\nSnXg/BGQdQ2kVgo6mYgcIRUCCZ9zsGaGdxXQN59A5RO8m8FOH6I9AJE4pkIghxcKwcp34eNHIOcz\n7xzAhX+H0wdDSnrQ6UTkGKkQSMkK8mDJRO9msI3LoXoj6PUPOG2wbgYTKUdUCORQebvg8xdh1mOw\ndS3UaQ39/wNt+kOyvjIi5Y3+V8t+u36Euc96fQTv3AQNf+YdAmpxPiSV1oeRiMQzFQKBTatgzlOw\n4CXI2+lt+M/+LTQ+K+hkIhIFKgSJqvAKoE+f9E4EJ6dC2yvgjN/ACacEnU5EokiFINFsXw8LX/LO\nAWz5yrsJrMud0OFaqFwn6HQiEgAVgkRQkAdfvgufvwAr3wMXgsad4JzboU0/XQEkkuBUCMqzjV/C\n58/DwrGwY6N3A1inW+G0QVCzedDpRCRGqBCUN3tyYelr3q//dXMgqQK07Old+3/iebr8U0QOoa1C\neeAc5MyF+c97RWBvLtRs4TUA1+4qHfsXkVKpEMSz3I2waCzMfwE2rYCUSnBKPzjtamjYUX0AiEhY\nVAjiTd5u+HIKLBwHq96HUD406Ah9HvdO/FasEnRCEYkzKgTxIG+3197/8jdg2STYsx2q1IUzrvdO\n/NZuFXRCEYljKgSxKneDd8nnl+/A6g8hb4d36Kd1Hzh1ADQ9R71/iUiZiHohMLOGwPPACUAIGOmc\n+1e0c8Qc52DDMlgxxdv458wDHFStD+2uhFYXQpPOuuZfRMpcEHsE+cBtzrn5ZlYFyDaz951zywLI\nEqxQgdfD1xdve8f9t671xtc7Hbr9wbvs84S2OukrIhEV9ULgnFsPrPef/2Rmy4H6QOIUgk2rvGYe\nFo6F7d9ChTRo1g063+Zt/KucEHRCEUkggZ4jMLMmwGnAnCBzRMXu7bDsdfh8DKybDZbk3eB1wQho\ncYG6ehSRwARWCMysMvAqcKtzbnsxrw8DhgE0atQoyunKSEE+rJkOi8Z7V/zk7YRaLeG8+70TvlXr\nBp1QRCSYQmBmKXhFYIxzbmJx0zjnRgIjAbKyslwU4x2bvTth7Sz48j3vLt8dG6BiNW/Df9ogqN9e\nx/xFJKYEcdWQAc8Cy51zj0R7+WUuFILvF8LqD+Cr6bB2NhTsheSK0PICOPUKr6OXChWDTioiUqwg\n9gg6AYOBxWa2wB/3B+fc2wFkOToF+bBqKiweD199CDs3e+OPPwU6DvNO/DY+S8f9RSQuBHHV0Ewg\nPo+NhELexv/Dv3iXembUhBN7QPNzoVlXqHJ80AlFRI6Y7iwOV+5GmPgrbw/ghFNhwIPepZ7JKUEn\nExE5JioE4di8Gkb3gZ2b4KJH4fShkJQUdCoRkTKhQnA4W9fBc729E8C/eBfqZQadSESkTKkQlGbv\nDhh7lff4i3fg+DZBJxIRKXMqBKWZcjv8sBR+/oqKgIiUWzrQXZIV78DnL3qdvbfoEXQaEZGIUSEo\nTt4ueOs2qNMGut4ZdBoRkYjSoaHifPoEbM+B/s/ojmARKfe0R3Cw3A0w81Fo1RuanB10GhGRiFMh\nONj0v0L+bujxQNBJRESiQoWgqM2rIXs0ZP0Cap0YdBoRkahQISjqk39CUgXoPDzoJCIiUaOTxYW2\n5cCCl6H90HLZeFwo5MgPOULOUVD4vMi4wuGCg6YLOYdzEHKOkP/o/OfOQUHIGy4oMn0oBAXOm1/I\nFX3uzcvhzQcHjv3jXNFh5/aPK/I85LyuKYpOGyry3Httf74D5+8OGbc/x/7Xi5tf4bRFs4L3WQ/5\nDPvyHph7X6cahfPdP6bIsg58bf/wga8XHXvoNK7E9xw8zSHLP2ie4WQq9fOEkelYldmsyjBUWXag\n8sTPT6fhcZFtyViFoNCsfwMOOt0c8UXlF4TYvGMvG3/as+/vpz35/gZs/8aocGO8Nz/E3oLQAY97\n8kPszishMvcuAAALeUlEQVRgd14Be/JC7M7f/+iND7Env4D8Am/DLl5/QAaYGQYk+SNs32uGmTfe\noMhrRpLtf5/5L3rj9r9v37yt9PnhT+ePOiCfN84OGCac95TwXjt4QopmOHjYin296HyLPuxbF1b4\nuh34njA/T1koqzmVZZ9RZTWr5KTIN9asQgCwcwvMfx7aXg7VD98t5u68ArbvyiN3Tz67Cje6eQX+\nRji0b0O8c28+G3P3HLDB35S7h8079h7Rj48kg9QKSaQkJ1HRf0xLSaZiBe8xLSWJGhmppKX4wxW8\ncRVTkklJNpLNSE5KIjkJkpKMCklGknmPyUlFXjOjQnLha0kkmTd9kr8hTNq3kTtwONls33TJSftf\nS046cHjf+ymysSyycT1g/MEbV4psuA/eQBfZABXd8B4wb/UKJ1IiFQKA7P9B3g4466ZiX16zaQdv\nL17PzJWbWPHDT2zZsTfsWackG7UrV6R21TQa1MjgtEY1qF2lInWqVKR24V/lilRNSyEp6cCNrPf+\npKj8IhCRxKVCkL8H5jwDzbsf0p7Q6o25/P2dFby77Hucgzb1qnJ+6+NpeFwGVdNTqFwxmfSUZCoW\n+RWenlr43HutanoF/RoVkZimQrB4POT+AP2e2TcqFHL8b9bX/N87X5CanMQNXU9k4BmNqFstPcCg\nIiKRkdiFwDmY9Tgc39brahLYk1/Aba8s5M1F6+l+Uh3+emlb6lRJCzSmiEgkJXYh+PId2PgF9BsJ\nZuTuyee6F7KZuWoTd/Q8ieu6NNNhHREp9xK3EDgHH/3Du0rolP7syS/gl6PnMvfrH3n48nZc2r5B\n0AlFRKIice8sXvMRfDsPOt1KyCrwu1cWMvurLSoCIpJwErcQfPwwVD4eMgcy4u3lvLVoPXddeBKX\nnFY/6GQiIlGVmIUgZx6smQFn3sh/Z3/HszPXcE2nJgw7p1nQyUREoi7xCoFzMPU+yKjJu+kX8pe3\nltOr7Qn8sXdrnRgWkYSUeIVg1VT4+mPWtr2Bmyauon3jGjxyRSZJuntXRBJUYhWCvF3w9nD2VGvG\npZ+dRP3q6fzn6izSUpKDTiYiEphACoGZ9TSzFWa2ysyi1zv8hyPgx6+5cftgKqSmMfqajhxXKTVq\nixcRiUVRLwRmlgw8AVwItAauMrPWEV/wkokw63HG0YPFKe0YO+wMGtWMbBvfIiLxIIg9go7AKufc\nV865vcBYoG/ElhYqYPOMpymY8EvmhloxpvpvGH/dmTSuWSliixQRiSdB3FlcH1hXZDgH+FkkFvTZ\n41fTavM0apLLzFBbPj79Ecb2Op2M1MS9oVpE5GBBbBGLuzznkG5azGwYMAygUaPDdxZTnIKqDVge\n6sZP9c+hTfeBnF1DewEiIgcLohDkAA2LDDcAvjt4IufcSGAkQFZW1lH1tXjmkAeP5m0iIgkliHME\nc4EWZtbUzFKBK4E3AsghIiIEsEfgnMs3sxuBd4FkYJRzbmm0c4iIiCeQs6bOubeBt4NYtoiIHCix\n7iwWEZFDqBCIiCQ4FQIRkQSnQiAikuBUCEREEpw5d1T3akWVmW0EvjnKt9cCNpVhnPJG66d0Wj8l\n07opXSysn8bOudqHmyguCsGxMLN5zrmsoHPEKq2f0mn9lEzrpnTxtH50aEhEJMGpEIiIJLhEKAQj\ngw4Q47R+Sqf1UzKtm9LFzfop9+cIRESkdImwRyAiIqUo14XAzHqa2QozW2VmdwadJ2hm9rWZLTaz\nBWY2zx93nJm9b2Yr/ccaQeeMFjMbZWYbzGxJkXHFrg/zPOZ/lxaZ2enBJY+OEtbPfWb2rf8dWmBm\nvYq8dpe/flaY2QXBpI4OM2toZh+a2XIzW2pmt/jj4/L7U24LgZklA08AFwKtgavMrHWwqWJCN+dc\nZpHL2u4EpjnnWgDT/OFE8RzQ86BxJa2PC4EW/t8w4KkoZQzScxy6fgAe9b9DmX5Lwvj/t64E2vjv\nedL/P1he5QO3OedOBs4AbvDXQVx+f8ptIQA6Aqucc1855/YCY4G+AWeKRX2B0f7z0cAlAWaJKufc\nR8CWg0aXtD76As87z2ygupnVjU7SYJSwfkrSFxjrnNvjnFsDrML7P1guOefWO+fm+89/Apbj9cce\nl9+f8lwI6gPrigzn+OMSmQPeM7Nsv09ogOOdc+vB+3IDdQJLFxtKWh/6Pu13o394Y1SRQ4kJu37M\nrAlwGjCHOP3+lOdCYMWMS/RLpDo5507H2029wczOCTpQHNH3yfMU0BzIBNYDD/vjE3L9mFll4FXg\nVufc9tImLWZczKyf8lwIcoCGRYYbAN8FlCUmOOe+8x83AK/h7br/ULiL6j9uCC5hTChpfej7BDjn\nfnDOFTjnQsB/2H/4J+HWj5ml4BWBMc65if7ouPz+lOdCMBdoYWZNzSwV70TWGwFnCoyZVTKzKoXP\ngfOBJXjrZIg/2RBgUjAJY0ZJ6+MN4Gr/6o8zgG2FhwASyUHHtfvhfYfAWz9XmllFM2uKd1L0s2jn\nixYzM+BZYLlz7pEiL8Xn98c5V27/gF7Al8Bq4O6g8wS8LpoBC/2/pYXrA6iJd3XDSv/xuKCzRnGd\nvIx3eCMP7xfbtSWtD7xd+yf879JiICvo/AGtnxf8z78Ib+NWt8j0d/vrZwVwYdD5I7xuzsY7tLMI\nWOD/9YrX74/uLBYRSXDl+dCQiIiEQYVARCTBqRCIiCQ4FQIRkQSnQiAikuBUCEREEpwKgcQFMyvw\nmz1eYmaTzaz6Eb7/PjMb7j9/wMzOO8Y8Tcxsl5ktOJb5lCUzG+A3c/xm0FkkvqgQSLzY5bxmj0/B\naxHzhqOdkXPuT865qWWQabVzLvNI3hDJppmdc+OAX0Zq/lJ+qRBIPPoUv+VGM6tsZtPMbL7f6c6+\npsbN7G6/k5SpQKsi458zs8v851+bWS3/eZaZTfefdynS+crnhc1zlMbMXvdbdl1apHVXzCzX3wuZ\nA5xpZh3MbJaZLTSzz8ysipm18Z8v8Fv2bOG/d1CR8c8UFhLzOl2a789j2rGvUklkFYIOIHIk/A1h\nd7x2XgB2A/2cc9v9DfpsM3sDOB2vfanT8L7n84HsI1jUcOAG59wnfguTu8N4zy+cc1vMLB2Ya2av\nOuc2A5WAJc65P/ntXn0BDHDOzTWzqsAu4DrgX865Mf40yWZ2MjAAr9XYPDN7EhhoZlPwGnw7xzm3\nxsyOO4LPJXIIFQKJF+n+8fgmeBv09/3xBjzoN6kdwttTOB7oDLzmnNsJ4BeHI/EJ8IiZjQEmOudy\nwnjPzWbWz3/eEK/htc1AAV4rleDtmax3zs0FcH7TxWb2KXC3mTXwl7fSzLoD7fGKCkA6XmuWZwAf\nOa8DGJxz4XYeI1IsHRqSeLHLPx7fGEhl/zmCgUBtoL3/+g9Amv9aOA1p5bP//0Hh+3DOPYR3vD0d\nby/jpNJmYmZdgfOAM51z7YDPi8xvt3OuoHDS4nI5514C+uDtHbxrZuf60452+7uFbOWcu6+keYgc\nLRUCiSvOuW3AzcBwvz34asAG/9BJN7xCAfAR0M/M0v3j+xeXMMuv8X51A1xaONLMmjvnFjvn/gbM\nA0otBH6OH51zO/2icUYJ030B1DOzDv5yqphZBTNrBnzlnHsMr1XPU/Far7zMzOr40x5nZo3xzpF0\n8Zt7RoeG5Fjp0JDEHefc52a2EO8cwBhgspnNw2sK+At/mvlmNs4f9w3wcQmzux941sz+gNfVYKFb\n/cJSACwDphwm1jvAdWa2CK8Z5tklZN9rZgOAx/1zCbvw9iQGAIPMLA/4HnjAP99wD173okl4zUHf\n4Jyb7Z+MnuiP3wD0OEw+kRKpGWqRo2BeP7Vv+pezxgz/ENVw59xFQWeR+KFDQyJHpwCoFms3lAFP\nAj8GnUXii/YIREQSnPYIREQSnAqBiEiCUyEQEUlwKgQiIglOhUBEJMH9P1Fb8o9u+MrtAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1296dffd0>"
      ]
     },
     "metadata": {},
     "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": [
       "<matplotlib.text.Text at 0x1296c6c50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEKCAYAAAAfGVI8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAhGRJKcgEBFJcgoCEZEk9/8BGBd4JKX73oUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1295dacf8>"
      ]
     },
     "metadata": {},
     "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 0x12de25588>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEKCAYAAAAB0GKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dd8c080>"
      ]
     },
     "metadata": {},
     "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": [
       "<matplotlib.text.Text at 0x12dddea90>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEKCAYAAAAB0GKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxQLTGZNdnwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x132306e10>"
      ]
     },
     "metadata": {},
     "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": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAD8CAYAAACcjGjIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nc2LZjTAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dde97f0>"
      ]
     },
     "metadata": {},
     "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.           6.18161082  17.48546882  23.79928199  32.07353102\n",
      "  38.40607579  46.76238796] [  0.           6.52203326  18.7589197   24.07489413  32.78748297\n",
      "  38.5386345   47.21468159]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAU4IZmZWfgJKdhC8OXMEegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1324932e8>"
      ]
     },
     "metadata": {},
     "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": [
      "[ 1.07402112 -0.04599678]\n",
      "1.05507018262\n",
      "1.07282909576\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEaCAYAAAAcz1CnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dded7b8>"
      ]
     },
     "metadata": {},
     "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": [
       "<matplotlib.text.Text at 0x1325f4e48>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEKCAYAAAAIO8L1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncKQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12ddc16d8>"
      ]
     },
     "metadata": {},
     "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": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIhITJQ4REQkJv8fYSyUO2glbEQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1326ed208>"
      ]
     },
     "metadata": {},
     "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 = 0.9664739715532878\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: 0.8526738059811085\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 100 $\\mathrm{\\mu m}$ ELAIS-N1 observations, and try to find its normalization factor. \n",
    "\n",
    "Let's load the stacked PSF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11f93f080>"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVkAAAFMCAYAAABh6c/zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvV+orVd1/j/22edvzh9MYhpoQ6xSg6gELUEvQgUpklYo\n/YMN9UikVUr1pkRKqbX4hypWaOuN1Ba86EUs2FBvvOhVg0XQ4kVAJZH0QmjFKppaY885yTkn55z9\nvehvbsd59ucZY75r7/zWMuwBm73W+8455hhjjvGMZ631rndt7ezs7MShHMqhHMqhvCByZN0GHMqh\nHMqhvJjlEGQP5VAO5VBeQDkE2UM5lEM5lBdQDkH2UA7lUA7lBZRDkD2UQzmUQ3kB5RBkD+VQDuVQ\nXkA5epDKbty4ER/5yEfi3//93+P48ePxsY99LF72spcd5BKHciiHcig/VXKgTPZf/uVf4urVq/GP\n//iP8Ud/9EfxiU984iDVH8qhHMqh/NTJgTLZxx9/PH7pl34pIiJe97rXxRNPPGHHXr58OZ544om4\n4447Ynt7+yDNOJRDOZRDOTC5fv16PP300/Ha1742Tp48uXj+gYLsxYsX48yZM7vPt7e349q1a3H0\n6N5lnnjiiXjHO95xkMsfyqEcyqG8YPIP//APcd999y2ed6Age+bMmbh06dLu8xs3biDARkTccccd\nERHx93//93HnnXdGRIR+w3dra8uulc+5bwa741tbW3Z+Pnfjxo3dc+P41tbW7vF8bOgZ43WePj9y\n5Mju+Bs3buyxZ/yNseM4xSSvO87r/zxGY9HpdrGh+VlPtp305viqPRQz2jPne4677gmtlXUN39SO\nIUeOHLFxHnLjxo1d/7J9OR55312u63wdp/tDa2mOHTly5KYcVqFYuzjSPrk46z7R3lX+Z7+o7mhd\ntUl9dsez3h/84Afxu7/7u7uYtVQOFGR/8Rd/Mb74xS/GW9/61vja174W99xzjx073iK4884742d/\n9md3j7uipmMOOPKxKpFovVxAWnA0bwZks+QEUaBRYMhAXvlPyUrg5hKxKuLsf47NKFoFXZUxh2KT\nbXFgnH3SYsl+6fiuCMnXrK/zRwuVdA2gzWMy8HUNhux1Puk5Ojb+RoN3uevAXG1Sv6uYzjaUrIt8\n3N7exuY41nBS7T3VD+Xmqm9rHijIvuUtb4kvf/nL8Tu/8zuxs7MTH//4xxfroEIisHFSsZbMtBzj\nzCxT7SFbnE05SWis674RcRPLzQWv6yp7rOyshMZoUuo4LXoFyQwuxDpVT57v4uLO5xhrc1KbHWNR\nUaDT2FPjoJzp8kPXd7kyI1Q3GdRJb0USnA2Ue64mqL7IHrcH9FzXpvG0f5on6rMSrIOSAwXZI0eO\nxJ//+Z8vmuM2Wc9pgg9xbED1VIxqqb35f9ZT6XNMpBo3AJaSn5I+n8+2uc5PxypW2I3N+nKjUn8p\n8d3YbENuPDpe5445g33oGrROtt8JFb76pW+lVKCjOtwxahrOD9dsXc5RntGeLJEKzGlMXsPlKcXT\nvdKk3KpAmOwgG1eRAwXZVYUK0gFs/p/nUkC1y44/fc8tr5vPOTbSMT8Sl+jqeyVj7o0bN8qX1zRv\nBjwIPN37XzpOEzj7Wr3lQsXg/jvf8v6rz5nN0dyZY9lu18x0PoGm6h8vffUthbwe+aiNmJqw88nl\nOzUg8l91OODX8dQIHfg6gqSyBCDV7xlC50B4qWwEyEYwkBFrpc0hlpJ1EgvTMTlJCRSoq1OSky86\nT310Y/WDoQyw2V4qaOcvrb8kdku7/CgSKuKKkbgCcv4Q8Iw5+sEi6e2AoprnYkisVdercmDGBrc3\nVROgunGEwoE2AW7WM8bkvdd8pprX+laApWZCGEFCTawCeXd+qWwMyEbMvX+lx8ccZaB5A/R9qbxW\nZrcVc6K5tKHkQwd6muwK3JntkT3kUzeGpCvKWaEPIPR95lmbHFMd51RP13hpXjeGipiaj86h5kf7\n2DEmBRZaX6WLqXvu9js3k3F+CQDO+LekmeQY0Bqqs8IPqueDANchGwGy9LKBAubmjv8UpBmAyucr\noO1soM6cbenYnCu2CuiWJAUlZFegOt4lpNsH/USWdHf73h3Le61gTjHvGgcBZjd+XEmgQK8+Zrbm\n9oAYZtZBMXHjKbdpnRmg6ZpBXq+qS1rf+UhvjTkbOhKSj+ecId8JxFeVjQDZCAYq17F0jr6vNAPK\n+XlO/CGaAFqYet4xKN3MkTiu+F0yZpllo+pXpadjNzNz3FzHjMb/iqFWBVXljCteYlv5uB7TS+5c\nY9Q1u/eBK1JARa9+K6N1e5zXdMcdGXF2ZzvUpmzDsJ/ecyZ9408/hMvNS3VU8an8zcdoT6kZriob\nAbIzTlQbpEU5NiVfD0iFqyCkm+CAboYxqu16GZZLAgdo+ZhjJjM2kG9ZlysWsnV2bfqyxRhXFYTb\nM7dOZdesD11DcUBSNTPXUFUvNUgFU/2g1zV3FfJF7dX3zjvWTetpflZfOFGAm9lPwgBtbiNOQ5wN\ntGcHAaoqGwGyQyh58jFXdAQGA9SqT+9VX944ZTBZXMJqd6ck1WKqEpX8Go+Hfbnr59jl+fSBg9pH\nvlCsqqKowDLbnc+5faW1aR3d81mWP1tIxHrUdipMYkcOrPJ5xyozcBBAdAxU/XFNgYBeHyv46/8h\ndFmYrq36nA+jJuk4Aa3T0R2jc9WXHGZkI0DWsYdVO9s4PtvlK/0637HLSn/VsfU4xaICGdVDgDlk\ngNB4n3TYRd86o7Wcj7PsuGIsNG92nLNnjOkacqXD2aJ6qysoiHW5BkUxorcsqjx1ccvNtXp14Vie\n+u7Wyzmlel2tqM68btX8nX+qV2tQ13ZSAfGsbATIUuJXHdd1V9pQYm0daDmw0Mc6p2MGaicxG2d3\n/q756OpdoufH7vpfBQrHNjpgr1hG9kUvP3M2k8yw1CVslcZWPrucrMCjW5ced4VdnSOQITurhkeX\nMOY81HmdPRF7X8FUNV01Cf3vvvihr/C05lycVF4UIEvF3CWbY2wEnm7TFJjyJi3tdqpD9Tt9DmzI\nbmooCp7kw2yxKgi67q8sh4CemtnQ3dlB5zp2