{
 "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": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log10(psf))\n",
    "print(r'$\\int\\int$ psf dx dy = {}'.format(np.sum(psf)*resol**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd0841abf98>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Without obscuration')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now suppose that we observe a point source, and our image reconstruction has a ...This will shows a a blurring of the image, with a gaussian of 10\" FWHM. Let's generate this blurring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fwhm = 10.\n",
    "sigma = fwhm / 2. / np.sqrt(2. * np.log(fwhm))\n",
    "sigmasq = sigma**2\n",
    "kernel_blur = 1./ 2./ np.pi / sigmasq * np.exp(-(r**2/2./sigmasq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999996"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check our kernel is properly normalized\n",
    "np.sum(kernel_blur*resol**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# apply the blur\n",
    "psfblur = signal.convolve(psf, kernel_blur, mode='same')*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd08292c908>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(y[ycen-500:ycen+500], psf[ycen-500:ycen+500, xcen], label='Original')\n",
    "plt.plot(y[ycen-500:ycen+500], psfblur[ycen-500:ycen+500, xcen], label='With blurring')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the effect of blurring, the, observed PSF is wider, and we have lost some flux in the central core. Suppose now that we observed this psf with sources of unknown fluxes, so that we re unsure of its scaling, and that a background remain in our observation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psfobs = psfblur * 2. + 1e-4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The question is now how to recover the PSF that serve for our observation. For this, we will use the PSFs curve of growth. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 212.10000000000002\n",
      "10.0 212.10000000000002\n",
      "20.0 212.10000000000002\n",
      "30.0 212.10000000000002\n",
      "40.0 212.10000000000002\n",
      "50.0 212.10000000000002\n",
      "60.0 212.10000000000002\n",
      "70.0 212.10000000000002\n",
      "80.0 212.10000000000002\n",
      "90.0 212.10000000000002\n",
      "100.0 212.10000000000002\n",
      "110.0 212.10000000000002\n",
      "120.0 212.10000000000002\n",
      "130.0 212.10000000000002\n",
      "140.0 212.10000000000002\n",
      "150.0 212.10000000000002\n",
      "160.0 212.10000000000002\n",
      "170.0 212.10000000000002\n",
      "180.0 212.10000000000002\n",
      "190.0 212.10000000000002\n",
      "200.0 212.10000000000002\n",
      "210.0 212.10000000000002\n"
     ]
    }
   ],
   "source": [
    "radii = np.arange(0, np.max(r), resol)\n",
    "growth_psf = np.zeros(radii.shape)\n",
    "growth_psfobs = np.zeros(radii.shape)\n",
    "nbpix_psfobs = np.zeros(radii.shape)\n",
    "for i, radius in enumerate(radii):\n",
    "    if ((i % 100) == 0):\n",
    "        print(radius, np.max(radii))\n",
    "    if i == 0:\n",
    "        idj, idi = np.where(r <= radius)\n",
    "        growth_psf[i] = np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] =len(idi)\n",
    "    else:\n",
    "        idj, idi = np.where((r > radii[i-1]) & (r <= radius))\n",
    "        growth_psf[i] = growth_psf[i-1]+np.sum(psf[idj, idi])*resol**2\n",
    "        growth_psfobs[i] = growth_psfobs[i-1]+np.sum(psfobs[idj, idi])*resol**2\n",
    "        nbpix_psfobs[i] = nbpix_psfobs[i-1]+len(idi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd0828a2e10>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, growth_psf, label='PSF')\n",
    "plt.plot(radii, growth_psfobs, label='Observed PSF')\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This strongly rising shape of the observed PSF is a sure sign of an non zero background. Let's determine it. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix_psfobs, growth_psfobs)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When plotted as a function of the intergated area, there is a clear linear relation, that we will fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "idx, = np.where(radii > 50)\n",
    "p = np.polyfit(nbpix_psfobs[idx], growth_psfobs[idx], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Correct PSF and curve of growth\n",
    "psfcor = psfobs-bkg\n",
    "growth_psfcor = growth_psfobs - bkg*nbpix_psfobs*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd0827ea278>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, growth_psf, label='PSF')\n",
    "plt.plot(radii, growth_psfcor, label='Observed PSF')\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='direct_ratio'></a> Let's have a look at the ratio of the two:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Ratio of encircled flux')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:], growth_psfcor[1:]/growth_psf[1:])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Ratio of encircled flux')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Due to the different resolution, the ratio is not constant. Let's note the calibration $C(r)$. Let us assume that our observed PSF encirled energy is of the form:\n",
    "\n",
    "$E(r) = \\alpha C(r \\times \\beta)$\n",
    "\n",
    "Where $\\beta$ is the fattening of the PSF. If we differentiate as a function of $r$:\n",
    "\n",
    "$E'(r) = \\alpha \\beta C'(r \\times \\beta)$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# compute the derivatives\n",
    "deriv_growth_psf = (growth_psf[2:]-growth_psf[0:-2])/(radii[2:]-radii[0:-2])\n",