pv+piLvmQexO7SMwrfK1augE4BQ/1zzVT9Ll8mro\nqRqzG+OamTbTvNYMmFU1mt8myb7rPLcXSrL0PPmh+vYjawfZIRUouUSiYzOsk4qsSshqfiWuO7sN\nXrIOvU9EvmcmUTWW/F/XzWyhKuzsW+WP+8ZdBuvcRCrmR7Htbuqjc5c0cwUwxxRn9bm5DgCIAbpc\n0kbYgbhrTOQnSdaZG6r6NdM41Qdlwjqe7Mi+V4SG/MgxWPLtSpK1gyx1f308002qbqmBpqLVTZnV\nreNInztH+jQhXKfW8VXRdUUxJAMaJSUVr0tA1UPvASq4OD0j0Wm++kLgpfZojDsAIb/Jz6yb9rED\nZtWtMntPhGo+NYEZEkM+02NqmjO+dbZ3YJl1VLdyrBquNv/xt98fFVg7yEZ4BuqYlc6lOapLu5PT\nQ+t1IK+MamyYK7LOF7XXreNEQbCas7TLq32uSXRFTOtQ4ndgrGBZMSTyqSrW7KOzTW1wdmWdKpUe\np9flq+Y56e72ptKhZKXS5c5pPua3AzqyRHtBZGQArbs3AzWHMUePzZC8SjYCZCNuDnD1EpGKSVli\nBaLVV2yzOKDXeXQD5/G4YoGVuGTV9WZARddWuzogrcYp860KMIvuJ70XqkBGDNEVkPOhskOPzbC1\nWcCm89owCTh07kzuOOaW13BAm8fSqxod2wF+fu4+TMvz9VVR9WFqJRUz72qHMGW/slEgmyVvYAV0\nNKfSm48TUNNNWXRzc5dbejesqrvT46owdcxMUtCas8mk45SBzDBWTfKxB/rhhluzA/Gq4FcV2puu\niTpgXrLm0sassXU+0Fpu3SU1lc/l+lKAHXUzzrmYUq44skP1qeRC96GrMzq3imwEyM6AhmNM+ViV\nLPmYK1AHeo495zmO+RJr0zUd2OXkqZJD52sDoW+8qM8zQE3FR7dCJKFCGnrGyzR6aUYNTtfRIlJw\nqBinK7wuLrMg5gDE6ewaX2Vf15Bmmur4gFTf08x5qLFe0qxpjOaD5jwxWOer3uugI1lOiOWuKmsH\n2dmN0WTvmK8rRhWXJATGmXGpTmVlBPjE+DrmVoE9gY8mflXYFat2RUtr0rkK1KloOqn2vWMdrmAI\nOKiRVGsuLVQiBG4NFfJBc0ttVztcs9Zjri4rf6sGqMfzh3DjP90Jr8uTCrTzfEewaD903JI8JdkI\nkCX2l4N7/fr1m8atcr3ljB0V+Kmtul4FMMQ2KnY6IxVQuWKblRk/OyZQ2TweKyuq7JlhFg4UaUwH\njsqmVhVqiEO6QnbNjABam4QDE11bbcgg69j3DABX8zogdcBZrT2bG/SlnKyDYrFf2RiQdUlWOeu6\ntwMXKvAqMdxaFYumNTVxaSwBmzaTyl9dq5MupgQMg6XTXc/GHP2hwFmbCChmztPjGbAlgHNNk+aS\nHpJOxywTrWygvCeA1b2k+OQ7XhFwk/9qR0VQZptc1UjU56oulxAByvfBsPcjGwOyQ2aC71hg/rZS\nHk86VF+ep8nukpOSWpPSsYHOV9U5/HM6sx30e2bkP9lEvrt4z4ja0bHWDlzovO6hruHiXRU9AV/W\n5VgZ+Z//62N6TnY4XXkcPdZjbv9drmQbZ9cfY7rcId9mrhjJ+onAUN1WYExNcxaTZmTtIDuEnIvY\nu9F0nJ674xXAdgk9k1zjeQY6Z98MC9IkIpudTdQ0qrHVlRIVQKmtFTg7P/SDLwUF19zy8cyy85oq\nqzCebq90r6tm4nKyOtcxxso+13Ap1ylfXU3ONFvN36x/xIlqxTVJB5bUEMkOHd/FZL8AG7EBIJsv\nGI6oOzdtris4F+gZ4Ks6HbHXfE7Hu3VIXJNxXbpKpqoQZuwhZlQlf0T/jTE3L/ulNhDAas7ovjow\nV38cgClwkx9V05wFv9zoXYzIR91/50fF3qgJdr7ROQXoqnZUf96jfIWJnu9yXcfqseyv+k82OvBe\nVdYOspWz7hglpwuEfoMjj9Wumo9RcHUMre/GOPZBQnPzWvnymq5IOgak81yhLAVmd17BsAM/BVm1\nX8fqtbu5+Iltq8wWGIGNrtPFrWrG5DOBaF4rv51E94cgW5YwNapV1xjVT9esxrF8ZQF9FqFzXd7P\n5inVxdCrROynHmSHuC6s3dgBXNelFGQd+DkmSMXpiojARH11yUnHRwK6b5fR+nkteqz2KEuiWJC9\n6g8lJTWxGaEbfJN09lJcqUlTg3WM0BX0DJBXNquf1HDy+5b0QZX6k4FY95maj8bJxcL5osc68kRf\nVnAxdDWiOZbn697NgqbqXVXWDrK5A1Ow8rjx393pf0jH5HR9BWgCRUpQB+xZjyZxliXAQwXlxkXs\nvQ5xZn31yzEKfezEFUSerwyH1qY40VUOuiYBhtNJzFH3ms6Tb24tp5uA1u1btldvFE52ukaQbczj\n3VdZnS4dW+UIAaYe17jm+8J2xMI1jizks4vRiwpkqYt2CasbQx/aZADXO7WP83lTdC2ykexQ9uCA\nmnzTYxWAdt9mcUld2U7HyV61zxWFguQM0JLtKhTnClBn8kfPqz0VA55tXDo3/6ccqvymfdC1ZoGQ\nfNB9qa4prfRmyboGUYiIPa/KaC0FuY4M5fWU1ef/M8BJvqwqawfZiJ5VDHFMwxUHJeF47l466Dl6\n2ZHHuo1wx2eYtZ6jdfUT2W6tyr5ZljB0uoLSOQ5UKlspF9RmV3zOppl1icERCNFbN+QzrZEfU2PX\nX43I+e1unpIJROer2pT9o2tBFfxUqhzNY/SPmiU1TCJFzpe83tCXXyXNkoYq/1aVtYPsbFehY8Tk\nqLBzQs0yHrJPgcAxgRn9XTGSzKwXEch2M4tQNlPZ5/ZnpomQECBS88xjaRzdyIfWd2Cdgc0V4Jin\nvxbh9KrtVVPWvaQcnfGPfJsFJher/NzVDDUh0lPVTLbV/eBpRYYoxhlgqwbtfH4hZO0g64SCp4+3\nt7fbZNe7/DiQcpuZxy0BV2e7rukAXHXO2Ocua+oAsQJGZVHOl1UaZTWXCnyGrTk2qXEntqONiH4d\nlvZP7VSWmPVXjc3Zq42JXhnQXs/odo01S9dwq18tIJtUnx4b/w+CRY49deTK1SA11FVl7SBbde88\npmMkOleDRKBN5x0r0PUdqJNfSzfJJZ/z3RU5+eFsn2Wmzp5qjltX/7tCoOZW5YHO79gc5R4xy6xr\n5uvDxLxH09fbZFL+uAascxzw61y1U/e+88HVQo5X1lftrfpBQOvGuRhQjTiwpPofjVV1vihAdohL\n1tnNd8+z7urmMu6lh+vs1TFKsGqzXBd166ku97tZMzY6ncrICITU3o4dd0Dr7FlSvMQCnf7qa5xa\nbEOql6JuvlvD5ceMDzMNYsY+p7taj/Zu/NE1rxXYZXscBqjNCsyaCwSOFUlRHfsF1ixrB9khlFQV\nkA6pGJs73xWnMsFK3K84aFfXS6p0LDEPJ1UyEZDQ+f0mUdVUHIunOGU7NXYaL7I776nLhZnGXRWr\n87EDL/rliPHn7i8xy/5UqtgOoR/TVNG4V+Nn6yS/p139ACgBcdd485gRV0cW3HznGz1eRdYOsrl7\nucDqeB0zuuc4T5tPG+kY4gxTrYpYNzUXneqjzaTv4KsfqjvPd2zYFY3zV8FE13dMtktQx1aowKpC\nd8ywGzOkuiSOGnan1+1NjqX+OWbmYuEasq6t+5Zzi/JixMP5pserOLsb0+d9dM2S7HJzND+qmlKh\n3NZ1NN6rytpBNqLuLg4wqyIl/aQ3b47rkB0bc2wmr0sdd3RdktyR3dpVwlGBdh28ml/56JiaruWY\nhAMK1wicjdmH3HSdPrWhKkZ93N36zjHbwV71GlFqUK55VTng4ql5l+dS/qt+Iihkw4iLu4cFral/\nzs+ueVMtU6yIEOlc1+hWlbWDrPsZXipGF7Q8P0vF6MZjV2SukFWWdObKhuxnVTxZh/OLCiwLfVGg\nKh56rkJMyyV7xxBdsVV6qCirvVU97jfGuqJzcVddld48P7PJqqnlMZrnLl+6HF+yLxoH0ufAu6rj\nKm/JHwVo+sUF0kV72uXKqrJ2kI3g7qJCIFttiH7DKzMIAnH31V61s7KR/CEWQc9JhyZQBgO1X98b\ndj+T060728Wdj91YXYv2w4G07kuOTdZHgKD6XCNzjYHs1zVcI1Q7HZvKNmZ95L/maWeH2k1xpPFq\nv4IsxZd05OOzoEfigFvnzBAktZP0ub1fImsH2S6p8jgHWDpngI4moCYJ3QMhr0XdeKazUSJWXVKL\nv2MVJM7XIdXLZ2pY2e/8gQkxH9oXKmS1d7ZoZwuGYuLAkvbV2US61O8I/16688kBbT5WNcUlLMzV\nlHvrY4bouFhq3rm6pqZX+TvTLOixzq+uf64wZlVZO8hG1F0rP6YiqTpNDqoDlQweuuldQc4A6NKf\nkKliQMyN7M+Mncboe2YzoK5MKd9CMv93wKhApHs74+c4R4Xgrjul5pDjoqL2Zlt0Lu29vpdO8SFb\nCAS3tm6+ntbliq6hov5XYzUOuoYeI7tJl4u3AmzEzZd9aa6ofVXuVr662tD8cvOXyEaA7BBN5gjv\nIP3UTBYtRGITQ884pt/2mUkgB7Bkv+v2lV5dO9+Ja4yrGk3Wpwk5U5Tqj753SWs7oNW3a9QPBzRO\n3FcxyRY6TvGdBSO9aN2JNruI2HMdqcYh29cxO7dPxOq08VMzUD0zQrXnbKN4k880hhqV2u7AvLLb\nxaGL/6xsFMiqMw4c6ZhjDvq4umhfWUseQ4k3mAYVm2OcVFBqAyWNYwHV8+yTa0iUrLreeO4uwtf1\nKjtHzIihUNzz+pT0GmPyifahA5dZcK4avZufb7quBU66ifk7IOzYIsWFxqlNpLOTCvCqWLvGrcdH\nTpI9Wsva5HKsXcyWAHYlawfZUXT5+RBitiQuUA7oCFjoa49qZ36cmR0xFGIw5Fce6wCvSkYqnjyW\nAMWBFK1B6xEYdOIAXHXPJvXSfCD2Np7nvczHaa6e03XVvtygKnudX3RrQBrrcmwGDF0Dc7lFtldA\nXu25+3KCmzN+eijvha7T1Vs+Rvbul7mqrB1kh7iXA92t1vKfS5BZMMjj9GV5tpPm6HnyRRk1AbLO\ncays0q2x6BKsS1LyV5OcgIIa5Mw3fsgnsltjUtnuinz817cyiGFube39WRc3XkUv9Fe7xzHKWx2j\n/pNfgygoiaAGG7H3rZwur8c6Lt7aiCuSo2SIdDtWqThRAa3qodoi/2Ybv5OVQfY3f/M348yZMxER\ncdddd8V73vOeeP/73x9bW1vxyle+Mj784Q+X3XsIJZsDRUqaoWOIS5Bqg5Z0MLWt+omUCogUSPP6\nlIh5HboBua7png999JwSm0SBpmtyqkuZU8dAnB3K9mkcgYY2ZgWApYXlvsrpCED1Ejcfd4CUfSY9\n+bgDbs23TnQ9t1eqj2qb9oryh8a6/O4a0kwzUMB3OLRUVgLZK1euxM7OTjzyyCO7x97znvfEww8/\nHG984xvjQx/6UDz22GPxlre8pdVFQaTkUiBwgEDBUtFNoOcV+Odkqj79pALLelQ3gamuN8sw9Lxb\nv+vsOo7iPtOgKgZWgVqV4K55RfiX+Jo/9AGnNnBtiGrX8N9dm5xtzeOzfo1FBVQkmrv5WF6T7Kaa\n6uJOj3XN7E/V7EcdVTqVFVd2jfPu5jQaf9Wfv9BwENJTTZCnnnoqnnvuuXjXu94V73znO+NrX/ta\nPPnkk/GGN7whIiLe9KY3xVe+8pUpXVTMeo5+WK3aOOrSpJfm5PUcgBGI6bqOmeVEqPyipHfX9Xad\nnu6n6cbouh2A5nHb29t7Lh8blyCpr/RlEYq/2zcXpzxf11WpGpBjW/pc13Z6NE+ybWTn0rUoFvr+\npYJqRQ5IKPer+LqGRD5Ss6tyj7DB5VBlI9k68pNsXkVWYrInT56Md7/73fHbv/3b8R//8R/x+7//\n+zdt2unTp+PChQtTuiiQubPRpnRd0TGyrjs5VtQVjPODRDvpkSNH4vr167vP9b0lvSt/twadz35V\nzKNiqBQ3x86cDhV637vax7FmxWhInzIaKkrnaxW7ocsxu3GuavDqRxVnXc+BV3dnuDG3u80jNfF8\nTuOVc1bXc35S06S4OXbr7NcxIy7OVyc5f1aVlUD25S9/ebzsZS+Lra2tePnLXx4veclL4sknn9w9\nf+nSpTh37txKBmnwO9DIQt/kyHPyf7f59K0dVxSObTmm3SUKfTgynl+/fn33mPs9KrLPAYDqz4Xi\nGFwH0NQMso/VHeo7xlmB3YiHu7Z5xCyDj/uNLl2vuh6bQMbZ79ahmJIdjmw41pfnuFycbbjkt+4x\n2UR6yAaqV/fWi/o1KzmWVfxfCFkJov/pn/4pPvGJT0RExPe///24ePFi3H///fHVr341IiK+9KUv\nxX333TelS4tzCDEQJ2Ps+O9eJo5AV2NcMnYdUFltXkPffqjm5pd41ZwqFlln/lv6QaT6T3tUjR3H\nyKfuZaZbh8A866Nxqof2o1q/iqvOqT6UrGJUxZXWdHrIXpXqGNWDA84qTi7+pDfnh4J3ZZ/z3+Ur\niSNKVX4slZWY7Nve9rb40z/903j7298eW1tb8fGPfzxuvfXW+OAHPxif/OQn4xWveEU88MADU7pG\ngIcQkxpSOZ07YsUcsi7HEJau4TqrgiclSMWSO/vJR2dPxW6JETnm6AqB/Mnxys9H46muEKEYdklP\nxVbFqGJ3FXBprCLmPiypgHepOKB0+aTraNMY57sGQbnlalYb4ZJ9cfma9er6Y46SM7r6w/lCdq6y\nP1lWAtnjx4/HX//1X+85/tnPfnYlIyhpaWM0+AQ0eY4G0RV9nk9AqSBE9qtOSnZ9K6K6mQgVtK6v\nRV4xh6xLn2v86QoHYgcznT6zFbW5S2gFAL3WkwBk/F96z1c95+JPPmRfqiajQg0v66zi7PKBfqNK\nbc62zdytzTVC12ydX5242tLzVKND6Asl1ABnSNJaQfaFlIpZVgXomKGKK2YHlFWAKXHJ7mwjrT3E\nXXak62S2qf7rmuSDAhfpdfaqzSQaE3eh+EwSUyzc3CoHKoaW/XU5piCSj+W4OUbrGJk+7oAmH8t7\nNcMkCTg72zqwXOVYzktHmmb3kPTo2M6/qp5miEQnawdZxwrIYQWdkdRVIrjE0iBrYHUNJ654KxZD\nbNqxTrJnyea75kE2jTH6tUUdN8PiyI+sn8CyioFrTG49ahZOf8UKq1g5H8eYDmgVHKr8zMerpknj\ndnZ22s8FZkVztxrXESaq95kmQHNd414Ckh2pWlU2BmQdixjH80tF95Ioi3bLqqgrlkObpZ1PQWbM\ncV/NzWvRXa2yTQqy3b0S3Dp0nBhAFQ9ibk5yTBxAUuMcooxQWQmBaec3xWA8pv2ll55kp54nP8lW\nB1Z0Po+p7megpKRq9jq+ilEWuikS1W4FstSoSTqQJOLg9srpoka2xIZONhZkCWxUqHirZHJAm493\nwNsxAWK/1DDyGlp4FVPQ8wrCepz8nxFtHNqw3LWnGtuOUTgAqApC/clxzQCkushGWpOaMr2n3O0T\n2au54OJH+nS83hDbxTLHpwLlrmm6dRyoaX1Wza9r6rpO/t/pmgFwwpkZMjEjawdZ/VbKEHVaHaXv\nz5NQUg/91OXcmK4jagFpEehYx7zcBeKZFXcJS0lJjUxto4RSoBwAS6AwfB7H3CVjBNxZulzItmQ7\n8trjl2hnC6Rik44AZF+yPw60KJcpx6lBUl5UoKr2aW5WfnQg5WrSERY3lux2a1X5XonbVyIltP5+\nATZiQ0CWApmZUNdNXBekr63m8zPigNYlstpQ6cjnui5fMb5qHW0a+X9mpDqW/FCbdnZ2bvq22hib\nmRPZOSMzzGb8d5eCOZ3uJ6vVNxqTGaEDzWp9N4/8pGP69lLVUGdt0zFEAnKsyae89jju3i5TcXbN\n/Kik27fsvztGjZPm7VfWDrJZXBFVBdAB5wxoUNet1nCsKtunY/Ra4GrD1VbHCN39T4m5O/+1KLtX\nCAqiFWAdwRiZAAAgAElEQVTkIhsNr2t2nd1V0VKcaG/ouJ5X+2bYtvMpn58BHsc0CczcXtPYrNMB\no/535yqbiJ2TLRqffC4DLDUBzYUOEKmeXcOg2O5H1g6yWuTjWP5PY2ecp6/HumSgLkhCgJznO9ao\nCasMwIFVtlnXINZSFXjFSEl3xYZm40U+OJsqfRmoCegpls7PbJOep3mu6CiP1H6ypwJkvXDegRTt\n5Sw5Ud8d8LkG6M7p2jnmHSBSHqj+yv8ZMpXX12bXkab9yNpBlkQTexwbUh1zRaZ6Z4F6zNEEpSSt\n7vI+Yzedow0fNo33HQmcFASr4qQ5apNjQ9U50q92Vutn6ZqHY2zaFLK9+cO7cW8IXW/GNwKYvKYD\nkIrZqS1ub+i5i0W2KUt3m0FqIG4/ZgGq0tM1EMdiq32YsWl2P5bK2kGWnK6e6wX7FQscksfQNZpO\nqqB3nbRjSQ4gqpuoUGNw1/BWTakDwC7RiFkToDhW40RtqECNdDm79TaO+aYv7ochCahc3LK9DmCz\nPwT2ei7H2a1VxZJyV8HSMfNq7rA154CuO0S/Oq37WtnsiIUDcQew43HXpJwdByFrB9kIfkmmx4kF\n5cSeAUNKfNXl5jndLknzet0Yl7Dd+nSOxs7o1liqTXRunFegz42wKhay2TUkt7/Ofhqn62S781ee\nyX+37sy5/H709evX9+RZ1fQp78dzxzLH4+p36mb80PyeITNdY6rIhu7fbEMmO3RsR8DGunpFyji2\nH9kIkKWXAllyQN1lUWM+3dU+Yi9DzHft0jVmuxgBKIEH6cssJs/Lxa7MRec6m1z8ZhLYgVQ1V8fT\nczenAxESbV4di3S+ua8Uk8zkRM5PauQdY3SgqbrID4pfvgqi2u8x3uWx2lLliMvXbv28Ts4JR4rU\nLmd3tV4Vlzx2v6x2I0A2wm9edWNhFdfVx3NN0nE3qLxOnpsBmuwjFkdJSz7SjTmoOXT+dQBXgVte\n0/3ulCtsKkpqVLl5uKTuGkhViLoveU8ym3PAQeyV1qB4KMjnP3ctcdbjmo+SBT3vrtRwDZbu8q9N\nSed0+1D55nI/664Ak9gzSbeG2pP3WOPmmvV+ATZig0BWC1OD4O72XunLAKI/U0HHxjydn9d0G5XX\nVX90vvtlVFq78rMCgYplj+MZYCipNTE1trM20k+r6Hqa2FT4LjYOHCPm7salgEnMMUvHvgjwsw+0\ndvajA04nLp9nWKXmEDWTKt/UR2qcmk9EqKqvKVdxcOeotmZqNx/rcqiTjQFZSmwqQD3X6RuPqXgi\nwr6kcp1Xi1LXyJI/JCDAGhuoiUA66ZzOyQxH40U6nOT529vbe+KlgOfAKNvpQFb9JDurwq3mduBU\nsSm1n57TvlX2UBw6xtiNq3Kb6qVrjPRlh4rkODCvfHKN2/nm6pJ0q59KYjow1l/Q6PyakY0B2QgG\nlRHkDFg0zz3P7DEfyx1KuxUBfFXImhAKPB2AZLBVH8jvLsFcXCJ8UyHRcRqzbL/GXI+NeeRnBcCV\nv/m8A3q3V3regSEBbAcmHbvL8aEm3jWTrIc+lKlYWrVPXVPPutTuau2qCVdCdeXWmWm21d5V+LJf\nWTvIErujoOTHrtNXYEu/TJD1Zt2UFA4Iup8y0fF5bTfWdXHtspVQjLLPo0AJAFzxkB+UmARSM2yg\nA1Pnt8ZK46Z+zXzY6cCcHrvx7osF1Vouz6s9J/Ad/6uaqd7b1ZvPjOMu17VxqD8Elq6ZkV61nf5H\n8B3CyP9Vj68iawfZiL0bQYHV8cRWCaizLsciNamykE3U/XMCVeyHErVjDeoHjdPYVMnr5lGRztjR\n6XbfvKuE2Gnlk+bELGBX42aYax6nxygvCOzopTixzMpHyrnKPucz5bDapToJVEmIMLm3JzpdtL7L\nE6fbEbP8N0tqKlk7yFIXdc5rsuqf6qsSsmMTeWOqewTkdfVWe7MFocU4s6kV0+qKU885FqvMxIG8\nziM/1V+1U22dZSG5GLJO8pvs6mKdL6ivmpxjajSemr3GzzV31ePyMWLvJWrjP/ky8leFciPbVV39\nM9OkdI/oPdE8TvNDP7ylRqRxVH8ILzRu+5G1g6wWqOssET95KZCTfnt7e3ccJU7W485XHW1cheAY\nKn2jhe5sRWsMoQ/Iqlg53Y5RKOhmPXpBvhZw9TtkOzs/ecmp95cl8Fa7VN/Q4y45UiFA01yqGkjF\nkijOM8VIoKjMTPPBNYJ8nsBMbxOqv4yc90+vprlx48buHdR0zyrAz35o88n5T/tG8aa3JVz+Z/tc\noyQSRuOyfRmos57hx8CYVWXjQDaiZkx5ThbXSXUdFVqr2uxq3ZxgVdIS2JMdmlSUTJX/ZDMxBOdX\nx/ioMZFu8kuZxAyj6Hys1nV6nRAwUgNUnxWMSNw1yRRv11z0ec6XPN/FjZqss2cAofvRxUqcTs1d\nstP5kB9rLOmVpNPb2aH3BllV1g6yjo3k5zp+SC5SV2Cuk1Fw3Vp68xDVTwmQfXH3bJ0tendxPdmi\nduRz1Xm1b5a56dx8rip83bvMHNQ+bTJk1xKAzSDv2NWsOFZK9hAjVPtJB9nv4qr6OnaoUu1r9bkF\njV/aLDVfltg4Kzn+VYOJ2PsW4KqyESCb/4/HDhTct6/GmLzBFeDqWk7PmOdYdJX8dN59kyfbMpNk\n+S2MLjFdcVdMdRXWp/PyemoDgZ4DStcEnZ15fJUrGhOKo/rTNRe1VRm6y+lKv9oyQyQIhCtGXtnn\nWLqO73K7EteY8/yqmdHjKm+yP05H1rMfWTvIZtFizEk7bqzRBY5YUT6n44bMsKKq0CvgckybEpV0\nq00aH/fTJORDlzQV8FZj1b5qfgfomvgVU1J/uj2bzSGdS82vY5runOZLxfzUF2rEY56+L67ndU3K\ngyXNbBwf9uj76dnnyhc9NoR+r01t0SZGa1KN7YcNL5WNAlkF2HxsbGB+Y59AbEhVSBXjrNikAhsx\ntKEjr+OYxtLYdDblZB9CXx5YZX21owJrxySJOWjsqobV2Ux7SnngWJyTmYKcBWAaW7HumSassaWG\np2trrPQDM7XL2U8Ms1qXYuJqTmvS6aLx5EPX/Ny8n/q7cGUgIgBym+4A1hV3Xi8LjSFxTCUnQL78\nhDq6u+qA/FDJ591PmMwAZwWM2R/XHMZjYtYqDixcIS6xV+NWxY/WcezRNUvn3wwjpfzugHYIXbWh\n9ut72VVTd3vX1QDlq151o+BbERZHjFS62tUxNC+vp3jjSMNsfs7I2kE2on6pTp1d53S6qYu59QkA\ntJCqN8K1KbiO6nR3HXuw+fG/8kWlA/Fq3EzSaUETo9V4UIOsQLNixG5tna9gMRMz2hvaZ/VpiN5X\nQu1WoKN8cUzLNcDq14KXAhodr0C00lMdW0Koqj0mnHDkaIyjcx35mZGNANm8WZRIlJjKDrrNHuPo\nwvKsSwtXA16tpewir5vHuB8gdMXuwKkqBE2YDnzy3Gx7BR4OIHSs2kyJXzFKx0Q1BgRQLodmY9cV\nfadrzHGxI/vz8eqWh26OnnOkQPe5umOYHnOfeazKRvM5JVhKlJb8CnLH5LtGfhCyESCrgc6ftlaX\nLHVCRTKOu/VnipIAOYOZ6765cPJa1Zcd8rhxzIGg2tkl/AyzqnSpvuxvjoNjmRVQkm4nBNCz9us5\nV4Cu6Lqmlcc5EBmPaS9VN9XDTMMgcQBX5cWSdTSHSedsw8o2EFBqTTiGS+dmY7SqbATIDlFQpG7t\nkotYcFW8VWK6jq7FW22oznfsiDac/KaXmx07oyagerNv3eMZoKKmRmOqBuEAsgONMZe+Bt3N63TO\nMJsKJCk+2ogIiF09KNDoGM3j7IuLe/XtPpd7S8BY9WW96ruriyq/yCdHoAg76Abvs020krWDrAah\n+oaFYyhUfF0300Lc2tr71UUH2NVGV91Zi6Gb7xqFMsUheu2s2utsdra7ebOANQq9A6jM6PV4Li6y\noWocFYh3onmpQOh00R5TPmhRZ3+XSEUW1P4KECswcfbNvGyvSAmBptszN08bhLs1qMaeQNvFYD8N\nOmIDQDai7moVm51hCkP0O/o6J3+ry4Gj6ne2kH8KFq5odU4lM8wv66ts6vTndaqLznU/6CuZ6n8n\nrmDo3Kx0jYdyoAIrWpviRjp1bJV3JJSLjt3quhQD10BcA9Z1VIcD0wx2pEubVCZIZEMEs/GZ/M5X\nBR30vWU3CmT1sSaZAwp9rOKS1RVSNzdvNo3LSaEJQSy2AywCGSp+15Aq/XSuAv78n5qc6tX/I2ba\n6HR9/U/7MtOoyF/XhDQeHbhTY9f/+U/vdarjVLc2M9prFboput6ASOPY+ZvX7YQaB603c2tRNzfr\nnvUnn6swhl55/dQzWdfNIjx7pdubVXPGvPy/Oz67yaojM8Q8bglDceDg7k41880Y56NL1koIbN0Y\nZbDOlv2sN3Ig/+qD3nFqCLEgAiDX4AgAqhxywFQ1LB1D4KDztOlk28arNP36rgP8PFftmiEyZHv+\n72q2ajq0zmggWYav6pM+p5+xJ+J0EGx27SCrMkPt8383TzdAQaoSAsYIf9lKnld1UreWS7jc9ck+\n14Vn13Zss2IHQzfFoWpUrugi/DWkqms2tg7c8jr5Uj4HbmonjXHsSveR4pPnKxBUdnQgr2s6nc4W\n1eVsmQXfDqxmSEl+q0Wb3Xicm6zaVTWBimy4fVsiawdZVxCui3fJ7fSMx12hVgXXAfwqm0Hr6abT\n+8l5fE7SLqFnfVadWboYatEog8iJ24FrXq9raDO3pVO71D6n2/mqYxQY3D5WPlJN5Of6Sq4CZjpP\noNI1SLdP7pzudcVOna7cLMhWzVHKU9Khez9yR3XNfGg7IxsFsq6Iqs3VJNYuNsumSGbOk/0zLI/0\nu1hkvbRWfglcsYuqUWV/dIxrKmpHt141rmN8lT9O15hDxaa2UJF1vrh1cx4SuxrrZX0zrDP/GOWs\nPWQ7AV7F2Kt51eMKmIe4mhnnXIMnANT1NPZVPVONHdQHYGsHWSdd16xezuT57s7rWnx5nnbTyrZV\nN4E6K131oJ1XRYu7WzO/ZB5sg3TqPLXBvYXR6SLbxxr5v66f/7tG4prb+MtFk2Pg4urywoHxbLNw\nzCmv44TympqjNl+nZ4i75zHZTjGvyBL91/MzjbfKFc1Rqm2aXzUErctVZSNA1hWYA7PZRCaWQMWT\nx9A3amgjHEiTb65h6GYr49LuqiCsYFM1BvKJ4uDmd0BL4KAA5r5OrOvPgALlDBVRjot+QFixxgpg\n1QcFAgfisz6S/bPgRIDr1sm2On0qGbx1vWpNZz+tSY1P417luqt7ndt9jXjml6hnZO0gO8PAqrn0\nqwUaGOraOYHpN36cLj3X2UeFpUWgYxxDIp3jWHXt6oxteo7APjciZRoq1Hwq28ccN1fn0Hq059rM\nsn95TZqn+jsb1BbHgobPLrcc2GY7ZghJB/BjXGbVFMP8stsRjtkayblFH0TSfG0K1Y371dd83l1y\nSfPz/v3Ug2yE7zjjXB5Hj7PQpjrWUAEN6crHiAl2m0Edf2beGEfHnB/KvKqmQ+t0YKivChwQzLC9\nTrpCWmW+FuhsfMb5CuRc8VeAXzW8junpHqhf+lz3Sp/TnuU1qvsEzOwL5bzqyMDu3ppSvKh+OVfn\natxdHS7JMycbBbK5u0Xwe7AzBaA6h65OKHm1AChhnX5K5kqHO6ZgRWvMAoZrVG6O7oGyiIphZ335\nJud5vRmg7cYsZTTORvKDGpXmohZ7B8CdnQQepINAO/ugv1Cb7dVP/iuQoTzWGu1IUcWA869Q06V1\nTk8+1jWrrKeKdzd+FZl6R/frX/96PPTQQxER8Z//+Z/x9re/Pc6fPx8f/vCHd7vHo48+Gr/1W78V\nDz74YHzxi19cZIQD0SWFTDrHpuWNo+7cBZqS3DFmZ6MrPOdPxb701yGIuVT+kN+OwQypfv1TY5Jj\nVsVfbehi6Oyn8zP7S2vTJWZD6Ef1NGY5V5w+F3MX+8oHFyMXr+p9RooB2VIdo7/Z3/6q8pBsUVY6\nmkpnk1tPG8D42fTqh1RnpGWyn/nMZ+ILX/hCnDp1KiIi/uIv/iIefvjheOMb3xgf+tCH4rHHHovX\nve518cgjj8TnP//5uHLlSpw/fz7uv//+OH78+JQR+ttACkCU8EMq1pZFOzUlsZtHY6vEqy79mLG3\n0+90OnDQ9XSM2qRFSuyT/CGg7IAwgxzZOcNinW4aWzW3bBOd03k6Tq9kUd8dQJAu8tHF3REAB0o6\nlnRpLlFcaH80B4a4r6s6m8h+9bXyiy7n3NnZ2fMeuSMluTns99dqWyZ79913x6c+9and508++WS8\n4Q1viIiIN73pTfGVr3wlvvGNb8TrX//6OH78eJw9ezbuvvvueOqpp6aNyF1oaXfP//Xc9vb27l91\nyYzqI9vo+JCqqGeYRx7rfsNMbSU7KlbrCtHZ0tk37CGG5hicvnzt1lQhfTo3r00FVAGNjqPCq9iU\nsnZag9hdte/0Prjup96ir7Nd98z5l/XM1KabS/HJ5/Jx2iMVqgcC1Cxqd7dORWqWSstkH3jggfjO\nd75z0+LDuNOnT8eFCxfi4sWLcfbs2d0xp0+fjosXLy4yxLGH2cBH/IRBZp2uE3asrmO62rG1OHWe\n27DMBogp0OPOvi5BNPkrVuWK1ulTxkLziDm5824t0lv5PFtcpLMCTR2Xdbh1cu7R3cn0K6RDcn7n\nNRzjJxuz0O+H6XhdR/V0TJnWJXE1oHrI1opRaxxob7o19yuLP/jKSXHp0qU4d+5cnDlzJi5dunTT\n8Qy6lVTgox3PzXWdWZ/nb8xQoswAeRbaOAXfbq4+pnkueQigXTHk+fqFBD1Hl1SpfscWKkB2TGhW\nxlx9ZTHDcFVHtqfLQedD1pV/RHOcc6ChuUdAWMWWGrv7uvJSsHBMVK+NpfF6rnrbbDSYJYTESbWH\nWW/V+HXdPHa/X0ZYPPvVr351fPWrX42IiC996Utx3333xb333huPP/54XLlyJS5cuBDf+ta34p57\n7pnW6V5yqGiRjpcgVZGMefk/PSYbnG49N+yqNqNjXWqDfviQ5+VjFVPvYtolmhszjtN+jHPjrQH6\noCXHyvmsNo1jdI2u+pgbCfmU7ac1KBZUmAREjmG7Pci+Vx/U6kvqbJ/LkeqcAxQXl0x4qre0Zpqs\nntdc0XXJXo11ladkQzfuIGUxk/2TP/mT+OAHPxif/OQn4xWveEU88MADsb29HQ899FCcP38+dnZ2\n4n3ve1+cOHFiWidtuBZNFupc2t1zUug6bmO681nvOJ9ZoSt4YoKqK58jpqNMxsVQx7gYZqGbSatt\ndJu8ag1n51JmV/lJDWemWDRHaM86m9Vu/TYe3S9V9btGObNuN9fVlHtegasbm+OndjuAdO+ja05R\n3ebjVE8qrhHoutnfFwKAp0D2rrvuikcffTQiIl7+8pfHZz/72T1jHnzwwXjwwQcXG+AYQpYqyLr5\nKgocM0yt64q6GVWhV77MAOA47/xToeYydBAAEOup/FPbyR/nQ9bVxb3S5exwIFLNqYpUbdN51X0x\naH3KPQLcigRUTJTmqE00ropTl9cuJ6v7JuQ1x3z3KqYDW7VF8ys3P8qLPLfL+VVl7V9G0JcIFbOj\njXUv0bsEH3o6sK4C7Qpc2aQmQQW8eZzqI/8pSStAJn8o7h0LcMfUD+eXsmfHTFwOUBG4m5w4sHI2\nkr0VC+rsWkV0D1X/TEOL4Oub897S2155rOrTc+O8Y8V6zjW4nZ29b8FlfQ7sNV5DT5V7s3tOz1eR\ntYPs1tb/XWpFd/0foonugJA2jsY7vTrH6XNrVWBKyZEBxJ0ne8c5/eAg3xU+z3dJrutoceTErZiL\nAoCLwzhPhV01BWocxOZm2dmM/2NMBzoapzyObuhT6dH8qnKxsomeV5JjPGym+3mQPbR3+Zx+yKpN\nwpEh3XPKJWpCCsr5fJUjzoeDkLWDbIRnlFlc0cyMq0BiSTGO+XrOJYoT1yCc3VVxkm1V8+hscvHp\nEo4SntYmO6rEpyamPqrtxIZcI3UFORM7LVrHCgmA1XdqjATwNJfmq390x7QMeATitI7Oj7j5y0Tj\nHH0xg+qmq9cK7IjI5P/V/Cq2+/3ygcraQVY725AuwUjPzDoVA650EdC5burWmmGrZINLxupWbQQ0\nThQQSJ/q6ACjYp1jbLVnM3Fy++fEMd88V29+UgGcgv0As8He9H1J2iMHMhF7rzl2DSifU8Y203Rn\nGRvFWX3IzzObzTJ7OdhMrY5x1HjJR5dXBPzE0leRjQHZIS6AYyyBm45T/dXzvGbHGHMCOwaU7czr\nZVZKc/L6moAOYAi4OzYy07RUd/cyi4BAi2cAhru0qmIbtG7nqwMUBxSdn51NlMcdY1Nx+UTrunnZ\nP4pDZrYz+isdzmbKza5pVs1sNvfG+eo6aQVQapTO91Vl7SAbMfcSv2MtS5O4Ai5X8LoGfcNs/Ncb\nhWT9pLuy1T0mn7qkds0hFw8lmwPGLpGrsbMswRW60+GaYD5XAX3XqGgdtYfAyAF8/u9sq0T33X11\n2X1IXBEGlQ5k3Ry1Mx+jPXCMkr4hl+dVgJyP6V5QbR4EwEZsCMhG9O8F6rdHtAutsgYF3rHHDlzc\nZhP71mMO4LpEz7ZUgOaaS9XFnZ8VS1G7O9bRiWPFVIAU/wooKQ4aC/VHdY6C15vAjz93BQXZk9d1\nYzUupKvKheoXekmXAiEBoPNF7aX8d+uSP46IubkKpl0TqXBkv2C7MSAb4buNvrfVAcgMAFdA1AWc\nkrnr8F3R6F+eQywux4YS0SWmSsUIqzvJEyOsim8JM8oxpvUdU87niJUQaOocinX2gRqMnquu+ez2\nyLFY578DVAXJiL3Xrnb5oaBIe9jlRf7cwH2gVNVwlZ9ufWqaqnMWdPcLsBEbALKO4bhEGsdUFPwU\nqPO8CqQdUGqizYBhZ+/MOPVBXy5V88iWfGwGENXOCuBoTQdUpLM65gqOGsxMk5w9RwxOQZkaneaH\nAykFE12Xji8Fn9n9133KdtB+qA8aLyJIzhZX42qL2qTHqD4rG10dOFtXkY0B2SVFoo8r1lKtR4UQ\nEfh+6hjj1lNgIjDKcyuWRmyE/ND51dgukTqgpAR1Oqhx6Vgd3zEL8knBlgpL1yQ7nC+0p+Na5LxH\n7uJ3WocK3wFtFTsHwpXPOoZuBBThv9RBa1I9UjzU58pP52t1XiXvo6tzl7cHBa5D1g6yKgRQ9N16\nBWe38VlygB3wjO7rfg2BOjutXXVzWtMV95iva1WMcBbws2giUyPqkrlbk/ZNfXL6O3EA69ZY2pCq\n5q7gQyx/CZEg+0mfA7y8by7+ylSzfooB5X0HSu58tzd5Pn0F3MVxFZLRjeua/YysHWRHIF3RUbHn\nMXqLuY755aBV4EfApx2egI70LGEXlR0zc4gVVEKAPsO+8/HxmJpexbgpdhovWntJrCrgVXAc67m7\n+FfrV42MQMIxUdKbcz0/d82K2KfLcfKh+k8AWQG189WBWWbDQ+gmTBSjKpbUbPJ6bv7SeiLZCJBd\nCiKO/med1XrdOcdG83ouSfTrwfRzF7ROBQAzAEN6qubkHuc1lUlkm0loLd0vLXr3c+yuoDrwcyyp\na3COBaq+mVcVs3tMPiyxOc8nH1w+UCN1INTZmn2rapGAONupOZLXcTc0cnF29uX5Lr9Ux4uGyZJQ\ngizp+lmPjtFNUkZWzc+F5W5okfV0NmmCOiZGrKvy3cVVmVDla8Te9+eIuZB0thAo6Hf9ZwCqAwu3\nfpZuz50dec/culW887EuRmqHy6/K1nFef3lhnKPraKvY5McK3HSFBTHI/NjlfpVzpG+mBqu13Bqr\nytpBNsKzw3Eu4uYEcB9MVYEejyvGoWyO7Mg6lLVSt5z5UcWO5VRMpwLlKj5ZV5WMOibb65icW5+E\nrjGthOJcjaXYdU2VYqDNuZMlTcgdzzFxDbZqvFkPHcv+VL/dRn7r3lOduXXzY2K36pfOnWHZM/vY\n5f04vt9fRlg7yNLLjK7gqqIe57PuCgC6ItXgzwB8liqpsq10rAJROj/b6au4drpn584w3hnmrfnR\n3R9UpWrcuo/U0GfiNuY61lntZ5cPFVhRo1vSVCP8t8Aqm8g+jWFXW10cqrE6fqb26N6/qq8ie/uR\ntYNsBSIuMFUwOmbiwJjm0NycRATgrvt2zYCAfz9JSrbl49TFq0ZXFXMWumlNx84GWyC7xjH3VVEC\nFmJHxHJonu77zs7Nl21RLumaDmBVql9BJqLhco70d8A01icbda7+VJCu09XcOJZ96hrw0gZdvUJx\nDJ2YebbV+bdUNgJkZz9cqZhaxdio4w8h1pL/080mloC8E7JTk4+SX5NVbdPnxNL0tnSUpO6er+OY\n+wnnpQlJ4Ddzb+FqLXd1wPBT77Q1Y19VhPpf46rjKZfo21DZVj2uueDOkS/Zju7VQAV0+XyOk95l\ni0C30kH/Oxbq1ul8dOepya4qawfZIW6Tq0IewaVbp1F3dR+s5DHjeLXBjm1o0pO+7IPa7nxW/RSj\nUahUgBXQki53vAI8J66ZOJ0kGkdXFLSvbu/cGtlWB2B0nMbQfmnDd82/apTUEJWF0/66fKd1XO5S\nwyX/qsbhiERHWrTpVPs8pHrrp2qyeR/3e3/ZjQHZig0RK6H/WY8b4xiJ6smMTS/boaRzSaJ+aJEq\ncFSgU4ESxcIdq4ok2+T0dZL3gFhc5+PQkf+cP3k9xxgdmOT/+sGqrqN26A9Lal7ltYi5Vnmq/hAo\nj7EOaLqvs7pXcPQWQs5R8lfX1nl5DQXp/MFwlV8ax7wHFGOKH+msSNQMAZiRjQHZiLqz6jF6TklI\ngSLWMwNgZJNjQM7evL6CERWeSyBaLyerXtVATWCpz1po6hPNd6zTjcl2UuE6cfuuBad/le8EcDqX\nQCnnlyt+Xcv5kXVSjlREwcVt6KGfx1kCLDRWAVn9oLWqxu/yyt1RjOJC+0zEI9s1SyhmZO0gWzEW\nOnS7+QYAACAASURBVFa9DJpJaAItx1yqzXEAURVQHq/vtdH7iBW4VEmka2RwqO62T3opjsqUXOM7\nKCagtnWgS8yxYnXjWMXOuqaieak5PcOqKFfzWpW/mq+VvcomnT15vANKsq8DqIo5kh+u4TtfXQMi\n3/Ixt6f7zeO1gyy9bHFMU8Wx1DHeJRMFNK9NX18cYygBqqSa2eSO/WhcukSkxtVdHJ5FAYEAogIL\n51cVgyoe2nRnwFV15bkOFKihOHtnminl38xalcyAjI5zzXI8dz8HQ/6451W9utyu8o8ea/OnvaVm\nQHZkHzJZ0L+DkLWDLLGEcTyif6nuxs0Uiq6VdSpYzwAFbbgCtEuyqohdN6fxFfvSNV2jIVkCBo5J\nVHs6Hlcsg8CK9Og4uhRw6NTmoy//dQ3KwW7vcj5kdjT7c/bduZmmTbF3TZt0a97S8fy8ajx0vFtH\nx+WxM2RoVhRk98tiIzYAZI8cObLn0+7Z7q+J7jY+j8nSsT8V7aSqvwNn3byumJ2fzsfK3mynG6sA\nTcw32+dioVI1qaph5MdUfNQk9GqNqrHmPeoKS/OrKn6aNwA2j1tyXwg97xoPNXXdr2Fz/k9X3miu\nqi10S8RqP6lGu7ipDp1HeeHyfrb+dX63L52sHWQJbIgR0ga6QlP9FXOi9asu7FhLBc5ZrzKm7e1t\n9DGDANmidjpA18fZzo6djOfjCotciPQT0y6OXWzyuPxWjbOz0kHxo4ZITYyAxYHrUptmmswqLM6t\n6YBRgVjHunUp59yNW5xNdHyGxRIAahxc7ShBoTrR3HWNa1VZO8jq11Qrh6hYxrzxnzZsiANbHaOF\nNsPUnB06LvuYX5rS13VnGaIrJuffmLtUP93XVwFy+OS+rUdAruNcw3U+u8JzxxREtre34/r169jE\nZ9gM+UJjcpE7wKx0dTmteqjpzgKW2jCbk5V0YFrNcb44HWSnsvUxTnOssmcV2QiQXfKNCioWLXrq\nWl2yZNbWJa7reqrL2d+Bt47pGIxjsG58XoOE4up0VOdnwY+S3jE/XVf9VRaqx50929vb+JVgstPl\nTgdA1ddTq/3WJrdUZoCsAl21xeWFi0ulz9miY5Y0PMdutYnPNOsZMtLJRoAsMUxNui6RXYCIHXaM\nll4uzIIXrZHHO7+WsFe13SW+S5DqmNNDx+im5w74Im6+JGY2oTtbXW64gqwKn74OSvq00VY3fyf7\naP/p/NCd7VOdLn/J366x6thsN329fIbxzQBUJi86T3NHY+9im8/t7OzsvuVVsXX1ab/gOmTtIEvS\nMSd9TPMoafTbJTnRlyRgJVU3105Kv7Hkmgzpd2A2A1h0Ifr4737KOsdNAYZ8pv8aA4qZY7PdHlRF\nkQF5xgbSq0CrN3LPPhKbiuD78+r6FQN3wKy+VX6M8Y5Zu6seKjtonPumpCM5VAd5TJVHOe66Vq51\nEldD5PcqshEgWzG7cX6IBjjP615OKfvqWIDakR/TTUxyp1RbXAeu1qcCdLbpPAeyXSHqeBd7Wtft\nnytiAu0OfFXyflaNUm0i0YLNNtJfXt/lDTWKDkzyuCqOavsswNK+Vg2oipu7P4H+qVRMXNd3Qnuk\nOh2zzXZQM5glVTOyESAbsTcw2rUoiWcSQTvcbPLMAFIFcu5ORASyVFAKQFVSOkBVZqzHHRPW8fmY\n+3Yc+UT26C0LFWAJgJSh5+f5pjhOKAbkg64zxtC43NRnLxvT8+5uY465LSl8YmTkW/ZR55Ad3a8n\n5LzV/0ttphu6u7rpgJZiuQTI9yNrB1ntoEMqMCTgJTZDSUkJpUms9lTsVvXmORmUIm7+QThNCv00\n3gG42pCBKwNg9TPVdExjUjW2in3Rf9VHgLEKcyGZYXtjPt3O0fmi62vcHHCrbTMyE5sqx0mf+lY1\nRmpclKfVWtpIloBVto9Igf5VcXbruuOuOe1H1g6yQ2aYiEpOBmKNEYEbTsCX18nr5fM6jt4S0DWJ\nEZJ/BPrkPzUCWoPApkscSrBuX6gB6pr6l/3sALECdN13ahTObwc6zpd8vrtlJq3ZsVFqstV+ub12\nczLrzvbo/Kp56dqUJ1RLSljyGNcsyCcC2+GT5gsxVjrmiNpBytpBdr8OOVaZdecgu5tN69yOzUb4\ne1XqTVjy3KX3+aSEmO3UmqjdT6fTOh2IjnhSIdFcLTLVq2CkNujx3Djz3m5vb9tfU9C1Z+Oax7lb\nCc6wV9dEc3y2t7f3nCN7xr7mmIxzFMOOiVJDpOujHfPPa1Md6ryZeOhYGpf1u3109d7Zs19ZO8iS\nuALN5/W4m0MXII/xruBpXQp8xbby2m6N8XVi9zPTWWfVgdUm5wd1+moO2azx1n3RmLq4km3ZFgcu\nA1jz3/Xr1+PGjRtx7dq13bgfO3Ysjh49GltbP3k7pfu5lyoW5Eve/6qBzBTs0EH3TtDLHA9aFBDp\nfXPn+5g/jql0eap5pI0hx5XyLY+hptI1dfWna5qryEaCrBN13DFATdAcPNcZqw2gNcgmYhKZaczo\nI9FE6oAgg11mezou29B1/HwuF0AlXbPsjrs9G4D6/PPPx/PPPx9Xr16Na9eu7X6pZXt7O44dOxYn\nTpyI7e3tOHr06C4zVIaYH8+wUWVlld1Z3FhdLzP0vN+zLNsdcwxy/CcGm9enuVUeEGul/FSdrlYd\nKI4GpGRlJj7dPjk7l8pGgGzHXkiqlwTELh1zmwFqYqdkQ1W4NH4Jk6yAljpwXoPeQ6S1K3DJok3M\n+eBi2xWmspj8f2fn/35z6erVq/Hcc8/FlStX4uLFi3H58uW4du3aLos9depUnDp1Ko4fP777l+Mx\nk2MuB6jwKsbmQEuLOdtUveXkmmLFxmYaB/k6zutvwzmAdutlNp7vg5HPaV7ONnL1gUC6qvmDZK0k\nawfZrrCJIdI80qublDexY3OVnRWgkQ+df+482ZqBXs87RjbbxcdYZ4Mbo6LM2d2joRICiwGw165d\ni8uXL8elS5fiwoUL8aMf/Sh+/OMfx5UrV2J7eztOnjwZ586dizNnzsQtt9wSZ86cuQmosz0EDPmc\nfkut2mMF4JncdmDUgep4nsfnv2otqidq5l2NVfVDsdKaG82OcoKak1s3/ydb1B4H4DOgvoqsHWTJ\nMd2sir7TRkb4D6UqmWFy2nF1nkvMLjE60HNA6UAxn1d9zs7ZJpMBSPVRU9S/zud8bvwf770OgH32\n2Wfjxz/+cfzgBz+I733ve/HjH/84Ll++HFtbW3Hq1Kk4c+ZM3HbbbXHHHXfcVMTHjx+PY8eOxfb2\nNtqebXb2aM51HyZ18dTjjmlV81YBhwzIFZBVrzzUJteIqloiwlPpz/81r1ytrCIHpWujQNZ1T0fn\nqyTJ5+kOV5U44M46K8ZQ+eo6r1un0jkDWM4HmkPNo2Nfo5lVl7o5G7N+Yll53gDZy5cvx3PPPbcL\nsN/+9rfj+9//fjzzzDNx+fLl2NnZiZMnT8bp06fjwoULcfny5V39ausMW3NCLNuxqewnsUR6Gd5J\nbmbdq5xsc56n9jmGl/Vo7uv6+kpBY1PVFkm+tpzYdtapvjgmPN76oLGq/yDY7RTIfv3rX4+/+qu/\nikceeSS++c1vxh/8wR/Ez//8z0dExNvf/vZ461vfGo8++mh87nOfi6NHj8Z73/veePOb37zIkAp0\nKHFo01xHrQrYrT3W7X65dIC4+/XSqlNXjJj80M3PdlWg4ZjlOD5zWRnZ5EAlJ7Gu3zUlYj87O//3\nNsHzzz8fV65ciWeffTYuXLgQTz/9dHz/+9+P7373u/E///M/ceHChbhx40acPn06zp07F5cvX44b\nN27EsWPHdj8IO3r0aFy/fn33Pr5qA/lFMaeGTz6Q7rwG3fXN6SZ2SaBF4OAANu+ly62u+VMOuSs5\nuvrT57p2tWcd26ZcI4JHNbcfaUH2M5/5THzhC1+IU6dORUTEk08+Gb/3e78X73rXu3bHPP300/HI\nI4/E5z//+bhy5UqcP38+7r///jh+/HhrgDpH51XyOPpqYhe8jmHpnY/c+4jaKXMnJ92VLxWjUv0u\nARxzqoSAo4uPszsXrLvTvtqqOsnu3Ayef/75XSb7zDPPxDPPPBM//OEP49vf/nY888wzcePGjbjl\nllvi9ttv3wXY8dbBmTNn4sSJE7uXfI23DKpGN3xxcezYMLHFGVDQGBBYUAMfx10j74R00V648VXT\npPPdPBePGR2zYyg3DwJch/hrHv4/ufvuu+NTn/rU7vMnnngi/vVf/zXe8Y53xAc+8IG4ePFifOMb\n34jXv/71cfz48Th79mzcfffd8dRTTy02pkpY6tij8PKnky5xu2Ig3WSXgl3XIfP4KuHcJjuAo/PE\nlFzyOsZYFZCOUSbjvqbaASzFi86P92SvXr0azz77bFy6dCkuXrwYP/rRj+KHP/xhPP300/GDH/xg\n9++HP/xhXLhwIS5duhTPPvtsXL16dffm3ASmuUHkl7zjub7NkI/pNwf1Wl5dk5qm2uPu86DxplhX\nb5G5+Hd5TeOzrXqDJJcT9CWRcVwbn/pDeaL6Kc5OFEfUpiUNyknLZB944IH4zne+s/v83nvvjd/+\n7d+O1772tfG3f/u38Td/8zfxqle9Ks6ePbs75vTp03Hx4sUpA4g9EfgQ48rSgWvFxrLefL2dJpy+\nJaDrDKG7+jjgo2QjqYCTXg24JkGxyMcqPSruXJ6rX2HOY6o1aJ9HoY1LuMbfc889F1evXo3Lly/H\n9evXY2tra/e922vXru1eQ0uF79ai+Cl45XP5vGueBLS6H3kM1YaCDs1Xm53kvHTjKNf18QDICgQJ\nAOl3/bItGgsiFg4XZhhwtlvH0n18V5XFs9/ylrfEa1/72t3H3/zmN+PMmTNx6dKl3TGXLl26CXRn\nxXWhjrWNsdrtnB4V2rh8kfMQZTRqO7Ed1w0dQxrr53G6viaTHic/aR2No7I0Zw/FfpxTFqfz9B6m\n1f7mvRggSYA4vnAw3nM9fvz4Tc+PHj1q94