    "deriv_growth_psfcor  = (growth_psfcor[2:]-growth_psfcor[0:-2])/(radii[2:]-radii[0:-2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 60)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KFtkFgCo2RzonSqkJJraDQ3cb9HbbX+A3/yzSuRmZyefDqZ12ynGllBojsR0cOhvtNiUPXO7I5mWkChfZANd4LNI5UUpNIAEFBxFZIyIHRKRMRO7z8/4qEdkqIh4RuWnAe3eKyCHndafP+fNFZJeT5v+KhKHOp7PJbpMyQ570mMkutdsGDQ5KqbEzbHAQETfwCHAtsAC4VUQWDLjsOHAX8MSAe3OArwAXAhcAXxGRbOftHwD3ALOd15oRP8VQYio4HIloNpRSE0sgJYcLgDJjTLkxpht4Cljre4Ex5qgxZifgHXDve4CXjDH1xpgG4CVgjYgUAxnGmI3GGAP8Anj/aB9mkA6nWik5K+RJj5m0QohLgnoNDkqpsRNIcCgBTvgcVzjnAjHUvSXO/rBpisg9IrJZRDbX1NQE+LGOWCg5iMCUC2D7r6GtLtK5UUpNEIEEB39tAYHOBjfUvQGnaYx51BizwhizIj8/yBHOfQ3SSVFccgC45mv2Wfati3ROlFITRCDBoQKY4nM8GagMMP2h7q1w9keSZuD6Sg6JGSFPekwVL7FrURx8MdI5UUpNEIEEh03AbBGZLiIJwC1AoD9hNwDvFpFspyH63cAGY0wV0CIiFzm9lO4Afj+C/J9bZxMkpIM7LuRJjykRO0trw9FI50QpNUEMGxyMMR7gXuwX/T7gaWPMHhF5UERuABCRlSJSAdwM/EhE9jj31gNfwwaYTcCDzjmAzwA/AcqAw8CfQvpkYBukQ9AYbZw1FWpaunjk1TIOnW45815LZw+e3oHt8GGQXgwtp8L/OUopBQT0k9oYsx5YP+DcAz77mzi7msj3useAx/yc3wwsCiazQetsCklj9Kd+uYW6tm5WzyvgWxsOsONEI4/esYJer2Hxf/yZWy+YyjduXByCDJ9DepFtd+jpiI51sJVSUS3GR0iPLjgYY2ju7OHPe0+z5VgDh6tbAfjz3tPc/bNN/OszOwB48p3jVDZ2cOl/vcLeyuaQZH2Q9GK71dKDUmoMxHhwaBxxT6X/WLeHyx56lU1H6s+c++22k2f2/7K/mud9jl89UM3Jxg7eORKm7qbpRXarwUEpNQZiPDiMrORQ3dLJz/5+lJONHWw51nDWe/npiZRkDa7W2XjYBoWjde0jy+twMp1aO51jSSk1BmI3OOx4CppOjCg4bD3WeGZ/89EG4lzCE5+8EIB5Rem8ed9qjv7X9fzvrcvOXPfHnVUAHKltG2XGh5AzA1zxULM/POkrpZSPKO/jeQ7Pf8puJfj4t/V4f2lh87F6JmencMnMPB75yHKWT+uvprphySQun5XHsq+9BEC8Wzhc0zq6fA/FHQ+5s6B6X3jSV0opH7FbcujTHnwbwJtltcwvtgPnvAYmZ9tqpOvPK6Y48+wqpezUBL7yvgWU5qbw0YumUdHQwapvvsrTm08MSnfUis+zA+FOvBP6tJVSykdsBoeeDrt1J8BVXw74NmMM1S2d7Kls5vrFRWfO37t61jnv+9il03nti1fy3vMmAXC8vp0vPbsz+HwP55oHIS4Ztv0y9GkrpZSP2KxW6htJ/P4f9DfkDuO3Wyv4wtM7uGfVDADWLCqiNC+VqTkpnDc5sB5Pi0vCPMFfehHMvhrKXgnv5yilJrzYLDm0OutGpxUGfMv//PkgAI+/eYRFJRnMKkjnvedNCjgwACTEuXhw7cIzx5/65WbqWrsCvj8gUy6E5gporx/+WqWUGqHYDA6dwa/jcLLRVkX19BrmF418or47Li7lJ3esAGDDntPc/9tdI07Lr7w5dlt7KLTpKqWUj9gMDh3BTdXd0d171vHMgrRRffz8Sf3B5Y1DNbR2eUaV3llynfaPOg0OSqnwic3gcKbkkH3u6xyHqlvOOp6Rlzqqj5+UmdSflR4vr+yvHlV6Z8maZhvaaw+GLk2llBogNoNDRwO44iAhsC/5/VVnB4cLZ+SO6uNFhIc+uJjH71oJwD89uY1nt1QMc1eA3HF2QFxtWWjSU0opP2Kzt1KHM6eS+FtwbrDdlU2kJLh55CPLyUiOIzM5ftRZ+PDKqWcd/+szO7hxWQkuV2B5OqfcWVBzYPTpKKXUEGKz5NAZ2DoOx+raKL3vBX6x8RjnTc7kynkFnD8tJ6RZ+dnHVp6Zi+lUc2doEs2bAw1HoLcnNOkppdQAsRkcOgKbjfWNgzVn9pdOCax9IlhXzC3gv29eAhC6qTUKF4LXAy99BbxjsNCQUmrCib3g0FoDJ96G/HnDXnqioePM/oJJ4Vtnema+bft45NUQtRPMuMJu33oEjv0tNGkqpZSP2AsOZS9DTztceM+wl+6pbDqzP3uU3VfPJT89EYC3yuspD0XpITUPpq+y+9r2oJQKg4CCg4isEZEDIlImIvf5eT9RRH7jvP+2iJQ6528Tke0+L6+ILHXee81Js++9gpA8UX25nYk1f/6wl5ZV939RTx9l99VzEREeu8sOjFv9P6+HJkDcsQ4SMzQ4KKXCYtjgICJu4BHgWmABcKuILBhw2d1AgzFmFvAw8BCAMebXxpilxpilwO3AUWPMdp/7but73xgTmsEADUfsfEpxCee8rKWzh9PNXZRkJXPtoiKS4t0h+fihnD+1v6H7H369dfQJikD+XF3fQSkVFoGUHC4Ayowx5caYbuApYO2Aa9YCP3f2nwWuEhnUj/RW4MnRZDYg9Ucge/qwlx2usYvyfOV9C/jBR88Pd67ITOnvHlvb2h2aRLOn68pwSqmwCCQ4lAC+ixNUOOf8XmOM8QBNwMCRZB9mcHB43KlS+rKfYDIyjcche9qwl/1l32lcAkumjGyN6ZH40pq5TM1Joba1i86e3uFvGE7WVGg6Cb0hnJ5DKaUILDj4+9I2wVwjIhcC7caY3T7v32aMWQxc7rxu9/vhIveIyGYR2VxTU+Pvkn69HmirgfRJ57xs09F6fvnWMS6dlUdhRtI5rw2lf7hiFp+7ajYAlY0dw1wdgOxpYHqh+eTo01JKKR+BBIcKYIrP8WSgcqhrRCQOyAR855S+hQGlBmPMSWfbAjyBrb4axBjzqDFmhTFmRX5+/rlz2lYNGEgfeqrubo+Xm3+4kcb2HlaEeMBbIEqcVeVCMt9SljMKu/H46NNSSikfgQSHTcBsEZkuIgnYL/p1A65ZB9zp7N8EvGKMMQAi4gJuxrZV4JyLE5E8Zz8eeC+wm9FqqbLb9OIhLymv7e8pFM6xDUOZU5hOcrybr7+wjyffGeWXenap3dYfHnW+lFLK17DBwWlDuBfYAOwDnjbG7BGRB0XkBueynwK5IlIGfAHw7e66CqgwxpT7nEsENojITmA7cBL48aifpuW03Z5jkR/fSfYiERxyUhN44Z8uA+D+3+4a3WJAmVMhLknXdlBKhVxAE+8ZY9YD6wece8BnvxNbOvB372vARQPOtQGh7yJ0puRQNOQlf9xZRVK8i/X/dPmZOY/G2oz8NL79oSV84ekd7KlsZtWcYarLhuJyQe5sHeuglAq52Boh3XQCXPFDlhwOnm7h5X2n+cfVs5mRH74R0YG4ar7N466TTcNcOYz8uXB6N5iBfQSUUmrkYis41B+xjbQu/wPa/rTrFCJw84rJY5yxwTKT45mWm3LWFB4jMuMKW2J69mOhyJZSSgGxFhwajvY30vqxo6KRuYXpFKSPXffVc1k0KZP1u07x+JtHRp7I3Ovsds/z0F5/7muVUipAEyo4HKtrY1puyphlZziTsmyQ+uof9o48kdRc+MCjdr++/NzXKqVUgGInOHS12kV+Mv1XGXm9hhMNHUzLDd8Ee8H66EX9I7lHNRnfpGV2W6ddWpVSoRE7waHV6cY6xBiHU82ddHu8TM0ZPyWHabmp/PVLV5KS4OYr6/aMPKHsUjsTbZ12aVVKhUbsBIeWU3Y7xOjoLccaAJhfPPZjG85lSk4KH7u0lL8frqOlc4TLfsYl2CnKT4ZgtlellCKWgkOrExzS/I9x+Mu+0+SmJrB0DCfaC9Sls/Lo9RreKh9Fg/LUi+DEO+ANwYR+SqkJL3aCQ9/o6CEGwO2saGJFaTZuV2gmfw2l86dlk5EUx592VY08kakXQ3eLHfOglFKjFDvBofUUuBMgOXvQW90eL8fq25lTmB6BjA0vMc7NdYuL+eOuKnZVjHDcw7SL7fbYxtBlTCk1YcVOcGg8bnsqDVgWormzhx//tZxer2FWGNeJHq0vvmcuAvxu+win386cbOdaKn81pPlSSk1MsRMcGo75HePwL0/v4Fsb7NxD460x2lduWiLT81I5Wts28kQW3QiHXoLmUVRPKaUUMRUcjkLW2SvAeb2Gl/fZtojS3JRxW63UZ3peKkdGExyW32EX/9n2q9BlSik1IcVGcHjjW9BRP6jkUNvahTHwqVUz+N1nL41M3oIwPS+V8to29lU1jyyB3Jkw9RLY/4fQZkwpNeHERnAof91u56w563RlUycAK0tzyEpJGOtcBe3G5SWkJ8WNbkBcwTxdGU4pNWqxERy6mmH2u+0Xo48qZ53m4qzxMdHecGYVpPPpd83knSP1I69eypwMHQ12OhGllBqh2AgO7Q2QkjvodF/JYVJmZBb1GYmbzp+MS+CpTSP89Z/prCvdPMJeT0opRcwEhzpIzhl0urKxg+R4N1kp8RHI1MgUZiRx3eJiHn/zKMfr2oNPoG/iwcYToc2YUmpCif7g0NMJPW2QMjg4VDV1UJyVhMj4GxV9Ll98z1y6PV7eOFQT/M0F88CdCAfWD3+tUkoNIaDgICJrROSAiJSJyH1+3k8Ukd84778tIqXO+VIR6RCR7c7rhz73nC8iu5x7/ldG+g3e4cxH5Cc4VDZ2RlWVUp+pOSlkp8SzeyRLiCZnw3k3w/Zf2+69Sik1AsMGBxFxA48A1wILgFtFZMGAy+4GGowxs4CHgYd83jtsjFnqvD7tc/4HwD3AbOd1dlejQPWtfjagWmnT0Xq2n2g8s6BONBERFpVksv1E48gSuOL/QW83bH8itBlTSk0YgZQcLgDKjDHlxphu4Clg7YBr1gI/d/afBa46V0lARIqBDGPMRmOMAX4BvD/o3INPyeHsBumbf2jnGPKaEaUacZfOymP/qRaqmjqCvzmzBHJnw6ldoc+YUmpCCCQ4lAC+rZsVzjm/1xhjPEAT0PdtPV1EtonI6yJyuc/1FcOkGZj2Orv1qVZq7/ac2b/+PP+L/4x3V8+361L8dusIex0VLYJTOkOrUmpkAgkO/koAA3+PD3VNFTDVGLMM+ALwhIhkBJimTVjkHhHZLCKba2r8NNC2Dy457Km0I4wfu2sFV84t8JfsuDerII2r5hXwyKtl7K0cwYjp4iXQdLx/ESSllApCIMGhApjiczwZqBzqGhGJAzKBemNMlzGmDsAYswU4DMxxrvdd7Nlfmjj3PWqMWWGMWZGfnz/4Aj9tDicbbFXM1Jzxs170SPznBxaTGOfie6+OYPnPGVfa7eFXQpsppdSEEEhw2ATMFpHpIpIA3AKsG3DNOuBOZ/8m4BVjjBGRfKdBGxGZgW14LjfGVAEtInKR0zZxB/D7ET1BRz0kpNmlMh0nnZHR0dgY7asoM4m1S0t4eV81rV2e4W846+bFkJoPR94IT+aUUjFt2ODgtCHcC2wA9gFPG2P2iMiDInKDc9lPgVwRKcNWH/V1d10F7BSRHdiG6k8bY/rWwvwM8BOgDFui+NOInqC9blA31pONHeSkJpCSEDeiJMeTq+YX0O3xnlkDO2AiULICTm4JT8aUUjEtoG9PY8x6YP2Acw/47HcCN/u57znguSHS3AwsCiazfrXXn1WlZIyh7HRr1Jca+pw/LZs4l/DXgzW8a46farVzKTkfDv4J2mohNS88GVRKxaToHyHdVn3WF98r+6t552g9axb6X0s62qQkxPGeRUX87O9HKatuCe7medeDuOCN/w5P5pRSMSu6g0OvB2oOQH7/bKx/PVRLcrybT71rZgQzFlpfW7uIhDgXP3itPLgbCxfAwhth51Pg6Q5P5pRSMSm6g0PtQfB02m6bjreP1HP+tGzi3dH9aL5yUhO4an4hGw/XBn/z4pvsFN7H3gx9xpRSMSu6v0FPO4viFNqmiy5PL4dOt7BkSmYEMxUei0syqGzqpK61K7gbp11qq5aObwzOLYOlAAAcuElEQVRPxpRSMSm6g0PjUbvNmQ7A4eo2PF7DvKKMyOUpTBaXZAGwoyLI+ZaSMqBwIRz7exhypZSKVVEeHI5DagHE25lX95+yI4nnFaVHMldhsWxqFsnxbl7ZXx38zbOusdVKzVWhz5hSKiZFf3DImnrmcPuJRlIS3EzPi+6R0f4kxbu5Ym4+z26pCH4q72UfBeOFHTpLq1IqMNEdHBqOnRUc3nEao+NiqDHa11fet5DkeDfffulgcDfmzrRtD9t+BV5veDKnlIop0fst2t0OjccgbzZgZ2I9cLqF86dlRzhj4VOUmcRHL5rGqweqg2+YXn4n1JfDkdfDkzmlVEyJ3uBQvddWlRSdB8Ch060YA/OLY68x2te7FxRhDLx+MMglRBeshfgUOLghPBlTSsWU6A0Op3babZHtxnrglB09PLcw9hqjfS2clEFeWmLwDdPxSTaQVm4LT8aUUjEleoNDc6Xtv59p2xz2VjWTHO9mak5KhDMWXi6XcOXcfN44WENPb5DtByXLoWoH9PaEJ3NKqZgRvcGhvR6SssBlH2Hr8QaWTMnE5RpyddKYce3iIpo7Pdz/2130BrMO6rRLwNOhA+KUUsOK3uDQUX9mqu4fvn6YnRVNrJiWM8xNseGKOQWU5qbw7JaK4KqXZlwJ7kTY/mT4MqeUignRGxx8pup+ae9pAG5cPrJlqKONyyW8+PlVJMW72LAniGVAE9Pgwk/Z8Q4n3glfBpVSUS96g4NPyeF4fTsfWjGZGflpEc7U2EmKd3PNgiJeO1CDN5iqpSvus0F14yPhy5xSKupFb3Bob4DkHDq6e6lp6Yr5hmh/rpiTT21rF3urmgO/KSEV5r8PDr9qpzxXSik/ojc4OCWHEw3tAEyZgMHh8jl2kaOgxzzMuAK6mqBqe8jzpJSKDdEZHDqboKcdUvM4VmeDw7Tc2JtPaTgF6UksnJTBaweCHPMw/V12W/5q6DOllIoJAQUHEVkjIgdEpExE7vPzfqKI/MZ5/20RKXXOXyMiW0Rkl7Nd7XPPa06a251XQcC57lvHoWABx+ttcJiI1UoA1y0uZtPRBtbtqAz8ptRcOyBu/3qda0kp5dewwUFE3MAjwLXAAuBWEVkw4LK7gQZjzCzgYeAh53wt8D5jzGLgTuCXA+67zRiz1HkF/vP31G67LVrMifp20hPjyE6JD/j2WHLnJaVMzk7mn3+zPbj5llZ8HCq3wrZfhC9zSqmoFUjJ4QKgzBhTbozpBp4C1g64Zi3wc2f/WeAqERFjzDZjTN9P2j1AkogkjjrX1XvtALj0Yo7VtTElJwWR2B/85k9aYhzfv205vV7DqweCaHs4/y4oWQF//R8dMa2UGiSQ4FACnPA5rnDO+b3GGOMBmoDcAdd8ENhmjPH9efu4U6X0ZQnm273xOORMp8dr2HaikXnFsT2f0nAWl2RSkpXMc1sqAr9JBFZ90f5b7no2fJlTSkWlQIKDvy/tgR3rz3mNiCzEVjV9yuf925zqpsud1+1+P1zkHhHZLCKba2qcX8aNxyFzChsP19HY3sN1i4oDeIzYJSLccfE0NpbXsbcyiG6tc94DhYtt6UHbHpRSPgIJDhXAFJ/jycDA1s8z14hIHJAJ1DvHk4HngTuMMYf7bjDGnHS2LcAT2OqrQYwxjxpjVhhjVuTn54Mx0HQCsqby9pE64lzCpbPyAnnWmHbLyqkkx7v5weuHh7+4jwhcci/UHYITb4cvc0qpqBNIcNgEzBaR6SKSANwCrBtwzTpsgzPATcArxhgjIlnAC8D9xpg3+y4WkTgRyXP244H3ArsDynFbDXg6IWsqW481Mr84g+QEd0C3xrLMlHjuvmw6f9hRyZtltYHfOO96O9/S1p8Pf61SasIYNjg4bQj3AhuAfcDTxpg9IvKgiNzgXPZTIFdEyoAvAH3dXe8FZgFfHtBlNRHYICI7ge3ASeDHAeW41XZq6kzKZ9uJBlaUxu7Kb8G6d/UspuWm8M0NBwK/KTEdLvo07HgSTmwKX+aUUlElLpCLjDHrgfUDzj3gs98J3Oznvq8DXx8i2fMDz6aPjnoAttUKnT1e3rOwaETJxKKkeDc3LpvMd/5ykIa2brJTEwK7cdUXYdNjsOknMGVleDOplIoK0TdCut0Ghz2NbhLcLlaWToxpugN1+Zw8jIFng+m5lJgO530I9jwPbXXhy5xSKmpEX3BwSg7lLQlMzk7GPQEW9wnGsilZXDWvgG9tOMC+YCbku+CT4PXA7z8LPZ3hy6BSKipEYXBoAOBAczyTJ+iUGeciInzr5iUkxbv4/mtB9FwqmA/XPgQH/wQvfTl8GVRKRYWA2hzGlfZ6iEumrKGX901NjnRuxqWc1ARuXD6ZJ94+zon69sBnrL3gk1Cz37Y9XPYFyBiH40d6e+wIeU83NJ+EhDTY9kvImmInFGw5BfPfC8naUUGp0Yi+4NDRgCcpi6baHmYXTOyR0efyqXfN4DebTvCNP+3j+7cF0fZ/0T/Y4PD2D+Gar4Yvg8Go3AbrvwRpBXBqpx0E6c/f/89u190LUy6ClFzImw0zr7TTlCulAhZ9waGtlgYyALh6QWGEMzN+FWcm8+l3zeThlw/yVnkdF80YOJvJEHJnwpKPwJvfjeyXasMx2PIzKHsZTu8G4wVxQ8n5cOFnoLfb5jU5x1aJdbdCxSZbsji4wZYgqrbDgRfgze/A5Atg0tLxWyJSapwRY4JYYjLCVqxYYTbf5WJzWx7/nnAfG/55VaSzNK51dPdy1f+8RnpSPH/4x8tIiAuwiam7DX68Gpoq4OMvQtHi8Ga0T3s9HHkdXv0G1B4ABKZcCFMugMv+GRIzwB3k75meTvjbw7D/BVtlZrww6ypYcgvMvQ7itWpSxT4R2WKMWRHMPVHXIG0ajrCrI5dlU7MinZVxLznBzVfXLuLA6RZ+s2mIqhh/ElLh9t/Z+vznPhn+WVu722HP7+B7K+CZu2wpYM1D8I9b4O4N8O6v2fXCgw0MAPFJcOX98Jm/wb3vwKWfs+uBPPtx+O4S2PEb+/lKqbNEV3Do7UZ6uznYk8+SKRocAnH1/AJWlmbznZcPUdMSxHoPGcWw5htQsw++f3F4xj94um0p4TuL4Zk7bcngtufg3k121HbuzNB+Xs4MuPor8PldcPvzdnzH8/fADy6x1WgdjaH9PKWiWHQFB4/9cjtqipieN/GWBR0JEeE/P7CYli4P9z23k6CqERd+AG78sW0Afv4eW90UCp5ueOXrNii8/l8weQXc8iT8w0aYfbUtuYSTyw0zV8NnN8FHnoa4RHjpAXj0XbDz6dA9p1JRLLoapHud4OAtmrDLgo7EnMJ07lszjwf/uJcn3jnObRdOC+xGETtyuqsFXvgCfP8iuP7bMPuakWWk5gC8eD+c3AKdjTDnWlj5CRsQzqGzp5cXd5+iID2Rg6db2HaiEbdL6OjuJTnBzfG6dvLTE1lZmkN3r5c1C4uYlhvAAlAul522fM574MQ78Nwn4LefhIwSW2qa914bSJSagKKrQXpOsdl4Wy8Lux9j39eu19HRQfB6DXc+/g6bjzbwwj9dxoz8tOASOPom/PHzthSx5huw6IOQlDn8fZ4u2+No00/g8Cu2e+m8622pZOZqv7d4vYYDp1t4/WAN7xypZ8uxBpo6+ts9clMTaOn0kJUST7zbRUqCm7q2burbus9ck5EUx5ScFBYUZ3DRjFxuWDqJePcwBWWvF47+FTb8P9tDKns6vPvrNr8TdKVBFRtG0iAdXcFhRq5Z94nJfCT+O7z2xSsjnZ2oc7q5k/d85w2m5aTwzKcvCbz3Up+2WnjqI/1rP5x3C5ReCpNXQt4c23DtcsPxt2zp4PhbNiD0dtlf4zNXw6p/hexSv8lXNXXw9KYKfrHxKHXOF/2M/FQWTcrk/csmISJMy0lhRn4axpizSgZer6GquZOObg+v7K/mWF07h2taKatupba1m4ykOOYUpvPB8ydz3aJiMs+15nivB/b+Dt74lu3hVLgIVn8Z5q4J7t9LqXEi9oPD1DTzP5+4mKdnPsQjty2PdHai0ou7q/j0r7by4RVTeOim84JPwBgbHHY9A1t+Dl7nF707wadXk/M3lTkF5l4LM6+CWVf77W3U5enljYO1/GFHJet3VeHxGi6ZmctN50/mwhm5lGSNrqupMYbXDtbw0t7TbD3WwP5TLcS5hItn5vK+8ybxgeUlQ5coej2w4wn4+/ds19qZq2H5HTB/ra2SUipKxH5wKIk393zsZpLf+w1uvyjAenM1yDdf3M/3XzvMj24/f3RTnnc2QXsdHHgRWiohLhkwULzUlibShx6k2NnTy/PbTvK9V8o42dhBZnI8H1hWwt2XTQ98uo8gGWPYWdHEi3tO8eLuUxypbSMjKY4PLCvhhqUlLJuShctfVWVPhx19vfUXdhXCqZfAsttg8YcgLsBp0cejng47tqS7zY7/6AvqcUl2Qa20QtuFWEW92A8Ok9zm3R/7HB//3FeZpVNnjFi3x8sHvv8mx+raefT287lkDJdZrW7p5LktJ/n5349yqrmTBcUZ/Mu757BqTv7wbQIhZIzh9YM1/G7bSdbtqMRrYGZ+Kh+7dDprl04iPclPtZPXC5t/agfVNZ+0bRIrPwFLboXUAEegjxVvLzQctW0nTRXQXGmryNpqbPVgez14OoZPxxUHrng7Cj2tAHJm2i7GuTMhdxakT9JSVBSYEMFh5ae/yfe//IXhe6KoczrV1Mkdj73N0dp2fnj7clbPC+9UJE0dPTzx9nEefvkg3R4vF07P4XNXz+biGbkR/29Z39bNaweqeezNI+w+2UxSvIvrF0/i1gumcP607MH5MwYOvQRvfNNO2eGKt5P9Lb/TTv431l+WHQ1weq8d3Hd6l91W74Men8F97kTInwPpxZCSZ0sEKTm2g0BCmm1wF5d9Nk+nnaqkrdoGka5mqD9ipySpLz87qMQlQ9EiyJ8HRefZbsnZpVriGGcmRHC49ht/4Gt3XhfprMSExvZubv/pO+w/1cx/37yEtUtLQv4ZlY0d/PRvR3jyneO0d/fy7gWF3HftvOB7S40BYwzbTzTy9OYK1m0/SVt3LzPzU1m7tIT3Ly1haq6f6q7Te211086n7Jd0xmSYfjnMvwGmXRza2WGNsaWAmv1QtQNObrUTETad6L8mOds2oBctxluwgNPJszjhzaPak0RVUw+1bV20dnpoaO+mtrWbbo8Xl4DXgNcYEuNcpCXGISJkJceTn5FIotvFpKxkSrKTmZSZSIm7kaSmI1B/GGoP2YkR68psqaRP3hwoWWHnsypeardxiaH7t1BBifngkF5car7/21e5/eLpkc5KzGjq6OETP9/EpqMN3LishP9Yu5AMf1UqQTpwqoUfvXGYddsrMcANSybx0YumsXxqVsRLCoFo6/Lwwq4qntl8gk1HGxCBy2blcc2CQtYsKqIgPensG3o6Yf8fbS+nI2/Y9hiA/Pk2SOTPh4J5thomJQeSsvyXMHp77JdsRyM0HoPag1Bz0DaIV++H7pb+a3NmwqRl9OQv4GTiTHb3TmVnYxLltW0cqW3jeH07Pb1n//+d4HaRnhRHVko8uamJJCW48XoNIuB2Cd0eL61dHjy9hqaOHmpauvB4vXgHfE3kpiYwOSeFGXmpzMhLZXJOMvMT65jhPUZCQ5nttHByqy19gC25TFpqR6kXLbYBo3AhJI+zmQ6MsSWltlrnVQPttXasT1erndqlu9W20ww89npsSSre5xWXBPEpdhoX3/cS0mw1XVoBpBZAar4N7GEqdYYtOIjIGuC7gBv4iTHmvwa8nwj8ArsudB3wYWPMUee9+4G7gV7gn4wxGwJJ05/E4tlmz46t2t4QYj29Xr73Shn/98ohijOT+cr7FnDNgsKgv8S9XsNb5XX85G9HeGV/Ncnxbm65YAp3XzadydnRO2ixqqmDJ94+zgs7qyivbcMlsLI0hyvmFnDprFwWTso8e8yNpxuOvQmVW6H8dTs7bF+w6CMuO6NsQortFeXtsTPNdrU4jcM+0gohbw69eXOpS5lJGZPZ1lnMzjrh4OlWjta10fe/cUKci+m5qUzPS6XU54s7NzWR4qykEQX+Xq+hsrGDysYOTvpsT9R3UF7TSmVT/8qBIjApM5nSvBSm56awKL2dhXKYqa07yKjbhTQcgZaq/sTTi22VVMF8u82aChmT7PmkjKDzek7d7fazW0/bV8tpe9xcaduQmk9imquQ3qGnmelxJdHlTqHblUynpNAhSbSTTDtJ9OImSbpJoptE00Ui3SSYLhJMF/HeLuK8XcR5O3Ebj9+0jSsOSSu03b4zS+y/QXrRgG0xJAZf6g5LcBARN3AQuAaoADYBtxpj9vpc8w/AecaYT4vILcAHjDEfFpEFwJPABcAk4GVgjnPbOdP0Z87CJebA7u1R8cszGm051sAXn91BeU0bS6Zk8Zl3zeCKuQUkxQ89Srizp5e3j9Tz6v5qXtx9ilPNneSkJnDXJaXcftE0slOjuDePH4dOt7BuRyUv7T3N/lP2V3xGUhwXzchlyZQsZhWkMasgjWk5KcT1NbAbY+vr+xqE2+ucl9NTyB1nuwK74iEpg57UYhq8KRz15LCjs4DddbYkdrim9UxJwCUwPS+VuUXpzClMZ25hOnOK0s/+3DHS0d3LycYODpxq4eDpFo7VtXGkrp3ymlZaOvu/COPdwtScFJZkd3NR0gnmyAmKu4+S2XqYxIZDyMAG8oQ0+2WYUQxpRXYurIQUez4u0f679vWyMsaWurqaobPZ2TZBVzOmsxnTVovLt9Tl8EgcDe48qsnlpDeH454sqnozqDcZ1JFBnbH7LU4A8OIiIc5FcrybpPi+rX25BLp7vXT2eOns6aXL07/t9vQHfDe9pNFBvjSSL03k0USeNFHobmZaXBOTXPUUUkd2bz2JZnCngd74NLxphUh6Me7MSUh6kQ0eyTm29JHibJOy7FQ08cmIyxWW4HAx8B/GmPc4x/cDGGO+4XPNBueajSISB5wC8oH7fK/tu8657Zxp+rNixQqzefPmYJ5PBcnT6+W5rRV89+VDVDZ1kprgZlFJJvOK0inISCIxzkVbVy+nmjvYf6qFfVXNdPZ4SYxzcfnsPG5YWsI18wtJToj9aSeqWzrZeLiOv5fVsbG8juP1/Q3ACW4X0/PsL/js1HgykxPITI4nzqeE0dnTS1NHz5nX6ZYuKhs7Bk2QWJKV3B8EitKYU5jOzPy0cwbt8cAYQ31bN0dq2yivbaO8po0jta0cqW3jaF37WV+YLrzMjK9nYWozM5KaKZYG8k09uaaObE8t6Z56ErwdxPd2EOf1v8a5F6HLlUK7pNAmqTR5k2nwJtHQm0y9SafGZFFNFtUmi9MmmwbJxpWaQ05aMnnpieSlJpCXnkhuagJ5aYln9jOT40lJ6A8CI5mZwes1TuDopbPHS2uX/W/e3OGhvq2b2tYu6tq6qW3por7djvava+3G09FEWncNBdJIIQ0Uin0VONsiZ5uA/9IIgEFwfbUp6OAQyNxKJYBPixcVwIVDXWOM8YhIE5DrnH9rwL19rZ7DpQmAiNwD3AMwderUALKrRiPO7eLDK6fyweWT2Vhex4Y9p9hb2cwzWypo7+49c112Sjxzi9K59YKprJqdz8Uzc8f9l1WoFaQnsXZpyZmG/NYuD4erWzlUbUdml1W3UFbTSuOxHpo7euju9Q5KIzneTWZyPJnJ8eSlJ3Dl3HxKslIoyU5mel4qcwrT/HerjQIiQm5aIrlpiawoPbv3km9V1anmTqqbuzjV3Mmp5k7+1tJFW5eHtm4PrV29tHV56Ojp/9tz4SWBHgyCQfAiJCfEk5wQT2qS/SJPT4qzn52aQE5qArlpiSzq23e+/DOT4/2PawkDl0tIcrl9/h9JOuf1vro9XucHRDcN7T00tvfQ0N7N9vYeGju6aWjrpru1AU+bLY26OhtJ9DSR2ttCvLeDJLqAnwed50CCg79/vYHFjaGuGeq8v3Kv3yKMMeZR4FGwJYehs6lCKc7t4vLZ+Vw+Ox+wvwL7iswpCe4xHZMQLdIS41gyJcvvdPLGGDp7vPT6lNTj3UJi3MQKqH3cLmFKTkrAAx57vYb2bvvruK9aWQCXCIlxrjH7ko+EhDgX+emJ5KcH39vLGENPr+Hz/xme4FABTPE5ngxUDnFNhVOtlAnUD3PvcGmqcUTEfpFN1C+z0RKRCVHVFi5ul0RtCSqSRISEuJEFzkB+/m0CZovIdBFJAG4B1g24Zh1wp7N/E/CKsY0Z64BbRCRRRKYDs4F3AkxTKaVUhAxbcnDaEO4FNmC7nT5mjNkjIg8Cm40x64CfAr8UkTJsieEW5949IvI0sBfwAJ81xvQC+Esz9I+nlFJqJKJqEJz2VlJKqeCNZJyDtioqpZQaRIODUkqpQTQ4KKWUGkSDg1JKqUE0OCillBokqnoriUgLcCDS+QijPKA20pkIk1h+NtDni3ax/nxzjTFBTWcdyAjp8eRAsN2xoomIbI7V54vlZwN9vmg3EZ4v2Hu0WkkppdQgGhyUUkoNEm3B4dFIZyDMYvn5YvnZQJ8v2unzDRBVDdJKKaXGRrSVHJRSSo2BqAgOIrJGRA6ISJmI3Bfp/IyWiDwmItUistvnXI6IvCQih5xtdiTzOBoiMkVEXhWRfSKyR0Q+55yPiWcUkSQReUdEdjjP91Xn/HQRedt5vt8409FHJRFxi8g2EfmjcxxLz3ZURHaJyPa+Xjyx8rcJICJZIvKsiOx3/h+8eCTPN+6Dg4i4gUeAa4EFwK0isiCyuRq1nwFrBpy7D/iLMWY28BfnOFp5gH8xxswHLgI+6/w3i5Vn7AJWG2OWAEuBNSJyEfAQ8LDzfA3A3RHM42h9DtjncxxLzwZwpTFmqU/31Vj52wT4LvCiMWYesAT73zH45zPGjOsXcDGwwef4fuD+SOcrBM9VCuz2OT4AFDv7xdgxHRHPZ4ie9ffANbH4jEAKsBW7BnotEOecP+vvNppe2JUZ/wKsBv6IXZEzJp7Nyf9RIG/AuZj42wQygCM47cmjeb5xX3IASoATPscVzrlYU2iMqQJwtgURzk9IiEgpsAx4mxh6RqfaZTtQDbwEHAYajTEe55Jo/jv9DvAlwOsc5xI7zwZ2vfo/i8gWEbnHORcrf5szgBrgcada8CciksoIni8agoO/BVC1i1UUEJE04Dng88aY5kjnJ5SMMb3GmKXYX9kXAPP9XTa2uRo9EXkvUG2M2eJ72s+lUfdsPi41xizHVlV/VkRWRTpDIRQHLAd+YIxZBrQxwiqyaAgOFcAUn+PJQGWE8hJOp0WkGMDZVkc4P6MiIvHYwPBrY8xvndMx9YwAxphG4DVs20qWiPRNSROtf6eXAjeIyFHgKWzV0neIjWcDwBhT6WyrgeexwT1W/jYrgApjzNvO8bPYYBH080VDcNgEzHZ6SyRg16deF+E8hcM64E5n/05sPX1UEhHBriu+zxjzbZ+3YuIZRSRfRLKc/WTgamyj36vATc5lUfl8xpj7jTGTjTGl2P/XXjHG3EYMPBuAiKSKSHrfPvBuYDcx8rdpjDkFnBCRuc6pq4C9jOT5It2AEmAjy3XAQWy97r9HOj8heJ4ngSqgBxvp78bW6/4FOORscyKdz1E832XYaoedwHbndV2sPCNwHrDNeb7dwAPO+RnAO0AZ8AyQGOm8jvI5rwD+GEvP5jzHDue1p+/7JFb+Np1nWQpsdv4+fwdkj+T5dIS0UkqpQaKhWkkppdQY0+CglFJqEA0OSimlBtHgoJRSahANDkoppQbR4KCUUmoQDQ5KKaUG0eCglFJqkP8fq0ZCO1Z+dQ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:-1], deriv_growth_psf)\n",
    "plt.plot(radii[1:-1], deriv_growth_psfcor)\n",
    "plt.xlim([0,60])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compared with the growth curve plot, the derivative show clear maxima and minima that are out of phase. Findind the positions of the these will tell us if our assumption of homothetical variation is correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          6.18050404 17.4854638  23.79928199 32.07353691 38.40607579\n",
      " 46.76238796] [ 0.          6.5206172  18.75895207 24.07489413 32.78746844 38.5386345\n",
      " 47.21468159]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Find the local minima and maxima of the two curves.\n",
    "# To find a local extremum, we will fit the portion of curve with a degree 3 polynomial, \n",
    "# extract the roots of its derivative and only retain the one that are between the bounds.\n",
    "# This is what the following function does.\n",
    "def local_max(xvalues, yvalues, lower_bound, upper_bound, check_plot=False):\n",
    "    idx,=np.where((xvalues > lower_bound) & (xvalues < upper_bound))\n",
    "    p = np.polyfit(xvalues[idx], yvalues[idx], 3)\n",
    "    delta = (2.*p[1])**2 - 4.*3.*p[0]*p[2]\n",
    "    r1 = (-2*p[1]+np.sqrt(delta))/(2*3*p[0])\n",
    "    r2 = (-2*p[1]-np.sqrt(delta))/(2*3*p[0])\n",
    "    result = r1 if ((r1 > lower_bound) and (r1 < upper_bound)) else r2\n",
    "    if check_plot:\n",
    "        plt.plot(xvalues[idx], yvalues[idx])\n",
    "        plt.plot(xvalues[idx], p[0]*xvalues[idx]**3+p[1]*xvalues[idx]**2+\n",
    "                 p[2]*xvalues[idx]+p[3], '--')\n",
    "        plt.plot(np.array([result, result]), np.array([np.min(yvalues), np.max(yvalues)]), '-')\n",
    "    return result\n",
    "    \n",