X2p8qRCrTU9qwrg2P2RcfTHF2f7kPsbOxA0sVC8yCz\nTF17Nme6mLm1s76Z/at0a3yzZCY//B1fz96PLJ797ne/O77xjW9ERMS//du/xWte85q499574/HH\nH48rV67EhQsX4lvf+lbcc8890zq7IOVxFUhE+OKlgObx1Tnd4DyuKrwMgGOzOpDUBKOxyiBUp7Id\njRPFRVlDBTxdM8hAS2MqluHGZFuPHDkSJ0+ejJMnT8Ytt9wSt912W9x2221x++23x0tf+tK47bbb\n4md+5mfipS99aZw9ezZOnz4dp06d2r10i2Kr6+QYEiBqvlUMl3zI7E79jYiSMOgalKdkh47VfJvN\nT/0gOvun4hprFrcuAe9so3REYIawHbQsvoTrIx/5SHz0ox+NY8eOxUtf+tL46Ec/GmfOnImHHnoo\nzp8/Hzs7O/G+970vTpw4MaXPJVkFbrMykt918s4Gt4maqLph+pxuFE7d2oFS7q7KuAncCLjyWGXo\nTsgXBQ2VfMxdTlTFy607GtVgqmfPno1bb701Ll68uHu1wK233hrXrl2LkydPxu233x533HFH3Hbb\nbXHu3Lm45ZZbbvr2V3UDGcd0yK8cy47lKsASKOr+0vwxx9WE7lEGWKeHcln16eO8Btmp+a3rE/hX\nQnFSHW4eNbmsi+pozFvyG4QkUyB71113xaOPPhoREa95zWvic5/73J4xDz74YDz44IP7MiZLFTRK\nCLpJttM5NsVdRE7dc4i+DJ5NDEpkSqyKJXaA5xiNJlYuviwubtV6xBiUgWS21xWyNoSIuAlgjx07\nFidPnoyXvOQlceXKlbh27VocO3YsTp8+Hc8++2xcv349jh07FmfPno3bb7897rzzzrjjjjt22ez4\nMkJ+C0F90b0hP/N/fT8yx4uOq3Rg68TlLoEKxTivQ/6rjQRGNFZjVIFfBZwR/scjKbZV/LuxKrlx\n/v8CsuuQCgjy/wjPRElyUej1nFmvsljaqLym65BZV+Wr00Hj1NeZec7u/NwVRceYxhz1M79MpE+7\nx//xYWPFnCMiTpw4sefl+5EjR+L06dNx6623xrPPPhvXrl2L7e3t3cu27rzzzrjtttvi7NmzceLE\niTh+/Di+P+tiRj6q/11+EIgOvwloxvPqW4tkX2aOBA5dfWQ7iQiQDV1eO2DW53ls9qEjEq7eSHcH\nrGTfQchGgKzr5DOgOeZVXVPZXRdsB+y6lgIw3e1qFJK+dM5zaR1KmMruEa8cN5rrQIWOk40kbp0M\nvO7+qx3LUSA8efLk7vnBbM+dOxcXLlzYvZpgAO+5c+d2/waTHQxW4+YarYru0bir19bWFr4HrjHK\nc6umqA2e1td46TouR+i8rjX8IduqdVy+VnM6llmx0e6VAc3V3NS1sk0HAbprB9nq5UDE3pcz+dwQ\nByxOHBArgI7jjl2oLbS2sjVax3XoKhF1TdVHvirLdDo7oM76CKDGn/uAya2l4JJtyO+hjrcPxje5\nTp06FWfPno2rV6/u+jbee73llltuuiOX+2BnyMjH/G0/jV2Oq3vLScF2tlg7EJllowqGmpv0VskY\n1xGSfF4/J3D1R4BOPrpYUV53pKMStZ2Imqv5pbJ2kB3inKQk008rx2OXkAQUNF4BcPYlhgM4lYpJ\n5POzHdpJBaCVH65AO8al890YHdsBcLZX92QA5pEjR3bfpx2AN+4fmy/tGh92VXHVmGkR5vEOZLVp\n0l5VOTDLXCuhva/Y+TjvQNXZnpsoscTKb32u+0tkxAFz519VL3nvFUwPgsVGbBDIaoFHcJGPwhpC\nTLgDMlqHgFK7PM2nJBvnHfNW25cAjto+s04+57q1ggOt5ZLcgVQGIrLHFaPOz8x2vDyP+EkubG9v\n775fmy9Fyh+YDdCt9i/bT3HJ47O/MwWscxU8KmCshHI0252fVzoi9v7OmM6rru0loYZBBEaJ08yl\nf+RDRZo0d0kX+X8QsjEgSyyHOqEGwX2vXAvHsUMHyFXx6EXxbn19TBs+/rqXJAQCHbNW22iOA9+8\npo7Pxzu2TKA7U/wEsLkYI+Km97vzy3z1Sy8oV/CnS+zUVypY1Ud+V0BJ+lxekR4HLMoqdT21QfMw\nA56OdXZVYE+2ZjvzB9F5jtaK6hz/6euwap/GSP1XqZr/UtkYkHWXRc0Cn4pjGZlB6RqOzanePCc3\nBNcY8uPx5y4213VUh2MSrrB0bdUdsfdrwJ3QGvtNSFpX7wugj8dXaDPIOmDRPR42D+aUn7s4OcAg\n+10+VMShAwSSCrx0DWrwpK9qOOqvjsv2UN4SKOdjYz+r5uwIk47XGLhjhAXOj1VkI0DWAQedq5Ju\nhoVVz91tDbPOqktWiVOxSz1OjNUVsdPdJcYsmOicPHdJw1P9HZvNgOp0ZObTxbfy0RVvnqPvP9KV\nJFqs2vjoa8YUF2eH29OK8SrAdvkbwd82q5qVrqePKdd0rt4zZMavagzVzyA3eX7VOMmnVWQjQbbq\ngHp+nHObN2T25TitoRs2jjnW5GzPY/X9LR1Dydwl6sy5KnHJT9KptrmYq72uWeSxeW4GWpcHg8VW\nH/Y53Z39ea5+Gk97p2tRXlIxZ116VYMbl48NGwh4qobp1lGyQcBZgbXaVjUMx641xrqOA8UZckXz\n3Z50+TEjGwGylbMuicd/ugUadW0XRLp+cyYx8liVoZPeu6Uidf7OshlX2Hq+ayJZqgSn40u6vcbP\nraG2aOxmbKxYcmWbgoBjaJQ7es7ZlZnbDEvUeFT2d6SjIhXuWBXPoYu+3ONyje65kW2jBqI+qM86\nl2IwztGXQcjOn3qQJSergs0v2+hnOzL7oQ45nmvxuM3sEloLKScOfSinVxS4JOzYoTvesceleveb\nYK7Rdeu5scQwZtiGa75uLc0NXScz4WxXHufA1RW2rj8T+6yvAgbNi5lXUi6HOlHwJj9mGXGuE53r\nfNN9cnuU65f0HZSsHWRVXGI68HFFmV/eZbbrGAolqup1xVwVfJ5PF7dTAlPz0HgM0fcKXXF0xZvH\nznwoR/sxwwiynY4ROh0KELPFQXtDN4ehwqf9U9vzOGVqKrSm+qfMeLbxq91UG2N+Rx5c3dEH1C6f\nluzpDLA54lSBsANpyj2yYb9fRIjYEJBdwh7zuZk7Sek8fRnhflWBvslDAKpzlzC/3AxIf15Xi80V\n5wz70DXoovKuONzzbNssi9E9yb7kfZiJs2uWuZA6kKEYdjcqUd/IX3dsZp9GrlRxJf3Knh0poTW7\nvdY46h3ldH2qFSU+DnTdKwDXbLVm3P/sl14ne1CMdiNAloQSV4uEAI+KaOblhYoGmTbTJYT7Oma1\n0RXTdMkywwSdzTnB3VdDnVDc9bwr3CW+u5jPAqzuw8xc5wM1IZdX6jPppPkEQGqbuy5cQcWxYLJV\n41+RHvd4di0nFLtqXtdw6W27bn+cD0uIE8naQbZjFVmqIHXP3Ya5byNVa1ESdok0dChzpY2lZO9A\nK8/L45YwbGUV1Txa1wEPFWOnV/Nidj91TW1QxAQduGSpzut6ruk432mPqIlW6yhbrGKjNuXj+bHG\nhfIp++Wu8OhqwwGbA3uNAe1fx2S1WVJu7Bdch2wMyGqBU+AH68rO03smWZ/TQ0Ib0rFKtxFdoQ1f\nOtHEcaxQk6MDDUq6rIMuWVKGQaxMwYHsrMCAYkt+z+hR4HAgq4VK4JZtczbRWipkbxeLca66Laeb\nk/9XNzfS/CR9zmf9tQ4HVs5PIgbqWwd81NwdMRmSry6oSMVPPZMdMtOV8vMxR+fnMa7ra3fOOlzA\nqYt2/qgd5AvpduIYULadjpMdW1tbe36zidgJzc06KmaYbal0upgS6GmjIpv0cQXKjkW5hpLHkLgm\nmPW6/NNYUSw6mbGddM7kEomrQdfk6Jc7KAaVvdTEKOcqW/NYl0uztd7JRoBslQyUCFQ84zmBGm2G\nboQW7wwAkM4ZAK0YTnczFedH/tUB6urjuL65X31PXeNcMSd6PsMKSKdrqrSOY4w6pgLfsUa1R3mO\nXq3iAMkVpzYNJ67xzTSuCjT0ueYuxdTVHrHUKidU58xe5/Wc3pmmUDW0qsb2K2sHWU2U6mYPefyQ\nsVHux926ZHPs2W0aFZKyMt20rNtdAO3YYl6TikCL3Y1RWcKKHPtTsKAkpvg5BqJgMVP0ld15DdWh\nv9OVz+dL6PTmJdXanV8OkLu9UAJA5zT/ZvSO8TrXNRvNLxrT+UT1Mv67y6Uo9pQTgzToJX5kq2Ow\nBwGqKmsHWSrGjh3lxJpJKk0eAiYKONlASaiF43yhQnBg1BWUSzJqQHmeJqz+7pbTrWtUYNEBsib/\nDIDNCsWzyq2K3WV7K8ZFQKWyFJTc/mYdSwDC7QnNyTlAezX2fzQj+houAVxnY7aPAL2KM+HATDPM\n9na5s6qsHWQj+peDGgQdozpmmJ+eJzto47ItrniJOZG9md3mefrYFcKQfLcq0p/Xn2GEGkv9erCT\njgGNwiTQqnydYXquWUXs/YDD7Ytj1eN/lTddU1L9Yx7FQMdRLlBDzY+r66/1PK2TxfntWG/VaKq9\nVN+obh1DzeRDc41spXUr/fuRtYPsDFjlsSpdohMzId35HIEe2aZ26H1Jq0Lp9M5scE4oApCKRWjy\nEaiM/46tdsVGttL39el9YfVLbaW8qMDONRcHBm6uA2GdqwWv+qq8J9tmxufmVTVFZxeBeVdTjv0R\nQclrqK35HP3kev7vdGlsVtlbyiGXU7OydpCN8J2SOozrtPk8dcEheu9UDSwVTQX0ZPvooqrD3SeT\nwDzHgH7ihNbWxxofOl7FJM91yUlgS/uXf5F2e3t7z/1fiSU50eKivSMQ1MdLGloH4BSjsecKFlW+\njXmuibm9ID/p1p0zQgyR1iL9mtMdaSKAzM/dNzI7sHTntT61abv92I9sDMi6hHfdS4ssb4LTVTGg\nWTuHHgJbYpO6icQEydZuffXDFWZOqsrPbJdrNBXQql16TvdH2essIHQAo76ofa7ZEKBVa1NudUI5\n6sY5X8axjqURKOk+zoAX2ZD3jMgM5ab61pEZGtP5T+vRcSI8+Xh339+lsnaQndlUPaeb5t4zpCRz\nP01N9hAr1iJUcCMb8zodgFHik1TszdmhRaG6ljC7TihOKpWvuXHQnCpvqPBpnJ53x0lmGlZFBPLY\nDnwd6NLc7HuuCwJK2m9qivkc2UINnmpYHzsm7PZBryCqcoeez+aC+vGi+bXaCH7Z3AECJVkep0nl\nksixQxUqBgJVx7iUzZG9dNd99VljlMFHi4eYIz12BeuSeTBk8rkqgHy8+yFMmls1hY6p5jWyPvo2\nlAPgmQaiAKiPu5xRwHSiOTHmVT8KqL8OQLpczjlwpscVuFHtVeSKPqijsWqfq383/4WQtYOsgo1j\nY12xZ10RzJLcHZ3cSwIHSDPJ73RVjMWtPZ5T8pAuZ2vXRJQlOjaiQE7sQ1mU+5pux9JIf7bJFbfb\n2xmWVa1B57NeytcKbCrJupbexIeaLdngGnc3vmoSWae7moRyzYGsI1F53HiZ72LUNWIavyTelawd\nZPUnvruEVOahADvbrWY7mmOJKhVzmElst7bT14FsLs48xgG0Y4lL7CL941hXRB07cg1W9VCDUZt0\nT9VW9TP7kM9pI9Ex+uGK6td1FRgr4qF+V2CZQV+POzuc6Dpuv6r5Cpp6q013lQ79DpjGS/c0Hx9S\nkTUidEtuqUqydpDd3t7e/bSZbghcAUgGVUrKGXB1x/Snp50QQ6UE6ZjybFE5Rtzpp7F5zevXr++Z\nWzFNss2tpUm/vb29Z71KXEHk8wokaoPGzQG2+qggSgBNAEzrECCpDqeze7tHj6nNed3sI605/qpv\nThEYV3nhcmeWYXZ+R9x8G0i124EtCRGF/cjaQVaFOo5LTtd5VM8M+GYhVqIbVjFfHT/+a2HOJNXo\n9ATcajMVNj2uisZ1fC1Op78qorymforrAJL8VEDVx0ubrIIL2aDgM3Tpe7mZ4c4WatatQJHtZ29x\nBgAAIABJREFUqPaffHS5Ro2k+k96u8bf1Qcdd3bOzNcxqqf7ok6WpfHuZGNAljZOgWOWteVCrDpq\nlYy5y9P1rR2TUZvd2pSYet69DUL+V0lB8SM7iGVlG7MtxCDzesqaxnF977wCpryu2tAVgZ5zxTXG\n0aupbH+1pp5zgO3IAxW35pZ+i6kCi7wugbe71Z/LzfFH3ybTsZSvVdzovIKj2kK+d/lI/zXWXUyX\nytpB1iXNKLzxeEgeM/u9+5mgURFE7P1pFv3L9i75eZBsb/Yxz6VLrlzTIN20FgFs1pXHkD/aWFwz\ndPf5VV9dHGaLkQDJARb9PIrqJ39Uj5unjYREgVvH5qbj1iH9Gj89Phh454PaNW6HubOzE9evX7dx\nUZ/IjhxbR5RcrVdj9Hwn+UMytYVs2y/orh1kXRehYqgYGIlLPNKXj2XddKNkKkZiw2TvTFJQDKrk\nrNgygaueH/NyQ6GuTr4O+1ziE6DO2k9jKr+GD93XdCmO2iToOOUiAV/3/qljuKpPRZuXywXH2PQO\nVd1la1mf+jKOuQv33VfTK/+JLFX7QXtJdTh8prd2tMGPZjTEXTq2RNYOspWsencmKlQHhl1XVHZS\n6XTde0a00bjLzVQ3MSdtAGpvBioHwjpe40Hx0/WzrapnSQNSZqrimoLTqXvu9sixu06f6ia/CQxp\nDQeYZKuOowaQ5+tXfrNQA3N1kM8rSVEbK5Lgcpb2oRJHcrSmqv/UXFaVtYOsbqb7nj7Nc4FXsOrY\nbsfC3HO1n5I6z3UFQx1bgcyBvXbi/J8KpWKIOfb0QcHsSyyXnI7ZqS10nGLXAY9bvwP1yi4CCtpP\nd6xqCFlfpUttdY1Dm2IFnO6bkPl9Wzcmn1ch5ql2kv/ON5e/s0K6HOHIMdiPbATIRvDL/y65HNio\n/q4jUeE6FlWBB103qWvo4066sWSzO5/HuCInXzqbHMBqU6Bzec2Oget6Lj+qPaKGps0xf0hU5Z76\nO5Nj+vLTNfmKXdN5Gl/dAF/XJaB2+6zx0nx3bNTpdQRCdZF91bpU19kebUYkLwomm6UDWr24uwuQ\n6nDHqVjpHG14Veg6fgZoHavuHuc1NWndePftuNnm5ZJaWbDqduLsz+d0LRd3B470POukdWmOxncG\n/OiLN7O2ZdFXZ06HO96RhjFGv6XXNZSZZpPX17kEvjSvawY63hENqlMiSPuVtYPs7DWFNM4Fx329\njoCRNrazJY/JyafJS5fIZB1dR3fjdL3OT51LxxybUPv1sRYWgZ/GyZ2npuQAIZ/PQKDnuzXIRxqr\nktenGOSYur2i8RQrlQrsuibWNR+N6xhf/fbcmEvMWffR7ZnmTfVhKtmnNTn+6ysHB6zkW/dW46xs\nDMiSVB0ngtmUY04dE1JgzPq0YJQtafJqx6UOnI+r/ZSADkBmWFkeN5s0BKqavGQ7rU1Nr2oEFANn\n29DvxozHFfsh8FHAU50z57tGSPGqmpbmG9kwI66Z0n+tJ9oPZ0cV8y5Wrm5H3rlXS2pfJjrkCxEY\njc9+gXbtIEuAqOfz/zGOAI4SlM7n5Mof5lQJlIXsnP3qbe7sujYVD9mhvy6gdrlLVcgux0orcMg6\nuwKjvaj2W4874O6ajBNiN1lfx0DJLwJJLdZxrrrdJDE8XZd8JyAm2drqLwHLdurcPJ5yjIBxzKOm\n7EiKs2n812vXaQzltsa1asQOtFeRtYNsxDxbcB3YATUVtQZudoPJvlnfVMewQb9JlhPHXZNJBUp2\nOWY2Y28HLPkxgRElMxWF6nSJ7liW6qlsymt0fld3clO7xz5Wut1cBzIupwng3fEqr2caVPUTTDov\n74u7KU7FcKvPBhwDdX655letn2UGD5bKRoDsECqmVQCOkqgKcrVpYzwVAjEYEsf4qjuwzzA+N5fW\nV58qXXmO86tqVO6nd8bY6lcQNKYEyl0haDMiwKd183ltdtQ4utgQKXDn3F475tyJY55qS9W4VZer\nK41d19BzXTt/x+MZEKzqRPeT8ouae6d3iZQg+/zzz8cHPvCB+K//+q+4evVqvPe9741f+IVfiPe/\n//2xtbUVr3zlK+PDH/5wHDlyJB599NH43Oc+F0ePHo33vve98eY3v3nKAOo4xD4jfJepWNzMcRXH\nauhc3jzHpru11EaKgbKEah39njrF0DESSjZdi45Vtjj7HIDkInD3EsjSseOKzbgG7hgszaGm0Onv\n1h2+KwjTfN03atgErmqr+xq1+udIh9qnf3kt9UF1q1SxdjY4u1RcHbg9WiolyH7hC1+Il7zkJfGX\nf/mX8cwzz8Rv/MZvxKte9ap4+OGH441vfGN86EMfisceeyxe97rXxSOPPBKf//zn48qVK3H+/Pm4\n//774/jx460BmeVE1C9Ns1AnpE6V16H5akt+TAWqm+u6HdmV9VaAkUFc4+GYnQolChWGviykonYx\npfMUi4ibP4CgOIw8UFCmJkd+d+vT/jhArIqXYkQgNFPcujdZhzbUrDe/J0mil15lu4dUoD3Od3Nm\nakjnOiZK+1ntg8vRUTN0h7eu8dHa+wXYiAZkf+VXfiUeeOCBXUO3t7fjySefjDe84Q0REfGmN70p\nvvzlL8eRI0fi9a9/fRw/fjyOHz8ed999dzz11FNx7733tga4388ZzrmbxNBY100r/e5YV7RqE82Z\nSWSnd7bLqy5tDpXMslbHlujDD52jAKK/grHkjvZurfycirgSioEDD20QeV7FfLNO/e8Ap7M5zyed\nLsdcDnV55K4CUltoro5TtuzYrdqYpfuihfpaASvN7Wp0iZS/EHb69Ok4c+ZMXLx4Mf7wD/8wHn74\n4ZsS8PTp03HhwoW4ePFinD179qZ5Fy9enDIgd27aYEpsSurBgnLA9IYnFPDMDMax7oJxtYH+1J8h\n6ltmcF1hVECo43WtI0eO7N5RKY9Ruyn2uiaNcTrUVvIj+9/trbPfxZdYzGwTcjqdHs0ndwc3Aqxx\nfPxRzlGsHUurYqTnq/Updm6/HMjT+nm9bm+qRtsRmS4WrsnNNLtZaX+G8Xvf+168853vjF//9V+P\nX/u1X7sJgC5duhTnzp2LM2fOxKVLl246nkG3ki7QLuizd8dxHXp7e9sW78zfzJq6bjfHsSMC4jxn\nJh5dAiurcMVSsZQZBqaFTGBPY4idaNwqgFW/8nyKrdrtjqn+oSvnF8WJQKZal3xzoOyaG4Fn1cAp\nF9yf+ujsVv+qBlE1SLe2+3IT5TN9c67bk1WkBNn//u//jne9613xx3/8x/G2t70tIiJe/epXx1e/\n+tWIiPjSl74U9913X9x7773x+OOPx5UrV+LChQvxrW99K+65554pA1wAZ6QaX3VSAieXKMQ+ZhPH\ndc+sRwuRbBgyxqrNXeLl/5VojKpfCK2aTrd/GRxcUVSgXflCt2usxru4dXnlWNwA2AGy1XjNLWcn\n2eiIAe19fuzirE2U9FZkh+qA4ubOq60OeF1MHHi6HHV7obIEj5yU78n+3d/9Xfzv//5vfPrTn45P\nf/rTERHxZ3/2Z/Gxj30sPvnJT8YrXvGKeOCBB2J7ezseeuihOH/+fOzs7MT73ve+OHHixGJjctKN\n5zMvnfJzlySagDou26D26JpD9Po+tUPfN5oBo64L52J1cegYWVU4I+b5JS+99dGBq2MlQzQ2eokR\nNagOiMYYBTba53G+a+wZpCufupjTGMpLsptsyrlAQNQBAzUfAizSP+a5PctjNScq+yqgI510NQTV\n3AwBcfbsF2AjIrZ2ZijOCyDf+c534pd/+Zfjn//5n+Pnfu7npgs0F9D477qsgrYbr13ehUSTqrpo\nncCdbFQ79CWy+9MEyWvTJVxjncweK5agP3njYkJ6XLE69kK+ZRvd+39Oluiqmpdr5NknjYECvOZA\nlRMUaxqn8c1N0L13TTZVN9bOc+nnZsZxHa+NtPLTNZ0qjmQvgazLZ8IF0pXnf/e7341f/dVfjcce\neyzuuuuuPXHqZCO+jKAJMdONNcH1Wzd5Ll2rmfW4b6lk+xRA1X5iTLrRBFrULbWAq/sE5PEZVEiq\nhkVNQn10NtJxYjldo3T7lGPRAewYN8NACDjyOd1P98okr6UvVbMuarL02PlU+eFqR3OT1qwAdjzW\n/FX9aovGjAiF6upyztm3VDQmup4C8H7WitgAkKVP1ZV9EQioELMbhasMSBmAA5fZxHd2aVLmRCU2\nOsaNl+iVTcSycod2DIKKh3x1LNcBYBcr9TeDMMXG+Zl1uQKofMm69BUONUpii85XzbOxDzkH1TcX\nZ7Jd7dP9I6bnclRZnQNaWt8BbOUH5anzU+cQIDvdS8mMk4MA1yFrB9kKeDSJKHj5cQVcrmtWm6D6\nKel0fVpDmQwBxpABsHrj6FGsrutXtuYk1bWcPoofJbv6tr29PQ2AnS8VAM00h3ysYnK0Fl27q+Nn\nmmzXfNx8l0sdMNCajryovpEP1TWoWgNjvMsx1eHIUgekjjSoDldnY67m5Sq5t1Q2BmQj9oKVglHV\noalIImLP2wh5nv5gmq6Z9ZHd+phAkV4udQAxU5i0thbTTNLnud2P31GxEoPSRkkNrGqaeT0timoe\n7UnXOJ2Pei/gCricXy43XQG79XVdF0vyV5sjAW0el+3QPSbiM+bSB9QU+44c6FyNod5USW3PY11T\nzHqpaagsqUeSjQBZla6za/EpqxpBHz9hTABLhVvZ6Fgc2awv1+nWbApMah+ts0RHtpvi6G5mTL7n\nOd29W3WcuxnMDDPr7Or20BWZA6q8HjE8zQP1g0Cp840Ay/naAWUep8DrmlEXDxcXrauKnGjeunEk\nFWA6ne5YVQ/UTPfLYIesHWQj9r6XpVIViAZpjBn/3a8TVEmnxzS53BwdOwBWbcpr5MKgl2l0Xwda\n39lVJZY2g62trT3vU+pjV6BVs1CGpOIKmnyu2AkJ5Uf1FdHKR9WZCzfHwIEbgSrZ6xgw+ZWfu0br\n1lOdN27c2POtQBcnYrXVXsw0HfUj21g16Vkw7F6puRjuV9YOshlg6C5TORh0yYV73jElxwpnmOCS\njdAic8WiSZPB1f2wXx5PnZqSVYGGgKtbp2tQ6rc7P/zMCU43RsnrqM35WskKuCiGbm8q5jUDgi73\n6MsJzl63L+prRU5Ul3uv1bFkIjaUY8QsHSjq2vncTG1V38aabXDqO9n4ogNZeuNcmQFdPxrBm9Wx\nzSyOsWY9zu5sq+qr9I7zzg9n56obn9fXO/MT2GV7qiY0nhMgZx3uvPrngLICUNJPsaqaqB4bDS7n\nHAHyTLzIPvfqJMfN6SEg6thcBZD5eEdWSE/FtmnNzqa81kGwSsrFCozHnBcVyFYvT6vC0/FDqgDN\nslWXiLkoK4Y7wzIcmDi7HWg7sCfdZEdmIBTrGaaUx6q4O3VV4N3Z1EnVKLM/BGqagy72Op/Wq2I+\nc0xZG72Prjq0ceSvbes5aoJdvc02+4qF6/HqMksC2hkbXM52JOqgATZiA0A2bzh1fPfyhL5Xr5tU\ngdbQpeI2VfXPSqdPWfwMSydA0jXoecW2dG0SVySuAKhJDp+zPgKHrL+yewl7onH0uGpcVZNVQHS2\naP6R3wQ4lQ0aQ6oZXd+dJ9tcA1Z92pi2tvbes7haW2PfNbKqll0+uRgdNLgOWTvIkrjNHOeqjcnH\ncnJoN62KswJnBwIVmyGfVN8MuOhcZdcRfOkPsTMthG48nXMsrzvmYpH/r8JW3N5VoJbBkL6cUu2B\nCsUz+08NsWNb2a/KrrzvCiKDlMyA02iCM+xW13DjNS6uUelxyvHqGt58bCaus+f2KxsJshE/CR7d\n/SoLBZ4K1TENt66KMou8+W58pbdiODqewKNqRM4mx5Aq9urOVyxAmY8WrvtfxdKxOTrfgW22WQHM\ngWzl82w+uGZXAYKLkca3sj1/yOn2nwCziwXNqXJJ16P4uBonWygmZLeu7/aR8kjHryIbA7IUZBes\nfK4L/giiuzIhixZOXkv1V/dKmAE8Wpv8o3OZFblkouLI//OXNbTIaE21LY8bf+5m1I61UEHR3s/Y\n4grEAbgDJvKLmFXW7YBB183NhgCH5rjmkW2jt5xcrKg5zcRZ7ZtpRJUeam6qS5t09j9/UEv3ha2w\ng3Kiwpn9ytpBNifzDCNYojcLsY5xvEo2OkfA6pJD18/PFaizPXlt92l0nkvfWOuYF+lRG2nNbBuB\nBslMAXe2d820W9utQbEYcXeMs2pcCoZ5rYpF6Trdq62KGeqY7vJI91htVlvpeLUXZKerHUek9Cbr\nmh9Vs6p8c41vv1i0MSA7HufjGeC6IlWw0aQfkpNAE8IB6pJOP1NcQzpWQwmhiaxJ6hIzx4nmUoJ2\nTMD51Z1zBap+a9PNvmc7uoYx03h0rvskX3OD7ims+tR+8pGKXfOOiIhrPjM/wpnn0G07K//VLh3j\nmvYMYBHAagx0fHfvZrWtatL7BVWVjQDZIRnkuqDQZg8hhjjm6WPajC7YCsbaDNRmutlIZxclsCbc\neOw+vNEipGLsCinboDY70Fe7s55q7xyQuVg5gKJmXTUeFdVJTZri4mxxDdOtTc+rpqvrLf3KtI7V\nqwFcM9IacPZn2/OXR9Q+lzsuryifSCh/1S4HspSDS2XtIDvEJfV47pKmSsIhlAzuvI5xOnV8BUyu\nOByDIaDugKcqhCU373BFm89Xzcf5PgtubiytqwyEQMM15jyf1hpx07lLi875ovtFzNPNyza5PctS\ngUzWq/mnx3X+GEegrDZmO1y95XGdT2Nd2peZ/drZ2cG32EhedCBbdcxVgLRL3Bm7lhZVlyTu/bEB\naAqwCra5IPXeDA4Iq0Yy9FSsKMexYi3uzvyrJKprDJ0uLVZqyDqeGF0FQjSmsyU3Tx2f41wxtCqe\nDmBpPbXZxdqBmI7V3CHgrGxxdlHjzOOoyUTw3bpUvyNv+W+/ABuxISA7y3JcV3S/BDCj3zFAGjd0\nzTKHat1Oj5tLSeT+EyjQMdVd2ey+oaf3IMg+6b5VbNitq+vkc13cZnwcY+gbatTo8hzHxIgNVkCq\nQOyu1shC8aZx3S0CuwbibhxT5alrKCrVL/p2+1UBLOUZ2V4RkxcFyHbdzTlKLx/yY6eXAKcqYv2u\nP9lGRa7dklgDMTNXxGr3+OsajIoDoZ2dnZt8p67uEtYxzI4BVsWqMaH/WVfWQTnjmJaLQ7affMs6\nXdNQcCbRPVagVdtVf9dUqmME/g7UNc56SeSYn4/PAHtFlih2VUN1zbRqCJTbap+7ymNW1g6yI5nG\nHfUJWCI4aHkDqjfrdaP0mrscTGVfutEVsHRMRx9ndpB16xoKysSQSAcxGwd0VNgOPGhPqp/LcY0o\nP88fDlJSu0/xdf/HsTGuunNbV5QO5DRHSEY+6Vs7mlNqKwGfazIuv6qm586rjhyDnZ3/uzez+zp0\n9oN8JPBVuyh+Ggf1uds/ikHlO42tGuSsbATIzrCMPL6a744raOuxvPkEEtk2BaBZtjLGujEuIVSP\ni0/Xkd1YOk9AUiVbdS4XJdmffaf3gKkR6bru7ROKq649hBgs2ej8rvLBsbdZUXByLM7ppOMOdF0e\nVcRHG6T6T8fpRyepoZHddEzjXmEJkQ9qbh3RmJG1g6xjfyqOWeUuOfS5dTqhbj5sU5a79GW6s0cB\nYQbQhhB7m5mriUXNSG/3l210QEGsUQFWbahY7wxryc8pj8iWqggrIK2aORVrZzOBsOoZr/DyvCp2\nlTg/qpqjx8qwl6w1u07OBfVZa1PX1WYxk2N0vMOkWVk7yEb0bJTAIMJ/Ij7mjmOzNrgAa1LpRju7\nCbycnd1GLj2/hCXpeMfEiC3ktSuWTv5Xe0d7oGtUPhMLISCqQJjW0D3vcsGtpXZG/KRJVV/Zzmt2\na1WN3MWCwN6B7SAfepz2IQtdGtf5kfezY9PZPneZl5KSKq/3KxsBskMcwxr/Z75eWhWeA898vmLW\njrVoZyWAzfboXfppMytm4oBd4zALvAT+zg5nq2uS+rzST+s7oHXFRuBNH6hQ4XU+UV5QnKsYUaNR\nMHA/meTWy+c6YM7zq9sxVr5kn/IY1esIBO2l1pWzwZ3TpjLimV9dkf4Z//YrawdZAqVxXIUAUJMq\nz3P3nFWdei6vQ53U2TrDSim58nO1qSqALgmWsAsqmFkQI1uUnXVNg2JMzZUYqoKFa5LZNt1bBUGX\nf872imF1urK/dIVH9m0c75pftb8K4F1+5/lVE1R/st0V4yRxMXDn8lr5HK2rOdbFsarnGdkYkFWh\npHBjsi53js47gNX1nTjAdLryORpb2aN+KDioTgKbDhAcM8n2uQa3JDmrn0nXuRWYdKBGhVQ1b7U/\n++Z8dd+G0/i7tchXBQNdm8aRaO24tbPN+jNPanfV9B3gOt/HY32l4T7/cPHJsck+kO15HrFc9fsg\nZCNAdgg5p+9PVd0266EkrJhUDrze4Ud1ueLJ59WWbIcrRir06iuxjtF0flf2Zz1OKrDVMa5BOuZF\n+1vtpQOsbs9pLv139i8R1yQIQPTOXwSwrlF04OZyTOPmGkP1dl1E/S0rlS6+LuYuT+h/rl3NIb3k\nUH2j/FpV1g6yKtSdq+7run4+NsZRd+xs0TfOVSghq+5NSahg1OmcFcf06Hm3XrUfLpYOuDvGQzo6\nRjjGqJ1V3MY5vSqii7U2mRlfiH3lsfp15DxnPCYgpTldXDJYO7DK+robziiQuViMXHGko2oS5I+r\nd+eL6lYg1iZ2UEC7dpDNSaHXKVaFrscqZqTr6Frj/HiucwjUda0Z5kPJ4tg7JVzWTfZSLAjkq07t\nEqz7hQpdl87l+Wor/eTJjG6Kk4trFmrO1ZpLfCY/KtuIIXY5p+OVrakuJ7QXWR/di4JAlq5vznrU\n5q45uRxVgJ2NP/lMxINI0k/9N75yIAnUIvYWYCUzjG9GVwVeDriyfgdirlB1PMWB1lYbtDtnoW9l\nuUJWHVpAzq+Zwnb6HDMbDGg8pw8089hqfwkwXBxmm5MDjIoo0PzO3mpMHksMUffTAatbt/Kxynfy\ntSJPOnbW90pPPqc48//au9oQu84iPJtNt0o2oUL9UazplxaxYWmlWCH4UWxMKY1VaIVGLJogm1Co\nUVKbRqOWXYpSQVFaP6C/QiEuLRT/lFqCEuhHfgRrSEsUShDahJqIkmzU3XRz/FHe7eTJ88y85262\n9245A8u995z3zDsz78wzz957PtrM1av0HWS9qCRgTNHfBAJ1mBndXwsAis3he9bV1XGq40adHG1h\n4MN0svGMIaHPNfqZIPgo/Wouv98fHzWTyHYUxk48eNfmhdLXZrwCOz9W+RTFhenLckT9yIX6FIFg\ntiiWW4TdSL/2loMoarxqpGiTYtS92BJJ30E2K34zzaJYQnoGgdtxHpXEyKy84HdKqhhwjGJBWUyy\nMf4z+oV6avTVMh0EzYjl1VyRx3RlNhRRP8j4YmO/UOM+tKOM93b4W1FirrEmGTVqxjSZj6yBsfyM\nasRvR7vZuIg84Da2VsynCPCzJ0xEwta8luH6/SrnFnp150CAbFkQBmBmeiFrmKJ/j8mjgs/eq2LC\n8WhPGc8e1Y3jyqsCeOUrK1ZW8OxY70OUmDWNpYw1O/d7Ze9PLQtEoI3AuYxhNydhOpnvSqdiOKwZ\n4Bim38cAc4mBEoJlFj9saGUd2M1d0DYG0swf5pePCeYInueMOiNmnNnBQN1/nVTOFmLEx8/B1rst\n2CvpO8gWUUmtij8LQE1x+jnYthpAyYq/JHgNY2DfNarEYN3Xj0OmgswiaxTMbwQI5i8DuKi5MB1N\n09AfG1SjVcyN7cd5WLG1KS4WY++zAvCzZ8+elxfKD7ZdxcFvR3DD7+SzppM1e5XL3obiI7tUGIFf\nxYs1hbIN76gX2ejjVQOqtYQgk76DrAKObFsEbgpIyr4IQNgctcCOc7PEQH2YlJFE7Ck7LiscBTA+\n+VmCs7G4LbqJchmjPiuWUT5HsWOF7/d5kMMrrSL7FNNjucryCmPn92dnWaAdfoxvgsxO9E+BGn6H\nGq1ZRmLKserHa3ZfWm+HIlloh9/v52K1h43VH8tiueTPLqgRdm4dvmeiFgeTsUYyIGSgjPPheP+n\nGE8BKXxAogKmCNAVS/L2eH14Wg4ei18JqLgosFO2RvqUXwzI2HFmJmMZNRmvWzUoPCZjUahfbUf7\n1L/+aEvW1BjAoT3RukZkxutlvmFOsIswsIlmDToiIBErz24WvlA2OxAgq5iBYjEqGTN9ZXw01kvE\notQ8rEjZ4zVwDLONsUe1n+mLxjNm531SQIFzoERNiB3r58HYqNj78RGgtWXNbI7yPmruCFLol/Kf\n7Y9YcdaUmURMjNmo2LHZ+edKY2zYPtRbIyqnWYxU7RTBMaxmUXdtbGtlIEA2AxIzDgqYCIodsgTH\nLskCGwGRGX/elJ+75nxOVfQK1KMG4u3Df39ZbBWzYvNGDKFGV1YMqCtiR369cc7Ihgx4VQNkuRL5\nyS4FZ3a1YUuY294OZT9rQNlaex9ZbiqAw7yM6gz1+1phdRwRHe8n2sLOCmCxiGq/bYNg0neQxfsE\neMFFY0yHdU2232/DcVHh17ChMq5pzj2LIErw7NzAqECZb5iQRUdJYKbHJ1lUtKrxRfay/czerDCZ\nv6ygPACovGGxifxRxypBnVEzjICP7fNfcWAMFFhH+c9ylN1YpYi6mYqKA/MN96t4RY2RgT/6g8DM\nmobKJYyfImBtZCBAVt1fFZMHEz4DItyGxei3tWEVSlgCo+3ol/dZgZnyPbJTJUfmGysQ3zzUPUhZ\n8bFGo/yLbIsaaY3tKi+wwNhc0RyoK1v3yB602+uIfnzC+TCvlJ6mefsJtMw3v95K2JwqppkO1gjY\n+rHGgrEvxyjJSNZCMYBJ30E26yT+fcSoGIhF7I0JC7y3qwa02hRazQnYfhzr/Gz+CGAi8FD+MTbh\n9+Nn9usuHsuAjc2nAJYdW8s4mG2KHfm5IlGsUeV0NF7pYEDO7IvuXKcAC3OGAabKdRU+uunuAAAg\nAElEQVSjmtqI6kTpRZ1sW1RPbGxUF4t6dsGZM2ds586d9sYbb9js7Kxt3brVLrvsMhsfH7crr7zS\nzMzuvvtuu+2222xqasr27Nljy5cvt61bt9rNN9/cyhDvZHSFhU8A1ZWw02HCeF1tRbEls/OTG49T\nCRQBh7IhAoUawGCfWcGwwlQsgzEQ9DtKaNSZjYnWMgMFpjMCvZo18XOoGKkGpV7L+bRlGzvVjOW/\n/7U+O0+7vPdz1YAdsklvY5uYFTuiuo9iV6Q096wBY85iM6lt1rUSguzvf/97u+SSS+yRRx6xf//7\n3/alL33J7r33XvvGN75hmzZtmh93/Phx2717tz311FM2MzNjGzdutLVr19rIyMiCjMsWupcCYOMz\n4GEL0cZ+xQg8O4kKroj6QSWaPzr/M2K5CmAYK0NfGUNBiZhDOU4VTPmcNcyo2XhhYJXFpk0eMD0e\nzNgVUWgDaxBoAwIsbq9p9Avxi82j6sbHARsBxoExYBTF9pEhZ42XzbOol9Xeeuuttn79+vkJh4eH\n7dChQ3bkyBHbu3evXXHFFbZz5047ePCg3XDDDTYyMmIjIyO2evVqO3z4sI2NjaUGROzCC0sOlnQ4\nvgRYPZxOMZhehZ1xgLZ5e5H1sDFM2L9X7MbDNaDiYxGd7oNjEUzRLzwWmwva40EiemwNA1iMBSsW\nP696ooG3N/Md51LFOjc3R3Upe5GBMv14rCIKGRvPfMc5fPw8iKkYsLhhbtYAPLOzBjijJo/j2DZ1\nfBsJQXbFihVmZjY9PW333Xefbdu2zWZnZ+2uu+6yNWvW2K9+9St79NFH7WMf+5itXLnynOOmp6er\njWAJwfab5YzGv8fLCBVD9Ho8S2GLypgomztjasw/VUSsUKKFZwXLbGAgH40trwoAkZljzKMCQtuj\n+GWsBsf6S1jRRu8b81vpRX/VnfXLeFXoWc5HOYF+ssajTmPCfPY6VP7j8X4e9BPXv+zHCymy+KiY\nMP0qXhEByEA0ysVaSX/4OnbsmN177722ceNG27Bhg508edJWrVplZmbr1q2ziYkJu/HGG+306dPz\nx5w+ffoc0I0Ef/H0wSvdUv0rkQUgYgs4Dsfg1TBeX8baWAdX4yMWW9twIiBVxygdiuWyY71E5yQy\nO2v9VXNHjQHnQL/UfRGydWGg4fM0Yk3ogwKWCNwidspiG4GkGb/toLKXzaXGKbbK7FOx8a9RMyzb\nsziVcezCIFxX3LbQH77Co0+cOGGbNm2y+++/3+68804zM9u8ebMdPHjQzMxefPFFu+6662xsbMwO\nHDhgMzMzdurUKXvttdfs2muvrTLAswzspgrAsjHltLAIhCOmqJLDz+HHlvnUv6AK8GokAhFf4DVA\nGzGXMh5t937i3BgjPC7ThdtwjozdMP04Bu8RgD6WY/0aKtDweth4b7//EanoZ0Dix0YgymxRMccf\nuvDslIzJsXiq9fb7o2Oi+f2+4eFhW7ZsmQ0PD59XX8PDw/P7VW37BoJrwMYw39l/PQuRkMn++te/\ntpMnT9pjjz1mjz32mJmZ7dixwx5++GG76KKL7NJLL7WJiQkbHR21r33ta7Zx40Zrmsa+/e1v28UX\nX9zaGF8EjAVmx3odfpt/X8N8cFyxCTtaWWz2nHnUpWwtetS5kGg76mQ3H2ZJgSBRxqlO7scqRqHW\nSLEr1QjQ3rm5OWqDt7UUA/rkjyvfhfpmhD5mBcSAn+VaxNJ6eawSmx/tz5pTBKhRvrC6QXtVLigf\n0KasAUc2oS3eD9XwM9KEsVIsvxcZai6Elh7k9ddft89//vP2zDPP2Ic+9CEzO/fXcx88dgMHFMbq\nFHAhiGPCsgJGMC3H4K/3il1hkmWMjBUBzov/ppY/7PTY0SPgxG3MPxyPpxmhfga6ivk0TTMPssUX\nBCk/L8aYrbdnRmVt0SYEP9zGwACBnR0fgWD23DSV5wrwcTvmAOpVQBSBHctxltOsnrxdxaZiF55h\ngeuh6oWBt48xiicnTLfXX3QePXrUvvCFL9jevXvt8ssvp3ojGYiLEZiT5bVND1AgVebxc6oFzK53\nLvbiFTGq0FAPFp1KlFrfWaEwG/zcrMhUvCI2oNZN+dvWDw/yWKA18yu/IzBjPig71VpHeRjZynxi\nNvjfKtAmpp8BYNET1RqLN4Kmb4bMVgaIrDmwy3aZ7arRs5ixRunf+yveVMPBWPYiAwmyfl8RZFcq\nSdl7po+NqSkw9pmBXFTQjMmwsV43soyaYsR9inFkgI7FHxWCjwn7HhJ1RXMzYPRNjsXG61I/cuBT\nKqI1UHOoYs/yEm1hvqnj1PrWADjqyOZi82Fe+/j5mKqvz5jPuP6slmp/eFJNivkVkR30b6HSd5CN\nAhy9Z0VdXtXNVxTgqXGKqbICjexiSaLAhSVjdgUNgovyuRaYVYLhWjFGooo4sycqQARbVpioC2PC\nvlpgUvREpxoh8/IMT61FxFLxj+U0a1DeHrVeqtkzAER7/FjGWP2jbZQeHy/VADEekbA5vD+oA2PJ\nGkM05kLIQIBslIBljP9cKxHAZItTwyrVgqtXLFC0RzHjXjqqSkD0B4EsYjheHyveCOxrGB7aVRgr\n+7cOYx+xSgXC6BPzM8qPrPH6sTjef92E368zm5VfWe1EbDX6FR3H+tz1jLWMY5fkMoYYNSLma9v8\nV2vL1iZ6GIDPp/fMgxTb7jPTHYclnipCpp8lgWIYmDRYlOwYtJ+Nj1irGb+BsvLT7/PsgoEIPoQu\nskXZVt6rNWBjy6sqTPaq9qvCUT+ssjVjzbCcrRCxPjN9G0vvJ/vz9mRsTdmt9LPj8PlYEbHA9/jj\nagT2WE8RcEaXgTO7akAYcw1Pl/NrvhgyUCBb032ZlCD5xSxPqWQFFS0KFjzaw7o1+qN8VCwlE2YH\nJkYUO8b4Int9PDN7agAeASQCXzzGj1HMEXWo7dHcmb8qzggIah38Z/VLOoI7A8maU/3wWAZyaJPK\nG+8P/ovvmbg6RgmOUw3J2+PfY1yyBuHHKCbNmtGFAN++g6xZ/N2TClTkPGMpvjC9fvYlvSok1O8/\nR3aqYzMWkEkELBETzAQbScR+/dw+8RkDw4KPwALXy9uF+hF42LHMXtzGnmnmRcU70s8YHPrvvxuM\nGlGtL8puBBm2jixfGTix54PhD9JZ3bBcqXmqhD8G2XUZy7CExSUaE+VCGxkIkC2sswgCKTKXCGDZ\nsV4wadj4mmKKFi9jgP59toi9gG+kN/MtOicZ4xMxCQayfhw2QL8PWRMDnwggmF04F2NpjAlG6xSx\nL/RRPYooW38kDCz+zHcPpApAIiDDY/GrlqY5/ykgkW8qfhkQMhbO4hyxdbb2eGw5hunttQaLDATI\nmuX/dteARtPw7928MDCo6VYRsLM5Ijaj9DM9hR0wfVhQEROJQAJZHBYy217rl9/vx0T3o/A+lXkU\nSDJAzQpWsSK8eg7HMD9wLbx9/jvPWjapdGEcInDzY7PxjFQw4GFAGNVkBGzeHoxJZpeSiHTVEho8\nru0xSgYCZBn19/uKqM7iu6r/Lrbsw7HRZ1YQDGAUi8NkVswJ2RkrFnVdvLID9dUkVw2bj5KdsZ8y\nTl1jjr4zmxiD88cr5uzni364Yz4oxoQ+RTrUZ7Zd/XuL+4svEVDV2uC3sSvOVCxQWB6oBobrVVMH\nak4/V2Rn1kyYqOb5nmCyrMvie78IDFjKH2N+KCypMWkUg4sWH32p6YLKp4jN+DEqgaP5VAJFAKt8\nUkmYNQIFaEoPa5qMHXo7cTuLXfnMLlBQTYPpUDZnhYsNAWOiwEuBhmpGbA3w7AIcp3KQzed1luNY\nQ4p8jxo7mw/1suPb/ndSG+c2MlAgi9uUsADjl+5ZApbPESAzQCmvCHIRGEaL5ItXAZyfE+1jQKt8\nweT2cWNzsfHKNr9d2YWAETUunKONYEF7/f5O/H58+Q9IAYofo+xTDShrQmWsOk7FIbOHrV8WU8zb\nyH4fZ3UuKY6L9Pl9+FWLOv3O6/XzlWN984waNtYfawa9ykCArJmm+lkh+n0lMNldj5Qo4MjmRMEC\n9u8Z61IsltkWdWT1GRmcj1HETlUMMCGZX8oOfLQ1+h3NGX0uOlAP6mS2McZWwxSZqDX22xHkVfNi\ndiDI4An1ylcGtDXgq4iIX0fMpfJae7oZ2uh1qRxTx6p6y2LiffXHvieYbBvGyvaXYPjv/1TSsC6F\ndmQBVV2QFWrkHzYDVkx+Xy8SJU8RnJslH8ZTAQErRMW0fAIjAKH9eHxNE0Df2VjGGDEWLF6ow++r\nZT3YEPx/FJhDNXmLNqh1xGPZfKqBMUKA+lhuKRtUM8O8Y+uEgIw5GuWIspOtPfOzrfQdZIuo57yj\n06rDlI6KCVsYQ3SCt5daoG6jD4/1x3k7s4RU3TqLmZ8vujVjxO6itVFPkfB2I0tkczAdDOBZg1KA\nyHzDwsV8YnFjfvuxOJ75zXSw5hoVt7IrYnDMtvKZHe/3qebsx/i8Yv4w0PS+Mz9rmlXWINna4vH+\nuOjGQQuRvoMsS36WMAxY1HaV0OUY1dlxPx6rgu6LXp1nis3BNwD/nulWosAJ9yugiIo7Ar4aQGbr\n5serhsGYi9qHhaUaiGrgzDeUaM2j9xlYsv2qubL32GjU2AhIzc6/WkvZiXH3tuJ6MaBDwVwrJMnP\ny9aZAbXXg3ahL2gDA2Y1vlfpO8gqybobW+wi0aWvWcIrwY7I2FiWTKqzIov1oMF0MXtZkmesRzUo\n9W9+TVNi9ipRYKn0e//wu111PB6nCk2xLeWLajT4ns1TAJKdK8yaBAMvnKem8ZXP6mqt6Eo/bxPa\nyy60iMBXgRuOZ40fQR/1qvhjzfgx0bnoSl8bGViQ9YIByG79V1N4RbJOX+aL2F00X/RAxkwUcDMf\nWHKWz9F3v2gTAhJjnCiZfhU3BFn1gyET5QcDIlV80RyswHE/+oH7/eWybD87IyZrhqxhRmwsAmn0\npdjsRTVinCtrkDU5p+Zh5KamKUc2lz92STOL0UKk7yCbJRAK6+KZXtRfk6j+GLylmwIR1m2ZDTWJ\nj7ZFfmU+Z2P8OP/KmJWyiRWuj5max29HYPOvUV6U4/CxMj7WbdlPTaPwfrMGl+lUPqm5ca7oabMq\nbtmcUZx9zKL8UHpYzijCofI0atiR/ZgXbA61Zu8ZJhs9dTXqWjWC4FqbAEoHHuttVIWkFjAC2Rpw\nYrrYfN4+Nk6BLM6BfkeiCgj1MZ0RA0K7ezmWzd/W34wQlO01YFb+1LOnkIkxdsfWjNnnj0cWh0Ca\nkRVvP/saorxmzzNjdjJpA5A4jj1MM2sMF4LR9h1kWVcsgkykjFfCgEgxM6+LJZQPsmIxTI8fh+AV\n+ZHtV756G1SS4xkWSo8CGcbSmN+qOTI9URz9XEyvH4OAgxI1vjb7VPMvr+U4vBSaNeIi7HtvXw/+\ne1Lvb3nP1rPGRtyPNVjTRCMWm7E/RUjU2DIfzl8jkc9q/fyYCyF9B1m2WCqwEdtgepkOfwwCKRZ+\nBorMBtUwvH+oR7FOPw+LScSkooaCcWSglxVKNn/mb3RMtGaMRaH+CNjM6h5FkzUctNPrxDNN2Noq\n0ED/PNC2BULmmwdUtKe2ttDnmrXPckU1TMaKy2sGhLhWbVlpLeHJZCBA1ixmPQwUI5DzY3AxPONT\n9rDOzvQoQFCgxfzO4oI+YsK0KTjUHd3ARcXd64j2qwLA+Hk7vN7s+LYsqrYJeFEFrdbU253FBr8/\nzuZX+xUhYXN7P/x5rZktGFMGhGw9ojHMl/LH7qmANYn+R/ayWKi5axpuWxlYkPX71Gd/HBvHAq2+\nG2LMLrouHLejHgYmfj+7U5ha4IyNoN1R11bHeL3MZ2YH0+UBOip8BUQ1Sc4KGudkfkSNkR3LfMmA\nI7qoBNcFT35H/dFnNQeOQ/0MpDIw98f642rizfTWNI8ol7Jmr+wo4/HqOtZAolxpK30H2VomUoQl\nOwOxjHWUsWzBFFBFwBkVCm7PGEgmKinQbvQdT14vD/DL7GZzs+RX83k71VyKnSiwyNgQbvMxioBc\nFTPqUsdnd7ZC8etWbFQ3w2Y5jSxsaGiIfr2AMfPzMXsV2WG6MokaAoJk1JiVRJhQ26TKtujc5V6l\n7yCLnSViUl5YEFkhq4BlrE/pihZcJSDrtopRIBAoMGaxiYCoxJn5hnYqIPHj2FzsuIhh+c8RcKkm\nmrHKXkTF38/BmBCCZNM09NdslW84p2r2UQOvIRJe/BNm8T7MNQ3N78PHa+PcWbP0eiKfsFmyNcfz\n2hm5Ub4wHFqo9B1kzeJ/S1WXYoxHgRR7AJwCWZboZvzxyQiSWHBRY8Crqpj/TIcCABZL9pklpyp6\npcMfx9iD0oNjVJNjQIbjs3NEcf3Y5aOqSFleFZtqAE8xP+YHs0npjJoHxoo9TZaNx23evmg/e41s\nyz5neeTzzdcO1qu33x+HurFW2dgLBbR9B9ka9hMBQq9AEwErK1JMBAaQ0RxlW8ayWINhnxVjwH3+\nPbIVpYsdr2KPY2tBgtnsE9/sfEbC9vnHdPuGqo4rAB3lUsZ4MGZ+HzsbQMVDxQX1e91+W5TnjGzg\nWJbjkaimH4ERAznG2lkeRUQIQbKAr7cJmzWLUxlfXrMY9CJ9B1n1DHQFvmxBIzDEboUJVZOMqDey\ng3V73Mb0o0SJz3xg+pntyn4FrEy/spkxKWZ7NJe3T62d8lkxML8fj4nGqIbHgCE6nzUiEaiL5Y9i\njh5Y1ByoX9UJStGtcp79d6iA0h/P/I1ArwAljo1usj43Nzf/e0PRoS7sycgS6u5F+g6yEXAhEPbC\nDL0ePI518ghkMzvxvQIZ1BN1WXZ8xihKUqnEZ4Lb8euRMqYGOGtA0tujWBbaxliLigGuF4Kx8tuP\nYU9PQH+i+LI18q/Mf6/TAwXqiJpvlJ/MzrKtBnAwnlFOsPHMLmavWjcGtF4HgjeuddRoVW0veZD1\n4ovSd+iIVWSCAM0YBgNh3M8KpLzPHlsS