    "    \n",
    "max_dpsf_1 = local_max(radii[1:-1], deriv_growth_psf, 3, 10, check_plot=True)\n",
    "max_dpsfcor_1 = local_max(radii[1:-1], deriv_growth_psfcor, 3, 10, check_plot=True)\n",
    "\n",
    "max_dpsf_2 = local_max(radii[1:-1], deriv_growth_psf, 14, 21, check_plot=True)\n",
    "max_dpsfcor_2 = local_max(radii[1:-1], deriv_growth_psfcor, 14, 21, check_plot=True)\n",
    "\n",
    "max_dpsf_3 = local_max(radii[1:-1], deriv_growth_psf, 21, 28, check_plot=True)\n",
    "max_dpsfcor_3 = local_max(radii[1:-1], deriv_growth_psfcor, 21, 28, check_plot=True)\n",
    "\n",
    "max_dpsf_4 = local_max(radii[1:-1], deriv_growth_psf, 28, 35, check_plot=True)\n",
    "max_dpsfcor_4 = local_max(radii[1:-1], deriv_growth_psfcor, 28, 35, check_plot=True)\n",
    "\n",
    "max_dpsf_5 = local_max(radii[1:-1], deriv_growth_psf, 35, 45, check_plot=True)\n",
    "max_dpsfcor_5 = local_max(radii[1:-1], deriv_growth_psfcor, 35, 45, check_plot=True)\n",
    "\n",
    "max_dpsf_6 = local_max(radii[1:-1], deriv_growth_psf, 40, 50, check_plot=True)\n",
    "max_dpsfcor_6 = local_max(radii[1:-1], deriv_growth_psfcor, 40, 50, check_plot=True)\n",
    "\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "\n",
    "# Lets pack all of them, adding the r=0 point. \n",
    "max_dpsf = np.array([0, max_dpsf_1, max_dpsf_2, max_dpsf_3, max_dpsf_4, max_dpsf_5, max_dpsf_6])\n",
    "max_dpsfcor = np.array([0, max_dpsfcor_1, max_dpsfcor_2, max_dpsfcor_3, max_dpsfcor_4, \n",
    "                        max_dpsfcor_5, max_dpsfcor_6])\n",
    "\n",
    "print(max_dpsf,max_dpsfcor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot, we can deduce that our homothetical assumption is not perfect: the spacing increases for the first three (don't forget the point at 0, 0, not shown), is very small for the 4th and 6th, and gets narrower for the 5th and 7th...\n",
    "Let's plot the situation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.07402639 -0.04610159]\n",
      "1.0550300032613567\n",
      "1.072831254463463\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(max_dpsf, max_dpsfcor, 'o-')\n",
    "p = np.polyfit(max_dpsf[0:3], max_dpsfcor[0:3], 1)\n",
    "plt.plot(max_dpsf, p[0]*max_dpsf+p[1])\n",
    "plt.xlabel('extremum position of theoretical psf [arcsec]')\n",
    "plt.ylabel('extremum position of observed blurred psf [arcsec]')\n",
    "\n",
    "\n",
    "print(p)\n",
    "print((max_dpsfcor[1]-max_dpsfcor[0])/(max_dpsf[1]-max_dpsf[0]))\n",
    "print((max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets use the data before 20\", corresponding to the central core\n",
    "beta = (max_dpsfcor[2]-max_dpsfcor[0])/(max_dpsf[2]-max_dpsf[0])\n",
    "\n",
    "# lets interpolate at the scaled radius\n",
    "tckpsfcor = interpolate.splrep(radii, growth_psfcor, s=0)\n",
    "interp_growth_psfcor = interpolate.splev(radii*beta, tckpsfcor, der=0)\n",
    "\n",
    "# check interpolation\n",
    "plt.plot(radii*beta, growth_psf)\n",
    "plt.plot(radii, growth_psfcor)\n",
    "plt.plot(radii*beta, interp_growth_psfcor)\n",
    "plt.xlim([0,60])\n",
    "plt.xlabel('radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us check the ratio, using the psf with a corrected radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha = 2.005\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii[1:]*beta, interp_growth_psfcor[1:]/growth_psf[1:])\n",
    "plt.xlabel('radius [arcsec]')\n",
    "plt.ylabel('Ratio of encircled flux')\n",
    "plt.xlim([0,60])\n",
    "idx, = np.where(((radii*p[0]) > 0) & ((radii*p[0]) < 60))\n",
    "scale_factor = np.median(interp_growth_psfcor[idx]/growth_psf[idx])\n",
    "print(\"alpha = {:.3f}\".format(scale_factor))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have a much better looking ratio [compared with the cell where we computed the direct ratio](#the_ratio), and we have a decent determination of the psf scaling. The normalized PSF to use for our observations is then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf_obs_norm = psfcor / scale_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\int \\int psf_obs_norm dx dy = 0.966450534666256\n"
     ]
    }
   ],
   "source": [
    "print('\\int \\int psf_obs_norm dx dy = {}'.format(np.sum(psf_obs_norm)*resol**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, let's look at the encircled energy in the core of our psf:\n",
    "In this example, we have used the derivative of the scale factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "central core for observation: 0.8526531289184243\n",
      "central core for theoretical: 0.8526789463354869\n"
     ]
    }
   ],
   "source": [
    "idj, idi = np.where(r<max_dpsfcor_2)\n",
    "print('central core for observation: {}'.format(np.sum(psf_obs_norm[idj, idi])*resol**2))\n",
    "idj, idi = np.where(r<max_dpsf_2)\n",
    "print('central core for theoretical: {}'.format(np.sum(psf[idj, idi])*resol**2))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two agree extremely well. \n",
    "\n",
    "Unfortunately, with real data, it is not always possible as we will see to use the derivative of the curve of growth to derive the factor beta of PSF fattening. For real observation, one can use a brute force approach to try all the reasonable couples alpha, beta and try to match the theoretical psf to the observed one. This is how we will proceed next on real data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Real data: PACS observations\n",
    "\n",
    "We will look at a real stack of point sources in the PACS ELAIS-N1 observations, and try to find its normalization factor. \n",
    "\n",
    "Let's load the stacked PSF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fb65d9b8400>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd_im = fits.open('../dmu18_HELP-PACS-maps/data/GAMA-15_PACS160_v0.9.fits')\n",
    "stackhd = fits.open('./data/output_data/GAMA15-160um-psffromstack_20171002.fits')\n",
    "psf = stackhd[0].data\n",
    "hd = stackhd[0].header\n",
    "plt.imshow(psf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the resolution of the psf. Because the map is in units of Jy/pixel, this turns out to be:\n",
    "* =1 if psf at same resolution of map\n",
    "* otherwise, should be in factor of map pixel size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[0].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's build the growthcurve for our PSF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# find the brightest pixel, it will be our center.\n",
    "jmax, imax = np.unravel_index(np.argmax(psf), psf.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# build the array of coordinates\n",
    "x = np.arange(hd['NAXIS1'])\n",
    "y = np.arange(hd['NAXIS2'])\n",
    "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
    "xp = (xv-imax)*np.abs(hd['CDELT1'])*3600.\n",
    "yp = (yv-jmax)*np.abs(hd['CDELT2'])*3600.\n",
    "r = np.sqrt(xp**2 + yp**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# build the growth curve\n",
    "radii = np.unique(r)\n",
    "encircled_flux = np.zeros(radii.shape)\n",
    "nbpix = np.zeros(radii.shape)\n",
    "for i, radius in enumerate(radii):\n",
    "    idj, idi = np.where(r <= radius)\n",
    "    nbpix[i] =len(idi)\n",
    "    #encircled_flux[i] = np.sum(psf[idj, idi])*resol**2\n",
    "    #multiply by ((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10 as map is in units of MJy/sr\n",
    "    encircled_flux[i] = np.sum(psf[idj, idi])*((np.abs(hd['CDELT1'])*3600.)**2)/4.25E10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.0000000726000002"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, encircled_flux)\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the shape of the encircled flux, it looks like the background level of our PSF is not zero. Let's check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0012699062353931367\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2KyJh9uTl89hH2Tz58SLq16zK/114FGf0bK7uLOSQRXLEUDfscR6haw6TInhece9KLzJ9IfCCu//dzAYBL5tZ96LtJMxsJDASIDm56HVwkcQ1Z+lGRk1KY9G6HZzTpyV3nN6VhrWrxbosiXORXGP4yyFuOwdoHTbdiv8+VXQlMDR4na/MrAaQBKwtUsMEYAJAampq0XARSTjbdufywPtZvPz1Mlo2qMmLV/RncKcmsS5LKoj9BoOZvcN/f8P/hbufdYBtzwY6mllbYCVwAXBRkXWWA78GXjCzLoTueorkNJVIwpo1fy23TUln9dbd/PaYFG46+Uhqa9xlKUUlvZv+djgbdvc8M7semEHoVtTn3D3DzMYCc9x9KvD/gKfN7M+EQuhyd9cRgUgxNmzfw9hpmbz94yo6Nq3DxGuOpm+bhrEuSyog29/nsJl96O6/NrP73X1UGde1X6mpqT5nzpwDryhSQbg7b/24krHvZLJ9Tx7XHd+Ba4e0p3oVdWchkTOz79w9NZJ1SzpiaG5mg4GzgltNC11MdvfvD6NGEYnAys27uG1KOh9nreOo5Abcf25POjWre+AnihyGkoLhTmA0oYvGf6dwMDhwQhTrEkloBQXOS18t5YEZWQDcdWZXLhuUonGXpUzsNxjcfSIw0czucPdxZViTSEJbuGYboyal8f3yzRzXqQn3DO+ucZelTEVyu6pCQaQM7M0r4KlPFvHYR9nUql6Zh/6nF2cf1VIN1aTM6R43kXLgxxWbGTUxjaw12zijZ3PuPqsbSXWqx7osSVAKBpEY2rk3j7/PXMDzXyyhad0aPHNZKid2bRbrsiTBldTArVFJT3T3jaVfjkji+HzhesZMSWPFxl1cPCCZUad2pl4NjbsssVfSEcN3/GcchmRgU/C4AaEWy22jXp1IBbR5517++u48Jn6XQ7uk2rw+ciAD2mncZSk/SrorqS2AmT0FTN03gI6ZnYp6QRU5aO7O9PSfuWtqBpt27uX3Q9rzh1931LjLUu5Eco2hn7tfs2/C3d8zM92pJHIQ1mzdze1vzeWDzDV0b1mPF6/oR7cWGndZyqdIgmG9md0O/JPQqaVLgA1RrUqkgnB3Xpu9gnunz2NvXgFjTu3Mlce2pYrGXZZyLJJguBC4C5hCKBg+DeaJSAmWrt/B6MlpfL14IwPbNWL8OT1JSaod67JEDiiSBm4bgT+aWR13314GNYnEtbz8Ap75fAkPf7CAalUqcd85PbigX2s1VJO4EcnQnkcDzwB1gGQz6wVc7e6/j3ZxIvEmY9UWRk1KY+7KrZzctRnjhnenWb0asS5L5KBEcirpYeAUYCqAu/9kZsdFtSqROLM7N5///XAh//h0MQ1rVeOJi/twavcjdJQgcSmils/uvqLIGzw/OuWIxJ9vFm9gzOR0Fq/fwXl9W3Hb6V1oUEvjLkv8iiQYVgSnk9zMqgF/AOZFtyyR8m/b7lzGvzefV75ZTquGNXn5yv78qqPGXZb4F0kwXAM8CrQEcoCZwHXRLEqkvPt35hpuf2sua7ft5qpj23LjyZ2oVU1dj0nFEMldSeuBi8ugFpFyb/32PfzlnUze+WkVnY+oy1OX9qV36waxLkukVJXUid7/EWq3UCx3/0NUKhIph9ydyd+vZNy7mezck8+NJ3XimsHtqVZFDdWk4inpiGFOmVUhUo6t2LiTW6ek89nC9aS2acj4c3vQoanGXZaKq6RO9F4sy0JEypv8AueFL5fytxlZVDIYO6wblwxoQyWNuywV3AGPg83sAzNrEDbd0MxmRLJxMxtqZllmlm1mo/ezzv+YWaaZZZjZvyIvXSR6sn7exrlPfsm4aZkMbNeImTcO5rJBKQoFSQiR3EbRxN0375tw901m1vRATzKzysDjwEmE7maabWZT3T0zbJ2OwBjgmEi3KxJNe/LyeWLWIp74OJu6Nary6AW9OatXCzVUk4QSSTDkm1myuy8HMLM2lHBROkx/INvdFwfPew0YBmSGrfM74HF33wTg7msPpniR0vT98k2MmpjGwrXbGd67BXee2Y1GtdVQTRJPJMFwG/C5mX0STB8HjIzgeS2BFWHTOcCAIut0AjCzL4DKwN3u/n7RDZnZyH2vmZycHMFLi0Rux548/jYzixe+XErzejV4/rf9OP5IHbxK4ioxGCx0/JwB9AEGEhra889B24YDKe7Yu+iRRhWgIzAEaAV8Zmbdw09dAbj7BGACQGpqaiRHKyIR+XTBOsZMTmfl5l1cNqgNtwztTJ3qaqgmia3E/wHu7mb2lrv3BaYd5LZzgNZh062AVcWs87W75wJLzCyLUFDMPsjXEjkom3bsZdy7mUz+fiXtmtTmzWsG0S+lUazLEikXIvlq9LWZ9XP3g/2wng10NLO2wErgAuCiIuu8RWjQnxfMLInQqaXFB/k6IhFzd95NX83dUzPYvDOX64/vwPUndNC4yyJhIgmG44GrzWwZsIPQKSJ3954lPcnd88zsemAGoesHz7l7hpmNBea4+9Rg2clmlkmox9ab3V3DhkpU/LwlNO7yv+etoUfL+rx0xQC6tqgX67JEyh1zL/mUfXAX0n9x92VRqegAUlNTfc4cNcqWyBUUOK/OXs746fPJLSjgxpM6ccUxGndZEouZfefuqZGsW1JfSfXcfSuwrdQqEylji9dtZ8zkdL5ZspFB7Roz/twetGmscZdFSlLSqaR/AWcA3xG6myj8LiMH2kWxLpHDkpdfwNOfLeHhfy+gepVKjD+nB+dr3GWRiJTUV9IZwe+2ZVeOyOGbuzI07nLGqq2c0q0ZY4dp3GWRg3HAi89mdjbwkbtvCaYbAEPc/a1oFydyMIobd/m0Hs1jXZZI3InkrqS73H3Kvgl332xmdxG61VSkXNC4yyKlJ5JgKO7WDTUNlXIhfNzl1o1q8s8rB3Bsx6RYlyUS1yL5gJ9jZg8R6inVgRsIXZAWiakP54XGXV6zVeMui5SmSP4X3QDcAbxO6M6kmcB10SxKpCTh4y4f2awuT16icZdFStMBg8HddwDFDrIjUpbcnSk/rGTsNI27LBJNkdyV1Am4CUgJX9/dT4heWSKF5Wzaya1T5vLpgnX0bdOQ8ef0oGMzjbssEg2RnEp6E3gKeIZQf0YiZSa/wHnpq6U8OCMLA/5yVjcuHahxl0WiKZJgyHP3J6NeiUgRC9ds45ZJafywfDODOzXhnrO706phrViXJVLhRRIM75jZ74EpwJ59M919Y9SqkoS2N6+Apz5ZxGMfZVOremUePr8Xw3u3VHcWImUkkmD4TfD75rB56itJouKnFZsZNSmN+T9v48xeLbjrzK4k1ake67JEEkokdyWprySJul1783nogyye/XwJTevW4JnLUjmxa7NYlyWSkPZ7n5+Z3RL2+Lwiy+6NZlGSWL7MXs8pj3zK058t4YL+ycy88TiFgkgMlXQD+AVhj8cUWTY0CrVIgtmyK5dRE9O46JlvqFzJeG3kQO49uwf1alSNdWkiCa2kU0m2n8fFTYsclPfnruaOtzPYuGMv1wxuz59O7Khxl0XKiZKCwffzuLhpkYis3babu97O4L25P9O1eT2ev7wf3VvWj3VZIhKmpGDoZWZbCR0d1AweE0xr1BM5KO7OxO9yGDctk915Bdx8ypGMPK4dVTXuski5U9IIbjqul1KxYuNObp2SzmcL19MvpSHjz+1J+yZ1Yl2WiOxHVL+umdlQM8sys2wz229HfGY2wszczFKjWY+UrfwC5/kvlnDyw5/y/bJNjBvWjddHDlIoiJRzUeu83swqExrD4SQgB5htZlPdPbPIenWBPwDfRKsWKXvh3VkMObIJ95zdg5YNasa6LBGJQDRHNekPZLv7YgAzew0YBmQWWW8c8