2c3YF9OFNyU30+xJzVV0YkExpsO2Y+xq5mP+Ftux0TGQ\n9Pv9MXjyP7ISBHq0oYbRYVGX8eg/W68otzAnVY6oMWwOBUx+zkyYT96OKKasWUSA1ma7uqij7MOG\nHrFkP4fK+wstfQdZXDQEEcYUVGfM5vGvXtoAIxYzO95vz1gTY3wqORggs6Rn7AIbhn+NCtj7rJoV\nzsl8zhiYjys2EcZK2PFoL/Mtsps1dCWMYUUxL6J+7GTzqkYQjWV+qnVWRIPFj8UN/WR6vChQiwhP\nVAs4TtWSjwPaiWseNc5epe8gW6TtzVDUuOxfELyBs1oQz/ZwEdRCmp1/G0YsiLYFzHz3f+gf+sVe\n2XyYdFikjC0gK1MNxR9TWKhaw8gHvx9/XcYYRZ9LHvh96HPELpkoEFKgofzF+dVal9foeLbmDLDR\njpL7qjFmhCAiQZgzmU9eWG6y/WgjjkH/vG3ob+RLrfQdZNEBdWqTH6s6okq6ss+/ol62XwGI/5x1\nzEgigGA6vN+Y5KpY/H7WADCmijkwnVkBY9NiNmF8Ma7MVpYHzO5a9qYakAIwr1+N8Y2FfX/MzkBg\nuth64zj8uio6RgGJfx+RFz8Hq5koPjiHAnElrPFHOctyFP1R61dzhkit9B1kvRTHs8eFREmguqpn\nUKyw2y40vmf2RR0eFzljJ1EilVf2I0DEWjCBysnprImV+PnE9jYo+1ghZI/aYXarWNfEpoZ5+WPa\nFpXKCQYG3i72XjF0Fneci60J2oLH+uNq/FZrXHOMIiKYbxH4KtKD8zGyhGPYWrGcWaj0HWRVAUUO\nMgbmxYN0dAK5Yl0Ru2KJmzE6tF19jorfj8HiZXNGAI/b0AdlO/qeMUnGGhm7KGyMFQL6jbpwHxvP\nbIni7rfXgopv5H6bijueushsxPkUsERrwAQBVoEk08typIbs+P0Zi0RdihR4H1A3jqkhVBEbXoj0\nHWTN6oGm7FMFicHGx3uUY71eLIyyDxmeYqCoq4xnYNJGFGBiMvrb6iFjRN/Z5wgw/GcPqiw+kY29\ngAAD2CgmjI2ijSwGTBfuq21CqC9af+VjZlcUhzZgwABLNZ+aBspqTR3L7FX+qZiw8eo4XD/1wzU7\n/j0BslkHUzResVBccB9cZBaKVRVmpQJcgFmdBoVgF3VnNj4DR580PnHwX330H7fhnOyrAsbG0G9c\nnwgQUB+emoZriLFRfmB8/Cv66+OnYotz4pM78KoxlZP+PcYR46aENQ22n8UA54qYIGuKZvxH6cjH\nDJxxPL5iXWKuRsyZ1Xg0n6q9LPfaSN9BVokHO7OY2Sk2VsbiuXSok7EcFuCIaWQJxRqFOg71s+Ri\nrIqBmveR/aDIkgmbkrIBtyumoO5sxEA8iiECZAQ87Pho/dQ21Whq5vVxjZoBxrBtUTNbavPWf47m\nVc3JvzLCZHb+uazKZmZDzRrjOBWP0rwRpKPfgC6EDAzIqiLEfQxUGBONkswLA92aYsR9+D1w2cdY\nggcJVoCsU2egEoFf5Icvkja/qGZg1IYF+BtIF92siHFeFSe/TQEKjq31FxtQxHgwb7HRtgXVCMhU\n047+NY5ixRqA+n2D5W8WWza/F2SvfhuLI7OD6cYLG9jphFi3CwXggQFZszqG6vf74xRIs8THk9yZ\nPqZXJZUfH91DNfI3EsYsmc1ZY2HJpI5F3SwBs8ao2DGzS9kS2R9tVzoYE44KCtkoNsdaqQEanA/n\nVL6z9WC6MW+j3yIiAhPZzpptmUutH0rWKFHYo9UZefH72fvFkhRk5+bm7Pvf/74dOXLEhoaG7KGH\nHrKLL77YduzYYUNDQ/bRj37UfvjDH9qyZctsamrK9uzZY8uXL7etW7fazTffXG1IBrAMGNTxZuf/\nwOXH4SW7bA4GsIxNZoWPohIzEsViI5bHfFK2IbupaXYKPCOwjMZ6vSqmbcEt08UAJPJVfcZtLOZs\nPGvWHiDQTuV3lgcKbDK2ifNm86vPHnDbNErUFenAZsl0+jG+nnE+bLqLzmT/+Mc/mpnZnj17bP/+\n/fazn/3Mmqaxbdu22U033WQ/+MEPbO/evXb99dfb7t277amnnrKZmRnbuHGjrV271kZGRkL9Ufdl\nxY4AiK9Z4kTHtWVTUbEpdqbYXk0hIKPEOVF/bbErP1Qs1VNS0Q9VbHgM3oiFsWJWIAhGyj+cv7Z4\nGAiqfezXdbWm3l4WD1bk6v4YWTNj+pXvyD6jemR1VI7138GyqyZZo0QAxfnQt5p1UbGpjeOFkhRk\nb7nlFvvc5z5nZmZHjx61VatW2QsvvGCf/OQnzczsM5/5jD3//PO2bNkyu+GGG2xkZMRGRkZs9erV\ndvjwYRsbG0uNiAo6Yi5s0WpYMM6BOrNkYCAWgWFUbOiLf8901hQJ0xElH+ryFx0wf31BsCJmvkVg\nyNgJA5bIb6Y7KsRsG4I4+tXWz+gzghuClAI6pbs214aHh6mO2uNVcy/riY80L/tYrbPcifQr0FZ1\njXmsiIDX8a4xWTOz5cuX2wMPPGDPPfec/eIXv7Dnn39+fuIVK1bYqVOnbHp62lauXDl/zIoVK2x6\nelrqLDdbPnbs2Pw2LDRfyOxZVOx8VPUEVq9PsaWaboa6sRjZfNlzg9RCK+BGduDjxk49YwCLye9/\nrMMfB7DY1VMi1KO2/TgGnLguy5Yts+Hh4XOYEbI7Ng+up3+8CvqDBZs1XdVIPUCqmOPcSkeJrboy\nkcUV4+g/m537o6KqFbQxY4AYFxbTss2fx8388vGLvrdVsY6AGPWxWOBa4JxmZm+++aaZvYNZbaX6\nh6+f/OQntn37dvvKV75iMzMz89tPnz5tq1atstHRUTt9+vQ52z3oohw/ftzMzL7+9a/3YHYnnXTS\nybsrx48ftyuuuKL1cSnIPv300/bmm2/a+Pi4vf/977ehoSFbs2aN7d+/32666Sbbt2+ffepTn7Kx\nsTH7+c9/bjMzMzY7O2uvvfaaXXvttVLvmjVr7IknnrAPfvCD5/zb0kknnXQySDI3N2fHjx+3NWvW\n9HT8UJP8f/yf//zHHnzwQTtx4oS99dZb9s1vftOuueYa27Vrl505c8auvvpqm5yctOHhYZuamrLf\n/e531jSNjY+P2/r163syqpNOOunkvSIpyHbSSSeddNK75A/16aSTTjrppGfpQLaTTjrpZBGlA9lO\nOumkk0WUvty74OzZs/ajH/3I/vrXv9rIyIhNTk72dGpEv+TLX/6yjY6OmpnZ5Zdfblu2bKGXGQ+q\n/OUvf7Gf/vSntnv3bvv73/9+wS+RfjfE+/Dqq6/a+Pi4XXnllWZmdvfdd9ttt9020D6cOXPGdu7c\naW+88YbNzs7a1q1b7SMf+ciSWwvmx2WXXbbk1mNRbx/Q9EGeffbZ5oEHHmiapmn+/Oc/N1u2bOmH\nGT3J//73v+aOO+44Z9v4+Hjz0ksvNU3TNLt27Wr+8Ic/9MO0Kvntb3/b3H777c1dd93VNA23/R//\n+Edz++23NzMzM83Jkyfn3w+KoA9TU1PN448/fs6YQffhySefbCYnJ5umaZp//etfzWc/+9kluRbM\nj6W4Hs8991yzY8eOpmma5qWXXmq2bNlywdajL3TrwIED9ulPf9rMzK6//no7dOhQP8zoSQ4fPmz/\n/e9/bdOmTXbPPffYyy+/bK+88so5lxm/8MILfbZSy+rVq+2Xv/zl/Gdm+8GDB+cvkV65cuX8JdKD\nIujDoUOH7E9/+pN99atftZ07d9r09PTA+3Drrbfat771LTN7+2qj4eHhJbkWzI+luB633HKLTUxM\nmNk7tw+4UOvRF5Cdnp6e/3fb7O1rqN96661+mNJa3ve+99nmzZvt8ccft4ceesi2b99+ziV55TLj\nQZX169fb8uXvfEvEbG97ifS7LejD2NiYffe737UnnnjCPvzhD9ujjz468D6sWLHCRkdHbXp62u67\n7z7btm3bklwL5sdSXA+zd24fMDExYRs2bLhg69EXkMVLcM+ePXtO0QyyXHXVVfy90/kAAAHfSURB\nVPbFL37RhoaG7KqrrrJLLrnE/vnPf87vL5cZLxXx3x33eol0v2XdunXzV+OsW7fOXn311SXhw7Fj\nx+yee+6xO+64wzZs2LBk1wL9WKrrYfb27QOeffZZ27Vr1wW5fYBZn0D2E5/4hO3bt8/MzF5++eXw\n8ttBkyeffNJ+/OMfm9nbN46Ynp62tWvX2v79+83MbN++fXbjjTf208RW8vGPf/w828fGxuzAgQM2\nMzNjp06dSi+R7rds3rzZDh48aGZmL774ol133XUD78OJEyds06ZNdv/999udd95pZktzLZgfS3E9\nnn76afvNb35jZnbe7QPMFrYefbniq5xd8Le//c2aprGHH37YrrnmmnfbjJ5kdnbWHnzwQTt69KgN\nDQ3Z9u3b7QMf+AC9zHhQ5fXXX7fvfOc7NjU1ZUeOHFmSl0h7H1555RWbmJiwiy66yC699FKbmJiw\n0dHRgfZhcnLSnnnmGbv66qvnt33ve9+zycnJJbUWzI9t27bZI488sqTWYzFvH9BdVttJJ510sogy\nuCdzdtJJJ528B6QD2U466aSTRZQOZDvppJNOFlE6kO2kk046WUTpQLaTTjrpZBGlA9lOOumkk0WU\nDmQ76aSTThZROpDtpJNOOllE+T9yoN2xF54+EAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f3a2358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd = fits.open('../data/ELAIS-N1/PACS_PSF/ELAIS-N1-100um_psf_hires.fits')\n",
    "psf = stackhd[1].data\n",
    "hd = stackhd[1].header\n",
    "plt.imshow(psf)\n"
   ]
  },
  {
   "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": 192,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[1].header['CDELT1'])/np.abs(stackhd[0].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33333333333393333"
      ]
     },
     "execution_count": 193,
     "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": 194,
   "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": 195,
   "metadata": {},
   "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": 196,
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6666666828012"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11f8f3b70>"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFXCAYAAADUG/YoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIYQf+gu4ZQXztGV+oAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f9d92b0>"
      ]
     },
     "metadata": {},
     "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": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.01082e-06\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11f7daeb8>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFXCAYAAADUG/YoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nABBCCCFS0E+wWXb2eXUFUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e8fada0>"
      ]
     },
     "metadata": {},
     "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": 201,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[5000:], encircled_flux[5000:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50101.0"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbpix[5000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.26292443046e-06\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "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": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11f83b780>"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAFXCAYAAADUG/YoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e8fa080>"
      ]
     },
     "metadata": {},
     "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 100 µm PACS, taken with 20\"/s scan speed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = open('../data/PACS/EEF_grn_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": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11eced780>"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfUAAAFXCAYAAAC7nNf0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ed51438>"
      ]
     },
     "metadata": {},
     "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, 50])\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": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11e7c8c50>"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfUAAAFXCAYAAAC7nNf0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1217d1be0>"
      ]
     },
     "metadata": {},
     "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": 209,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11fd3eac8>"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfUAAAFXCAYAAAC7nNf0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e9556d8>"
      ]
     },
     "metadata": {},
     "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": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1.0\n",
      "1 1.001\n",
      "2 1.002\n",
      "3 1.003\n",
      "4 1.004\n",
      "5 1.005\n",
      "6 1.006\n",
      "7 1.007\n",
      "8 1.008\n",
      "9 1.009\n",
      "10 1.01\n",
      "11 1.011\n",
      "12 1.012\n",
      "13 1.013\n",
      "14 1.014\n",
      "15 1.015\n",
      "16 1.016\n",
      "17 1.017\n",
      "18 1.018\n",
      "19 1.019\n",
      "20 1.02\n",
      "21 1.021\n",
      "22 1.022\n",
      "23 1.023\n",
      "24 1.024\n",
      "25 1.025\n",
      "26 1.026\n",
      "27 1.027\n",
      "28 1.028\n",
      "29 1.029\n",
      "30 1.03\n",
      "31 1.031\n",
      "32 1.032\n",
      "33 1.033\n",
      "34 1.034\n",
      "35 1.035\n",
      "36 1.036\n",
      "37 1.037\n",
      "38 1.038\n",
      "39 1.039\n",
      "40 1.04\n",
      "41 1.041\n",
      "42 1.042\n",
      "43 1.043\n",
      "44 1.044\n",
      "45 1.045\n",
      "46 1.046\n",
      "47 1.047\n",
      "48 1.048\n",
      "49 1.049\n",
      "50 1.05\n",
      "51 1.051\n",
      "52 1.052\n",
      "53 1.053\n",
      "54 1.054\n",
      "55 1.055\n",
      "56 1.056\n",
      "57 1.057\n",
      "58 1.058\n",
      "59 1.059\n",
      "60 1.06\n",
      "61 1.061\n",
      "62 1.062\n",
      "63 1.063\n",
      "64 1.064\n",
      "65 1.065\n",
      "66 1.066\n",
      "67 1.067\n",
      "68 1.068\n",
      "69 1.069\n",
      "70 1.07\n",
      "71 1.071\n",
      "72 1.072\n",
      "73 1.073\n",
      "74 1.074\n",
      "75 1.075\n",
      "76 1.076\n",
      "77 1.077\n",
      "78 1.078\n",
      "79 1.079\n",
      "80 1.08\n",
      "81 1.081\n",
      "82 1.082\n",
      "83 1.083\n",
      "84 1.084\n",
      "85 1.085\n",
      "86 1.086\n",
      "87 1.087\n",
      "88 1.088\n",
      "89 1.089\n",
      "90 1.09\n",
      "91 1.091\n",
      "92 1.092\n",
      "93 1.093\n",
      "94 1.094\n",
      "95 1.095\n",
      "96 1.096\n",
      "97 1.097\n",
      "98 1.098\n",
      "99 1.099\n",
      "100 1.1\n",
      "101 1.101\n",
      "102 1.102\n",
      "103 1.103\n",
      "104 1.104\n",
      "105 1.105\n",
      "106 1.106\n",
      "107 1.107\n",
      "108 1.108\n",
      "109 1.109\n",
      "110 1.11\n",
      "111 1.111\n",
      "112 1.112\n",
      "113 1.113\n",
      "114 1.114\n",
      "115 1.115\n",
      "116 1.116\n",
      "117 1.117\n",
      "118 1.118\n",
      "119 1.119\n",
      "120 1.12\n",
      "121 1.121\n",
      "122 1.122\n",
      "123 1.123\n",
      "124 1.124\n",
      "125 1.125\n",
      "126 1.126\n",
      "127 1.127\n",
      "128 1.128\n",
      "129 1.129\n",
      "130 1.13\n",
      "131 1.131\n",
      "132 1.132\n",
      "133 1.133\n",
      "134 1.134\n",
      "135 1.135\n",
      "136 1.136\n",
      "137 1.137\n",
      "138 1.138\n",
      "139 1.139\n",
      "140 1.14\n",
      "141 1.141\n",
      "142 1.142\n",
      "143 1.143\n",
      "144 1.144\n",
      "145 1.145\n",
      "146 1.146\n",
      "147 1.147\n",
      "148 1.148\n",
      "149 1.149\n",
      "150 1.15\n",
      "151 1.151\n",
      "152 1.152\n",
      "153 1.153\n",
      "154 1.154\n",
      "155 1.155\n",
      "156 1.156\n",
      "157 1.157\n",
      "158 1.158\n",
      "159 1.159\n",
      "160 1.16\n",
      "161 1.161\n",
      "162 1.162\n",
      "163 1.163\n",
      "164 1.164\n",
      "165 1.165\n",
      "166 1.166\n",
      "167 1.167\n",
      "168 1.168\n",
      "169 1.169\n",
      "170 1.17\n",
      "171 1.171\n",
      "172 1.172\n",
      "173 1.173\n",
      "174 1.174\n",
      "175 1.175\n",
      "176 1.176\n",
      "177 1.177\n",
      "178 1.178\n",
      "179 1.179\n",
      "180 1.18\n",
      "181 1.181\n",
      "182 1.182\n",
      "183 1.183\n",
      "184 1.184\n",
      "185 1.185\n",
      "186 1.186\n",
      "187 1.187\n",
      "188 1.188\n",
      "189 1.189\n",
      "190 1.19\n",
      "191 1.191\n",
      "192 1.192\n",
      "193 1.193\n",
      "194 1.194\n",
      "195 1.195\n",
      "196 1.196\n",
      "197 1.197\n",
      "198 1.198\n",
      "199 1.199\n",
      "200 1.2\n",
      "201 1.201\n",
      "202 1.202\n",
      "203 1.203\n",
      "204 1.204\n",
      "205 1.205\n",
      "206 1.206\n",
      "207 1.207\n",
      "208 1.208\n",
      "209 1.209\n",
      "210 1.21\n",
      "211 1.211\n",
      "212 1.212\n",
      "213 1.213\n",
      "214 1.214\n",
      "215 1.215\n",
      "216 1.216\n",
      "217 1.217\n",
      "218 1.218\n",
      "219 1.219\n",
      "220 1.22\n",
      "221 1.221\n",
      "222 1.222\n",
      "223 1.223\n",
      "224 1.224\n",
      "225 1.225\n",
      "226 1.226\n",
      "227 1.227\n",
      "228 1.228\n",
      "229 1.229\n",
      "230 1.23\n",
      "231 1.231\n",
      "232 1.232\n",
      "233 1.233\n",
      "234 1.234\n",
      "235 1.235\n",
      "236 1.236\n",
      "237 1.237\n",
      "238 1.238\n",
      "239 1.239\n",
      "240 1.24\n",
      "241 1.241\n",
      "242 1.242\n",
      "243 1.243\n",
      "244 1.244\n",
      "245 1.245\n",
      "246 1.246\n",
      "247 1.247\n",
      "248 1.248\n",
      "249 1.249\n",
      "250 1.25\n",
      "251 1.251\n",
      "252 1.252\n",
      "253 1.253\n",
      "254 1.254\n",
      "255 1.255\n",
      "256 1.256\n",
      "257 1.257\n",
      "258 1.258\n",
      "259 1.259\n",
      "260 1.26\n",
      "261 1.261\n",
      "262 1.262\n",
      "263 1.263\n",
      "264 1.264\n",
      "265 1.265\n",
      "266 1.266\n",
      "267 1.267\n",
      "268 1.268\n",
      "269 1.269\n",
      "270 1.27\n",
      "271 1.271\n",
      "272 1.272\n",
      "273 1.273\n",
      "274 1.274\n",
      "275 1.275\n",
      "276 1.276\n",
      "277 1.277\n",
      "278 1.278\n",
      "279 1.279\n",
      "280 1.28\n",
      "281 1.281\n",
      "282 1.282\n",
      "283 1.283\n",
      "284 1.284\n",
      "285 1.285\n",
      "286 1.286\n",
      "287 1.287\n",
      "288 1.288\n",
      "289 1.289\n",
      "290 1.29\n",
      "291 1.291\n",
      "292 1.292\n",
      "293 1.293\n",
      "294 1.294\n",
      "295 1.295\n",
      "296 1.296\n",
      "297 1.297\n",
      "298 1.298\n",
      "299 1.299\n",
      "300 1.3\n",
      "301 1.301\n",
      "302 1.302\n",
      "303 1.303\n",
      "304 1.304\n",
      "305 1.305\n",
      "306 1.306\n",
      "307 1.307\n",
      "308 1.308\n",
      "309 1.309\n",
      "310 1.31\n",
      "311 1.311\n",
      "312 1.312\n",
      "313 1.313\n",
      "314 1.314\n",
      "315 1.315\n",
      "316 1.316\n",
      "317 1.317\n",
      "318 1.318\n",
      "319 1.319\n",
      "320 1.32\n",
      "321 1.321\n",
      "322 1.322\n",
      "323 1.323\n",
      "324 1.324\n",
      "325 1.325\n",
      "326 1.326\n",
      "327 1.327\n",
      "328 1.328\n",
      "329 1.329\n",
      "330 1.33\n",
      "331 1.331\n",
      "332 1.332\n",
      "333 1.333\n",
      "334 1.334\n",
      "335 1.335\n",
      "336 1.336\n",
      "337 1.337\n",
      "338 1.338\n",
      "339 1.339\n",
      "340 1.34\n",
      "341 1.341\n",
      "342 1.342\n",
      "343 1.343\n",
      "344 1.344\n",
      "345 1.345\n",
      "346 1.346\n",
      "347 1.347\n",
      "348 1.348\n",
      "349 1.349\n",
      "350 1.35\n",
      "351 1.351\n",
      "352 1.352\n",
      "353 1.353\n",
      "354 1.354\n",
      "355 1.355\n",
      "356 1.356\n",
      "357 1.357\n",
      "358 1.358\n",
      "359 1.359\n",
      "360 1.36\n",
      "361 1.361\n",
      "362 1.362\n",
      "363 1.363\n",
      "364 1.364\n",
      "365 1.365\n",
      "366 1.366\n",
      "367 1.367\n",
      "368 1.368\n",
      "369 1.369\n",
      "370 1.37\n",
      "371 1.371\n",
      "372 1.372\n",
      "373 1.373\n",
      "374 1.374\n",
      "375 1.375\n",
      "376 1.376\n",
      "377 1.377\n",
      "378 1.378\n",
      "379 1.379\n",
      "380 1.38\n",
      "381 1.381\n",
      "382 1.382\n",
      "383 1.383\n",
      "384 1.384\n",
      "385 1.385\n",
      "386 1.386\n",
      "387 1.387\n",
      "388 1.388\n",
      "389 1.389\n",
      "390 1.39\n",
      "391 1.391\n",
      "392 1.392\n",
      "393 1.393\n",
      "394 1.394\n",
      "395 1.395\n",
      "396 1.396\n",
      "397 1.397\n",
      "398 1.398\n",
      "399 1.399\n",
      "400 1.4\n",
      "401 1.401\n",
      "402 1.402\n",
      "403 1.403\n",
      "404 1.404\n",
      "405 1.405\n",
      "406 1.406\n",
      "407 1.407\n",
      "408 1.408\n",
      "409 1.409\n",
      "410 1.41\n",
      "411 1.411\n",
      "412 1.412\n",
      "413 1.413\n",
      "414 1.414\n",
      "415 1.415\n",
      "416 1.416\n",
      "417 1.417\n",
      "418 1.418\n",
      "419 1.419\n",
      "420 1.42\n",
      "421 1.421\n",
      "422 1.422\n",
      "423 1.423\n",
      "424 1.424\n",
      "425 1.425\n",
      "426 1.426\n",
      "427 1.427\n",
      "428 1.428\n",
      "429 1.429\n",
      "430 1.43\n",
      "431 1.431\n",
      "432 1.432\n",
      "433 1.433\n",
      "434 1.434\n",
      "435 1.435\n",
      "436 1.436\n",
      "437 1.437\n",
      "438 1.438\n",
      "439 1.439\n",
      "440 1.44\n",
      "441 1.441\n",
      "442 1.442\n",
      "443 1.443\n",
      "444 1.444\n",
      "445 1.445\n",
      "446 1.446\n",
      "447 1.447\n",
      "448 1.448\n",
      "449 1.449\n",
      "450 1.45\n",
      "451 1.451\n",
      "452 1.452\n",
      "453 1.453\n",
      "454 1.454\n",
      "455 1.455\n",
      "456 1.456\n",
      "457 1.457\n",
      "458 1.458\n",
      "459 1.459\n",
      "460 1.46\n",
      "461 1.461\n",
      "462 1.462\n",
      "463 1.463\n",
      "464 1.464\n",
      "465 1.465\n",
      "466 1.466\n",
      "467 1.467\n",
      "468 1.468\n",
      "469 1.469\n",
      "470 1.47\n",
      "471 1.471\n",
      "472 1.472\n",
      "473 1.473\n",
      "474 1.474\n",
      "475 1.475\n",
      "476 1.476\n",
      "477 1.477\n",
      "478 1.478\n",
      "479 1.479\n",
      "480 1.48\n",
      "481 1.481\n",
      "482 1.482\n",
      "483 1.483\n",
      "484 1.484\n",
      "485 1.485\n",
      "486 1.486\n",
      "487 1.487\n",
      "488 1.488\n",
      "489 1.489\n",
      "490 1.49\n",
      "491 1.491\n",
      "492 1.492\n",
      "493 1.493\n",
      "494 1.494\n",
      "495 1.495\n",
      "496 1.496\n",
      "497 1.497\n",
      "498 1.498\n",
      "499 1.499\n",
      "500 1.5\n",
      "501 1.501\n",
      "502 1.502\n",
      "503 1.503\n",
      "504 1.504\n",
      "505 1.505\n",
      "506 1.506\n",
      "507 1.507\n",
      "508 1.508\n",
      "509 1.509\n",
      "510 1.51\n",
      "511 1.511\n",
      "512 1.512\n",
      "513 1.513\n",
      "514 1.514\n",
      "515 1.515\n",
      "516 1.516\n",
      "517 1.517\n",
      "518 1.518\n",
      "519 1.519\n",
      "520 1.52\n",
      "521 1.521\n",
      "522 1.522\n",
      "523 1.523\n",
      "524 1.524\n",
      "525 1.525\n",
      "526 1.526\n",
      "527 1.527\n",
      "528 1.528\n",
      "529 1.529\n",
      "530 1.53\n",
      "531 1.531\n",
      "532 1.532\n",
      "533 1.533\n",
      "534 1.534\n",
      "535 1.535\n",
      "536 1.536\n",
      "537 1.537\n",
      "538 1.538\n",
      "539 1.539\n",
      "540 1.54\n",
      "541 1.541\n",
      "542 1.542\n",
      "543 1.543\n",
      "544 1.544\n",
      "545 1.545\n",
      "546 1.546\n",
      "547 1.547\n",
      "548 1.548\n",
      "549 1.549\n",
      "550 1.55\n",
      "551 1.551\n",
      "552 1.552\n",
      "553 1.553\n",
      "554 1.554\n",
      "555 1.555\n",
      "556 1.556\n",
      "557 1.557\n",
      "558 1.558\n",
      "559 1.559\n",
      "560 1.56\n",
      "561 1.561\n",
      "562 1.562\n",
      "563 1.563\n",
      "564 1.564\n",
      "565 1.565\n",
      "566 1.566\n",
      "567 1.567\n",
      "568 1.568\n",
      "569 1.569\n",
      "570 1.57\n",
      "571 1.571\n",
      "572 1.572\n",
      "573 1.573\n",
      "574 1.574\n",
      "575 1.575\n",
      "576 1.576\n",
      "577 1.577\n",
      "578 1.578\n",
      "579 1.579\n",
      "580 1.58\n",
      "581 1.581\n",
      "582 1.582\n",
      "583 1.583\n",
      "584 1.584\n",
      "585 1.585\n",
      "586 1.586\n",
      "587 1.587\n",
      "588 1.588\n",
      "589 1.589\n",
      "590 1.59\n",
      "591 1.591\n",
      "592 1.592\n",
      "593 1.593\n",
      "594 1.594\n",
      "595 1.595\n",
      "596 1.596\n",
      "597 1.597\n",
      "598 1.598\n",
      "599 1.599\n",
      "600 1.6\n",
      "601 1.601\n",
      "602 1.602\n",
      "603 1.603\n",
      "604 1.604\n",
      "605 1.605\n",
      "606 1.606\n",
      "607 1.607\n",
      "608 1.608\n",
      "609 1.609\n",
      "610 1.61\n",
      "611 1.611\n",
      "612 1.612\n",
      "613 1.613\n",
      "614 1.614\n",
      "615 1.615\n",
      "616 1.616\n",
      "617 1.617\n",
      "618 1.618\n",
      "619 1.619\n",
      "620 1.62\n",
      "621 1.621\n",
      "622 1.622\n",
      "623 1.623\n",
      "624 1.624\n",
      "625 1.625\n",
      "626 1.626\n",
      "627 1.627\n",
      "628 1.628\n",
      "629 1.629\n",
      "630 1.63\n",
      "631 1.631\n",
      "632 1.632\n",
      "633 1.633\n",
      "634 1.634\n",
      "635 1.635\n",
      "636 1.636\n",
      "637 1.637\n",
      "638 1.638\n",
      "639 1.639\n",
      "640 1.64\n",
      "641 1.641\n",
      "642 1.642\n",
      "643 1.643\n",
      "644 1.644\n",
      "645 1.645\n",
      "646 1.646\n",
      "647 1.647\n",
      "648 1.648\n",
      "649 1.649\n",
      "650 1.65\n",
      "651 1.651\n",
      "652 1.652\n",
      "653 1.653\n",
      "654 1.654\n",
      "655 1.655\n",
      "656 1.656\n",
      "657 1.657\n",
      "658 1.658\n",
      "659 1.659\n",
      "660 1.66\n",
      "661 1.661\n",
      "662 1.662\n",
      "663 1.663\n",
      "664 1.664\n",
      "665 1.665\n",
      "666 1.666\n",
      "667 1.667\n",
      "668 1.668\n",
      "669 1.669\n",
      "670 1.67\n",
      "671 1.671\n",
      "672 1.672\n",
      "673 1.673\n",
      "674 1.674\n",
      "675 1.675\n",
      "676 1.676\n",
      "677 1.677\n",
      "678 1.678\n",
      "679 1.679\n",
      "680 1.68\n",
      "681 1.681\n",
      "682 1.682\n",
      "683 1.683\n",
      "684 1.684\n",
      "685 1.685\n",
      "686 1.686\n",
      "687 1.687\n",
      "688 1.688\n",
      "689 1.689\n",
      "690 1.69\n",
      "691 1.691\n",
      "692 1.692\n",
      "693 1.693\n",
      "694 1.694\n",
      "695 1.695\n",
      "696 1.696\n",
      "697 1.697\n",
      "698 1.698\n",
      "699 1.699\n",
      "700 1.7\n",
      "701 1.701\n",
      "702 1.702\n",
      "703 1.703\n",
      "704 1.704\n",
      "705 1.705\n",
      "706 1.706\n",
      "707 1.707\n",
      "708 1.708\n",
      "709 1.709\n",
      "710 1.71\n",
      "711 1.711\n",
      "712 1.712\n",
      "713 1.713\n",
      "714 1.714\n",
      "715 1.715\n",
      "716 1.716\n",
      "717 1.717\n",
      "718 1.718\n",
      "719 1.719\n",
      "720 1.72\n",
      "721 1.721\n",
      "722 1.722\n",
      "723 1.723\n",
      "724 1.724\n",
      "725 1.725\n",
      "726 1.726\n",
      "727 1.727\n",
      "728 1.728\n",
      "729 1.729\n",
      "730 1.73\n",
      "731 1.731\n",
      "732 1.732\n",
      "733 1.733\n",
      "734 1.734\n",
      "735 1.735\n",
      "736 1.736\n",
      "737 1.737\n",
      "738 1.738\n",
      "739 1.739\n",
      "740 1.74\n",
      "741 1.741\n",
      "742 1.742\n",
      "743 1.743\n",
      "744 1.744\n",
      "745 1.745\n",
      "746 1.746\n",
      "747 1.747\n",
      "748 1.748\n",
      "749 1.749\n",
      "750 1.75\n",
      "751 1.751\n",
      "752 1.752\n",
      "753 1.753\n",
      "754 1.754\n",
      "755 1.755\n",
      "756 1.756\n",
      "757 1.757\n",
      "758 1.758\n",
      "759 1.759\n",
      "760 1.76\n",
      "761 1.761\n",
      "762 1.762\n",
      "763 1.763\n",
      "764 1.764\n",
      "765 1.765\n",
      "766 1.766\n",
      "767 1.767\n",
      "768 1.768\n",
      "769 1.769\n",
      "770 1.77\n",
      "771 1.771\n",
      "772 1.772\n",
      "773 1.773\n",
      "774 1.774\n",
      "775 1.775\n",
      "776 1.776\n",
      "777 1.777\n",
      "778 1.778\n",
      "779 1.779\n",
      "780 1.78\n",
      "781 1.781\n",