AChHlwlzoV3Z1G7emUeOb83w3q3UHcWInEkmsHQElgRNp0DDAhfwcyOAlq7+zQz228wmNlIYCRAcnJyFEqV0vDjis2MVncWInEvmsFQ3FfEX25zNbNKwMPA5QfakLtPACYApKam6lbZcmbn3jwemrmA575QdxYiFUE0gyEHaB023QpYFTZdF+gOfBycZjgCmGpmZ7n7nCjWJaXoi+z1jJmczvKNO7l4QDKjTu2slssicS6awTAb6GhmbYGVhLrYuGjfQnffAiTtmzazj4GbFArxYcuuXO59dx6vz1lB26TavDZyIAPbNY51WSJSCqIWDO6eZ2bXAzOAysBz7p5hZmOBOe4+NVqvLdE1I+Nn7nhrLhvUnYVIhRTNIwbcfTowvci8O/ez7pBo1iKHb922Pdw9NYN301fTtXk9nlN3FiIVUlSDQSoGd2fS9ysZNy2TXbn56s5CpIJTMEiJwruzSG0T6s6iQ1O1XBapyBQMUqz8Auelr5by4IwsDBg3rBsXD2hDpUpqqCZS0SkY5L8sXLONUZPS+F7dWYgkJAWD/KJodxYPn9+L4b1bqjsLkQSjYBAAflqxmVHqzkJEUDAkvF1783n43wt45rPF6s5CRAAFQ0L7atEGRk9OY9mGnVzYP5kxp6k7CxFRMCSkrbtzuW/6fF79djltGtfi1d8NZFB7dWchIiEKhgTzQeYabn8rnXXb9jDyuHb8+cRO1Kym7ixE5D8UDAli/fZQdxbT0lbT+Yi6PH1ZKj1bNYh1WSJSDikYKjh3Z8oPKxk7LZOde/K56eROXD24vbqzEJH9UjBUYCs37+K2Kel8nLWOPskNeGBETzo0rRvrskSknFMwVEAFBc4r3yxj/HvzceDuM7ty6aAUKqs7CxGJgIKhglm0bjujJ6Uxe+kmftUxiXvP7kHrRrViXZaIxBEFQwWRl1/AhM8W88i/F1KjSiUeHNGTEX1bqTsLETloCoYKIGPVFkZNSmPuyq0M7XYEY4d3o2ndGrEuS0TilIIhju3Ozeexj7J56pNFNKhVjScu7sNpPZrHuiwRiXMKhjj13bJN3DLxJxat28G5fVpxxxldaFCrWqzLEpEKQMEQZ3buzePBGVm88OVSWtSvyQu/7ceQI5vGuiwRqUAUDHHk84XrGT05jZxNu7h0YBtGndqZOtX1TygipSuqnypmNhR4FKgMPOPu44ssvxG4CsgD1gFXuPuyaNYUj7bsyuXed+fx+pwVtE2qzRtXD6J/20axLktEKqioBYOZVQYeB04CcoDZZjbV3TPDVvsBSHX3nWZ2LfAAcH60aopHMzJ+5o635rJhx16uHhzq9K5GVXV6JyLRE80jhv5AtrsvBjCz14BhwC/B4O6zwtb/GrgkivXElXXbQp3evZu+mi7N6/Hsb/rRo1X9WJclIgkgmsHQElgRNp0DDChh/SuB94pbYGYjgZEAycnJpVVfuVS007ubTzmSkce1U6d3IlJmohkMxTW59WJXNLsESAUGF7fc3ScAEwBSU1OL3UZFEN7pXd82Dbn/3J50aFon1mWJSIKJZjDkAK3DplsBq4quZGYnArcBg919TxTrKbfU6Z2IlCfRDIbZQEczawusBC4ALgpfwcyOAv4BDHX3tVGspdxasn4Hoyal8e2SjRzbIYn7zlGndyISW1ELBnfPM7PrgRmEbld9zt0zzGwsMMfdpwIPAnWAN4PO3pa7+1nRqqk8ycsv4NnPl/DQBwuoVqUSD5zbk/NS1emdiMReVNsxuPt0YHqReXeGPT4xmq9fXs1bvZVRk9JIy9nCyV2bMW54d5rVU6d3IlI+qNlsGdqbV8Djs7J5fFY29WtW5bGLjuL0Hs11lCAi5YqCoYz8tGIzt0xMI2vNNob3bsGdZ3ajUW11eici5Y+CIcp25+bz8AcLePqzxTStW4PnLk/lhM7NYl2WiMh+KRii6NslGxk1KY0l63dwYf/WjDmtC/VqVI11WSIiJVIwRMGOPXk88P58XvxqGa0b1eRfVw3g6A5JsS5LRCQiCoZStq9r7JWbd3H50SncMvRIalXTn1lE4oc+sUrJ1t253Dd9Hq9+u4J2SbV58+pBpKaoa2wRiT8KhlIwK2stt05OZ83W3Yw8rh03nqSusUUkfikYDsOWXbn8dVomb36XQ4emdZh07dEcldww1mWJiBwWBcMhmpW1ljGT0lm7bTfXDmnPH3/dUUcJIlIhKBgO0tbdoaOEN+bk0LFpHf5x6TH0at0g1mWJiJQaBcNB+GQqpZXxAAAKSElEQVTBOkZPSmPNVh0liEjFpWCIwLbdudwb3HHUoWkdJv/+GHrrKEFEKigFwwF8vnA9oyalsXrLLq4e3I4/n6g7jkSkYlMw7MfOvXncN30+L3+9LNQu4Zqj6dtGdxyJSMWnYCjGD8s3ceMbP7Fk/Q6uOKYtN59yJDWr6ShBRBKDgiFMbn4B//dRaLyEZnWr86/fDeDo9urjSEQSi4IhkL12Oze+8SNpOVs456iW3HVWN+rXVE+oIpJ4Ej4Y3J1/fr2Me6bPo0bVyjxxcR9O69E81mWJiMRMQgfDum17uGXiT8zKWsfgTk14cERPmmrsZRFJcAkbDB9nreWmN39i2+48xg7rxqUD22jsZRERoFI0N25mQ80sy8yyzWx0Mcurm9nrwfJvzCwlmvUA7M0r4K/TMrn8+dkk1anOOzccy2WDUhQKIiKBqB0xmFll4HHgJCAHmG1mU909M2y1K4FN7t7BzC4A7gfOj1ZNyzbs4IZXfyAtZwuXDmzDbad3UWM1EZEionkqqT+Q7e6LAczsNWAYEB4Mw4C7g8cTgcfMzNzdS7uYTxas47pXvqeSwVOX9GVo9yNK+yVERCqEaAZDS2BF2HQOMGB/67h7npltARoD68NXMrORwEiA5OTkQyqmTaNa9GnTkHvP7k6rhrUOaRsiIokgmtcYijtpX/RIIJJ1cPcJ7p7q7qlNmjQ5pGJSkmrz0hX9FQoiIgcQzWDIAVqHTbcCVu1vHTOrAtQHNkaxJhEROYBoBsNsoKOZtTWzasAFwNQi60wFfhM8HgF8FI3rCyIiErmoXWMIrhlcD8wAKgPPuXuGmY0F5rj7VOBZ4GUzyyZ0pHBBtOoREZHIRLWBm7tPB6YXmXdn2OPdwHnRrEFERA5OVBu4iYhI/FEwiIhIIQoGEREpRMEgIiKFWLzdHWpm64Blh/j0JIq0qk4g2vfEpH1PTMXtext3j6iFcNwFw+EwsznunhrrOmJB+659TzTa90Pfd51KEhGRQhQMIiJSSKIFw4RYFxBD2vfEpH1PTIe17wl1jUFERA4s0Y4YRETkABQMIiJSSEIEg5kNNbMsM8s2s9Gxrqe0mdlzZrbWzOaGzWtkZh+Y2cLgd8NgvpnZ/wZ/izQz6xO7yg+fmbU2s1lmNs/MMszsj8H8Cr//ZlbDzL41s5+Cff9LML+tmX0T7PvrQbf3mFn1YDo7WJ4Sy/pLg5lVNrMfzGxaMJ0Q+25mS80s3cx+NLM5wbxSe89X+GAws8rA48CpQFfgQjPrGtuqSt0LwNAi80YDH7p7R+DDYBpCf4eOwc9I4MkyqjFa8oD/5+5dgIHAdcG/byLs/x7gBHfvBfQGhprZQOB+4OFg3zcBVwbrXwlscvcOwMPBevHuj8C8sOlE2vfj3b13WHuF0nvPu3uF/gEGATPCpscAY2JdVxT2MwWYGzadBTQPHjcHsoLH/wAuLG69ivADvA2clGj7D9QCvic0rvp6oEow/5f3P6GxUQYFj6sE61msaz+MfW4VfACeAEwjNFRwouz7UiCpyLxSe89X+CMGoCWwImw6J5hX0TVz99UAwe+mwfwK+/cITg8cBXxDgux/cCrlR2At8AGwCNjs7nnBKuH798u+B8u3AI3LtuJS9QhwC1AQTDcmcfbdgZlm9p2ZjQzmldp7PqoD9ZQTVsy8RL5Ht0L+PcysDjAJ+JO7bzUrbjdDqxYzL273393zgd5m1gCYAnQpbrXgd4XZdzM7A1jr7t+Z2ZB9s4tZtcLte+AYd19lZk2BD8xsfgnrHvS+J8IRQw7QOmy6FbAqRrWUpTVm1hwg+L02mF/h/h5mVpVQKLzi7pOD2Qmz/wDuvhn4mNB1lgZmtu9LX/j+/bLvwfL6hIbUjUfHAGeZ2VLgNUKnkx4hMfYdd18V/F5L6AtBf0rxPZ8IwTAb6BjcrVCN0LjSU2NcU1mYCvwmePwbQufe982/LLhTYSCwZd/hZzyy0KHBs8A8d38obFGF338zaxIcKWBmNYETCV2InQWMCFYruu/7/iYjgI88OOkcb9x9jLu3cvcUQv+nP3L3i0mAfTez2mZWd99j4GRgLqX5no/1RZQyulBzGrCA0PnX22JdTxT271VgNZBL6NvBlYTOn34ILAx+NwrWNUJ3aS0C0oHUWNd/mPt+LKHD4jTgx+DntETYf6An8EOw73OBO4P57YBvgWzgTaB6ML9GMJ0dLG8X630opb/DEGBaoux7sI8/BT8Z+z7TSvM9ry4xRESkkEQ4lSQiIgdBwSAiIoUoGEREpBAFg4iIFKJgEBGRQhQMEhfMzM3s72HTN5nZ3aW07RfMbMSB1zzs1zkv6AV21kE8Z/q+tgqH8HrbD+V5IgoGiRd7gHPMLCnWhYQLeu+N1JXA7939+Eif4O6neahVs0iZUTBIvMgjNI7tn4suKPqNf983ZTMbYmafmNkbZrbAzMab2cXBGAbpZtY+bDMnmtlnwXpnBM+vbGYPmtnsoB/7q8O2O8vM/kWowVDRei4Mtj/XzO4P5t1JqDHeU2b2YJH1h5jZp2Y2xcwyzewpM6sULFtqZklm1i+ooUbQ8jXDzLoH69wcVuNfiqmnebD9H4OafnVwf3pJNInQiZ5UHI8DaWb2wEE8pxehjuU2AouBZ9y9v4UG9LkB+FOwXgowGGgPzDKzDsBlhLoP6Gdm1YEvzGxmsH5/oLu7Lwl/MTNrQaiv/76ExgOYaWbD3X2smZ0A3OTuc4qpsz+h8UKWAe8D5wAT9y1099lmNhX4K1AT+Ke7zzWzkwn1s9+fUAvXqWZ2nLt/Grbtiwh1P31PcIRT6yD+fpKAFAwSNzzUa+pLwB+AXRE+bbYH/cKY2SJg3wd7OhB+SucNdy8AFprZYqAzoT5oeoYdjdQn9CG8F/i2aCgE+gEfu/u64DVfAY4D3jpAnd+6++LgOa8SOrqYWGSdsYT6/tpN6G9AUOPJhLrGAKgT1BgeDLOB54LOBt9y9x8PUIskOJ1KknjzCKFz9bXD5uURvJeDTvWqhS3bE/a4IGy6gMJfjIr2DeOEvoHf4KFRsnq7e1t33xcsO/ZT3377+z6A4l6/qEaEPvjrEur7Z9/r3RdWYwd3f7bQhkJHD8cBK4GXzeyyQ6xREoSCQeKKu28E3uA/QzZCaDSrvsHjYUDVQ9j0eWZWKbju0I7QKFczgGuDb9qYWaegN8uSfAMMDq4LVAYuBD6J4PX7Bz0AVwLOBz4vZp0JwB3AK/xnaMoZwBUWGo8CM2tpoT76f2FmbQiNXfA0oZ5o43acaykbOpUk8ejvwPVh008Db5vZt4R6ldzft/mSZBH6AG8GXOPuu83sGULXHr4PjkTWAcNL2oi7rzazMYS6fzZguru/XdJzAl8B44EehE4DTQlfGHzLz3P3fwWB86WZneDuM82sC/BVqES2A5fwn774IdT76M1mlhss1xGDlEi9q4rEmIVGILvJ3c+IdS0ioFNJIiJShI4YRESkEB0xiIhIIQoGEREpRMEgIiKFKBhERKQQBYOIiBTy/wHta4HcJ7ergAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix, encircled_flux)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "75"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(nbpix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[30:], encircled_flux[30:], 1)\n",