      "782 1.782\n",
      "783 1.783\n",
      "784 1.784\n",
      "785 1.785\n",
      "786 1.786\n",
      "787 1.787\n",
      "788 1.788\n",
      "789 1.789\n",
      "790 1.79\n",
      "791 1.791\n",
      "792 1.792\n",
      "793 1.793\n",
      "794 1.794\n",
      "795 1.795\n",
      "796 1.796\n",
      "797 1.797\n",
      "798 1.798\n",
      "799 1.799\n",
      "800 1.8\n",
      "801 1.801\n",
      "802 1.802\n",
      "803 1.803\n",
      "804 1.804\n",
      "805 1.805\n",
      "806 1.806\n",
      "807 1.807\n",
      "808 1.808\n",
      "809 1.809\n",
      "810 1.81\n",
      "811 1.811\n",
      "812 1.812\n",
      "813 1.813\n",
      "814 1.814\n",
      "815 1.815\n",
      "816 1.816\n",
      "817 1.817\n",
      "818 1.818\n",
      "819 1.819\n",
      "820 1.82\n",
      "821 1.821\n",
      "822 1.822\n",
      "823 1.823\n",
      "824 1.824\n",
      "825 1.825\n",
      "826 1.826\n",
      "827 1.827\n",
      "828 1.828\n",
      "829 1.829\n",
      "830 1.83\n",
      "831 1.831\n",
      "832 1.832\n",
      "833 1.833\n",
      "834 1.834\n",
      "835 1.835\n",
      "836 1.836\n",
      "837 1.837\n",
      "838 1.838\n",
      "839 1.839\n",
      "840 1.84\n",
      "841 1.841\n",
      "842 1.842\n",
      "843 1.843\n",
      "844 1.844\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "845 1.845\n",
      "846 1.846\n",
      "847 1.847\n",
      "848 1.848\n",
      "849 1.849\n",
      "850 1.85\n",
      "851 1.851\n",
      "852 1.852\n",
      "853 1.853\n",
      "854 1.854\n",
      "855 1.855\n",
      "856 1.856\n",
      "857 1.857\n",
      "858 1.858\n",
      "859 1.859\n",
      "860 1.86\n",
      "861 1.861\n",
      "862 1.862\n",
      "863 1.863\n",
      "864 1.864\n",
      "865 1.865\n",
      "866 1.866\n",
      "867 1.867\n",
      "868 1.868\n",
      "869 1.869\n",
      "870 1.87\n",
      "871 1.871\n",
      "872 1.872\n",
      "873 1.873\n",
      "874 1.874\n",
      "875 1.875\n",
      "876 1.876\n",
      "877 1.877\n",
      "878 1.878\n",
      "879 1.879\n",
      "880 1.88\n",
      "881 1.881\n",
      "882 1.882\n",
      "883 1.883\n",
      "884 1.884\n",
      "885 1.885\n",
      "886 1.886\n",
      "887 1.887\n",
      "888 1.888\n",
      "889 1.889\n",
      "890 1.89\n",
      "891 1.891\n",
      "892 1.892\n",
      "893 1.893\n",
      "894 1.894\n",
      "895 1.895\n",
      "896 1.896\n",
      "897 1.897\n",
      "898 1.898\n",
      "899 1.899\n",
      "900 1.9\n",
      "901 1.901\n",
      "902 1.902\n",
      "903 1.903\n",
      "904 1.904\n",
      "905 1.905\n",
      "906 1.906\n",
      "907 1.907\n",
      "908 1.908\n",
      "909 1.909\n",
      "910 1.91\n",
      "911 1.911\n",
      "912 1.912\n",
      "913 1.913\n",
      "914 1.914\n",
      "915 1.915\n",
      "916 1.916\n",
      "917 1.917\n",
      "918 1.918\n",
      "919 1.919\n",
      "920 1.92\n",
      "921 1.921\n",
      "922 1.922\n",
      "923 1.923\n",
      "924 1.924\n",
      "925 1.925\n",
      "926 1.926\n",
      "927 1.927\n",
      "928 1.928\n",
      "929 1.929\n",
      "930 1.93\n",
      "931 1.931\n",
      "932 1.932\n",
      "933 1.933\n",
      "934 1.934\n",
      "935 1.935\n",
      "936 1.936\n",
      "937 1.937\n",
      "938 1.938\n",
      "939 1.939\n",
      "940 1.94\n",
      "941 1.941\n",
      "942 1.942\n",
      "943 1.943\n",
      "944 1.944\n",
      "945 1.945\n",
      "946 1.946\n",
      "947 1.947\n",
      "948 1.948\n",
      "949 1.949\n",
      "950 1.95\n",
      "951 1.951\n",
      "952 1.952\n",
      "953 1.953\n",
      "954 1.954\n",
      "955 1.955\n",
      "956 1.956\n",
      "957 1.957\n",
      "958 1.958\n",
      "959 1.959\n",
      "960 1.96\n",
      "961 1.961\n",
      "962 1.962\n",
      "963 1.963\n",
      "964 1.964\n",
      "965 1.965\n",
      "966 1.966\n",
      "967 1.967\n",
      "968 1.968\n",
      "969 1.969\n",
      "970 1.97\n",
      "971 1.971\n",
      "972 1.972\n",
      "973 1.973\n",
      "974 1.974\n",
      "975 1.975\n",
      "976 1.976\n",
      "977 1.977\n",
      "978 1.978\n",
      "979 1.979\n",
      "980 1.98\n",
      "981 1.981\n",
      "982 1.982\n",
      "983 1.983\n",
      "984 1.984\n",
      "985 1.985\n",
      "986 1.986\n",
      "987 1.987\n",
      "988 1.988\n",
      "989 1.989\n",
      "990 1.99\n",
      "991 1.991\n",
      "992 1.992\n",
      "993 1.993\n",
      "994 1.994\n",
      "995 1.995\n",
      "996 1.996\n",
      "997 1.997\n",
      "998 1.998\n",
      "999 1.999\n"
     ]
    }
   ],
   "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 25\"\n",
    "idx, = np.where((radii > 2) & (radii < 10))\n",
    "xv = radii[idx]\n",
    "yv = encircled_flux[idx]/np.max(encircled_flux)\n",
    "resid = np.zeros((len(rfactor), len(ffactor)))\n",
    "for i, rf in enumerate(rfactor):\n",
    "    print(i, rf)\n",
    "    tck = interpolate.splrep(radiuseff*rf, valeff, s=0)\n",
    "    yfit = interpolate.splev(xv, tck, der=0)\n",
    "    for j, ff in enumerate(ffactor):\n",
    "        resid[i, j] = np.sum((yv-yfit*ff)**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11e916b70>"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWIAAAFMCAYAAADx+rY8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121816c88>"
      ]
     },
     "metadata": {},
     "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": 212,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.000, ff = 1.000, residual = 0.024\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": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12041a278>"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFXCAYAAABOYlxEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fa5e630>"
      ]
     },
     "metadata": {},
     "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, 200])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.239737"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The two curve overlap\n",
    "psfok = psf/np.max(encircled_flux)/ffactor[fmin]\n",
    "np.sum(psfok)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psfok is the PSF that a source of flux 1 Jy has in our data, and is to be used for source extraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 100 micron source, e.g. `EN1-PACSxID24-ELAIS-N1-HerMES-1-29844`. We can see from `WP4-ELAIS-N1-HerMES-PACSxID24-v1.fits.gz` that it has a flux of 55 mJy. Maximum value in our normalised PSF gives a peak below. Since PSF is three times resolution of map, it could also be off centre. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: UnitsWarning: 'Degrees' did not parse as fits unit: At col 0, Unit 'Degrees' not supported by the FITS standard.  [astropy.units.core]\n"
     ]
    }
   ],
   "source": [
    "PACScat=Table.read('../data/ELAIS-N1/WP4-ELAIS-N1-HerMES-PACSxID24-v1.fits.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Table length=1&gt;\n",
       "<table id=\"table4877980504\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>XID</th><th>RA</th><th>Dec</th><th>F_PACS_100__A4</th><th>F_PACS_100__A5</th><th>F_PACS_100__A6</th><th>F_PACS_100__A7</th><th>F_PACS_100__A8</th><th>F_PACS_100__A10</th><th>F_PACS_100</th><th>Ferr_PACS_100__A4</th><th>Ferr_PACS_100__A5</th><th>Ferr_PACS_100__A6</th><th>Ferr_PACS_100__A7</th><th>Ferr_PACS_100__A8</th><th>Ferr_PACS_100__A10</th><th>Ferr_PACS_100</th><th>F_PACS_100__SKY</th><th>F_PACS_160__A4</th><th>F_PACS_160__A5</th><th>F_PACS_160__A6</th><th>F_PACS_160__A7</th><th>F_PACS_160__A8</th><th>F_PACS_160__A10</th><th>F_PACS_160</th><th>Ferr_PACS_160__A4</th><th>Ferr_PACS_160__A5</th><th>Ferr_PACS_160__A6</th><th>Ferr_PACS_160__A7</th><th>Ferr_PACS_160__A8</th><th>Ferr_PACS_160__A10</th><th>Ferr_PACS_160</th><th>F_PACS_160__SKY</th><th>HELP_ID</th></tr></thead>\n",
       "<thead><tr><th></th><th>Degrees</th><th>Degrees</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th></th></tr></thead>\n",
       "<thead><tr><th>int32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>str37</th></tr></thead>\n",
       "<tr><td>1425</td><td>243.636</td><td>54.4345</td><td>57.2211</td><td>53.53</td><td>53.1979</td><td>53.545</td><td>55.8204</td><td>49.5568</td><td>55.3478</td><td>11.1253</td><td>10.4247</td><td>10.5557</td><td>10.9084</td><td>11.5531</td><td>13.1853</td><td>8.18286</td><td>0.0</td><td>105.169</td><td>107.135</td><td>112.444</td><td>119.527</td><td>122.018</td><td>123.281</td><td>115.052</td><td>19.2912</td><td>16.3355</td><td>15.3392</td><td>14.6758</td><td>14.3281</td><td>14.8458</td><td>11.5986</td><td>0.0</td><td>EN1-PACSxID24-ELAIS-N1-HerMES-1-29844</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=1>\n",
       " XID     RA     Dec   ... F_PACS_160__SKY                HELP_ID               \n",
       "      Degrees Degrees ...    mJy / pix                                         \n",
       "int32 float32 float32 ...     float32                     str37                \n",
       "----- ------- ------- ... --------------- -------------------------------------\n",
       " 1425 243.636 54.4345 ...             0.0 EN1-PACSxID24-ELAIS-N1-HerMES-1-29844"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='EN1-PACSxID24-ELAIS-N1-HerMES-1-29844']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 0.0027 Jy/pixel, off pixel Max PSF = 0.0026 Jy/pixel\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(\"Max PSF = {:.4f} Jy/pixel, off pixel Max PSF = {:.4f} Jy/pixel\".format(psfok[cpix-1,cpix-1]*0.055,psfok[cpix-2,cpix-2]*0.055))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n",
      "/Users/pdh21/anaconda3/envs/new/lib/python3.6/site-packages/aplpy/normalize.py:115: RuntimeWarning: invalid value encountered in less\n",
      "  negative = result < 0.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl8AAAImCAYAAABtku8UAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nWET4AgAAsOj/A9jsJFvA2SDWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1217d1ef0>"
      ]
     },
     "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('../../dmu26/data/ELAIS_N1/PACS/ELAIS-N1-100um-img_wgls.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='EN1-PACSxID24-ELAIS-N1-HerMES-1-29844']['RA'],PACScat[PACScat['HELP_ID']=='EN1-PACSxID24-ELAIS-N1-HerMES-1-29844']['Dec'], radius=0.002)\n",
    "fig.show_colorscale(vmin=-0.001,vmax=0.003,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": "markdown",
   "metadata": {},
   "source": [
    "## Create PSF fits file¶\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: VerifyWarning: Verification reported errors: [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning: HDU 1: [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'NAXIS1' card at the wrong place (card 4).  Fixed by moving it to the right place (card 3). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'NAXIS2' card at the wrong place (card 5).  Fixed by moving it to the right place (card 4). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'PCOUNT' card at the wrong place (card 31).  Fixed by moving it to the right place (card 5). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'GCOUNT' card at the wrong place (card 32).  Fixed by moving it to the right place (card 6). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning: HDU 2: [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'BITPIX' card at the wrong place (card 2).  Fixed by moving it to the right place (card 1). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning:     'NAXIS' card at the wrong place (card 3).  Fixed by moving it to the right place (card 2). [astropy.io.fits.verify]\n",
      "WARNING: VerifyWarning: Note: astropy.io.fits uses zero-based indexing.\n",
      " [astropy.io.fits.verify]\n"
     ]
    }
   ],
   "source": [
    "stackhd[1].data=psfok\n",
    "stackhd.writeto('dmu18_PACS_100_PSF_ELAIS-N1_20170720.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeQAAAFJCAYAAABKLF7JAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f4c85c0>"
      ]
     },
     "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": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04898978"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}