    "bkg = p[0]/resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "193.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbpix[30]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.6879684551015494e-13\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.14570092e-13 1.54335340e-12 2.75125265e-12 3.92232927e-12\n",
      " 6.23420990e-12 7.35778840e-12 8.47726202e-12 1.07029305e-11\n",
      " 1.28997878e-11 1.39912829e-11 1.61720325e-11 1.72580137e-11\n",
      " 1.94299981e-11 2.15966232e-11 2.26820041e-11 2.48531217e-11\n",
      " 2.70199567e-11 2.81035042e-11 3.02635507e-11 3.13461059e-11\n",
      " 3.35078771e-11 3.56662593e-11 3.78278769e-11 3.99843395e-11\n",
      " 4.10649282e-11 4.32245831e-11 4.43048331e-11 4.64612070e-11\n",
      " 4.86176430e-11 5.07706779e-11 5.29236212e-11 5.40009656e-11\n",
      " 5.83087071e-11 6.04628514e-11 6.15390538e-11 6.36872336e-11\n",
      " 6.58402478e-11 6.79900385e-11 6.90678636e-11 7.12196640e-11\n",
      " 7.33704945e-11 7.55214317e-11 7.76729888e-11 7.98230941e-11\n",
      " 8.19748968e-11 8.30508413e-11 8.52034542e-11 8.62791522e-11\n",
      " 8.84309558e-11 9.05795420e-11 9.27299913e-11 9.48776914e-11\n",
      " 9.70329639e-11 9.91837428e-11 1.01332717e-10 1.01870522e-10\n",
      " 1.02946894e-10 1.06170102e-10 1.07244942e-10 1.10469127e-10\n",
      " 1.12618485e-10 1.13692758e-10 1.15840409e-10 1.16915548e-10\n",
      " 1.19063259e-10 1.20138357e-10 1.21212900e-10 1.23363055e-10\n",
      " 1.24435977e-10 1.26583855e-10 1.27658230e-10 1.28733136e-10\n",
      " 1.29805118e-10 1.30879514e-10 1.31147545e-10]\n"
     ]
    }
   ],
   "source": [
    "print(encircled_flux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radii, encircled_flux)\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our PSF does now behaves correctly.\n",
    "\n",
    "Now let us compare our growth curve with the encircled energy curve provided by the instrument team. We use the standard growth curve for 160 µm PACS, taken with 20\"/s scan speed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = open('./data/EEF_red_20.txt', 'r')\n",
    "lines = f.readlines()\n",
    "f.close()\n",
    "radiuseff = np.zeros(len(lines)-3)\n",
    "valeff = np.zeros(len(lines)-3)\n",
    "i = 0\n",
    "for line in lines:\n",
    "    if line[0] != '#':\n",
    "        bits = line.split()\n",
    "        radiuseff[i] = float(bits[0])\n",
    "        valeff[i] = float(bits[1])\n",
    "        i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb65d810be0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff, valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 100])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will work below 30\" where our PSF is well behaved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb65d783550>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff, valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb65d763f98>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff, valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux), label='Our PSF')\n",
    "plt.xlim([0, 60])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "rfactor = np.arange(1.,2., 1e-3)\n",
    "ffactor = np.arange(1.,2., 1e-3)\n",
    "# work with the data points between 3 and 10\"\n",
    "idx, = np.where((radii > 2) & (radii < 10))\n",
    "xv = radii[idx]\n",
    "yv = encircled_flux[idx]/np.max(encircled_flux)\n",
    "resid = np.zeros((len(rfactor), len(ffactor)))\n",
    "for i, rf in enumerate(rfactor):\n",
    "    #print(i, rf)\n",
    "    tck = interpolate.splrep(radiuseff*rf, valeff, s=0)\n",
    "    yfit = interpolate.splev(xv, tck, der=0)\n",
    "    for j, ff in enumerate(ffactor):\n",
    "        resid[i, j] = np.sum((yv-yfit*ff)**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fb65d6ccdd8>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KWtOrMAQcWIiSE4GyXsXhSiUCIYGJd4QzhS3WIAJltuI3Gc72Az1sCSIObOXOHdAyW6lMzFtK2+Bpe0IMMrNzEoPa5z6oX7kwPDWghLNAOtu0oKASllx9ll0uGcCN7Wh+am9/Ryv0RRSiL6rfaHoNwtL8VcT6oyCjlRAg5mTHIWa6WhWB1BFDfFVIFLcQ939Tu4r4w2KRsuJfClChzlgMVLKilvU/QrxyWSplLaHrVVR8IRGBFu7KW/VXMRGI4iBeuO3K1m8pcW41sA2GlQh0RGH7xm06hEpf/gU980hdeES34r1sF+IgBpkFCLVDXLgWZtLiPmQx6MLw1IACuG/vleDK3GWxDaBSMRVJMNFoFTGAHHPBIi7wjYV0Ze0qzmUE6L4c5eeZrZhDGzDTqxhL0dliTGVpfi/wwswKFgsV3xzffxNBhXTSsBeD0M3LeRXiFh/MyuzKusn4C+xFvWblXr9L5a8iIlDYB1SIQLZb4IQIpHlmCtsXJyLNzMuz3csrExYmYLmbaHDUy9azlenRCCdNzFtiUBB7cJuKQUe8ba8MTw8oCsABVKL4uslUvK7FySd9/w+o62kIzVwrs4WwyOprdqNWPDkzsM5I2yzIjrHsBPds83NZxR+m6Xj4DplE6yZTYZCYl3XpEW5BLm4YOPGMExUbFaTXm4hE8I/KuSmqb1kQdiwb0Iu4E85XQSECLdxMz14EWnhTBGrN2FbY6mcOPGTCVvzu5QYGGtfEqy224i1BW2zlERNz31DodHLKRLz52LMYmyxFvj0x6KLw3IBCHjAwZSp6OTAV6qndlAyonmQFzKuWCMECxOJhq34gRELtRfQxEUjdO83NMwHLLPg0dWjzG15EvDKxB6sAiOh6HFNRL1piZS2tHcpUotK2/SMXv6CPPR2TFqdMRXtSPWUlmgijvwpjrldJcjz77+T+MjDdCzRT2M7OWdliK94Zzs5ZocryU7AVKOh0tpLPW9lziGtDelTa5sOc1HflznKomCmDd3YyHzAzXxmeG1BQgPHaJpApHDWfij/V/gRq/6kC11Y8eCoOeAuQ+YPQ0ibCws1cm0UgBRHVregqrMASzq5FdEBz+4MUEei+gm9LA6jbAro7huJBBTDnN0D7Q5SzC+QkODbkVUsP84YFKIANDFl4aWALVoDXvBzFHxK2pKIJOvsYjkJwIpA5wnkRiEiISstjoL+lsE2bDD1bgTjU6XgoneHAeFlhYtGe30oTQebu+14Myg5xZ5W2GVhUDPIHQGUx6DCwXBieHlBswBG67qp/A/NTMYank6PsqMARC18V7i7w6g5/F2CBTMuXwHdaYJ1A0l49hlKXVU0LTSlWBtliTqvsW/H6FQcqdEevP6lqmJoDWgMeE9JcC5w4FLqo54lijqRmZa2AtG0uVF2gznywA4kGClMRSDcYOhGIRIGLhdv3lG+dFbZ25KRT2HrzsnZPa1vtDOeZSVbYriC8ER6R2UoUi7rSNujPioOcgg8LgKNikL1IIQblvUFarlkIdOLYx+xveGV4bkAh7XPxyPT9JUzF5qVSZy80VzZ2k+G7fiX4qlA/AqHtsQfaYODuBLciikDMxlbIiT5eDAKAsPfHB0uHtdmYilqC7kAXUFYRb6L4Iy1t7yWg0sQhZStk9S2gLuYoG3F5AqgIa7EDm3TRBvrmQmUvE70K6PUiUKWwBfp5K4zxnJXMVgZLkLCQrY2GylQeZStZDPIm5iNi0J1Fo0fKOPQs5cxiRjFoZmaO/ivXhecGFHQQB/zq5QBXViM1Q5KylKXR+2FXMABbHUUcANgdM9kmox2BALReWgFScaMd5iEAtAL3/vMLbV420QU3mV2ryBB7e3/k2XCtIHRbuqggf5tj3MhUzKQr7+NPf2t8X9pfjSZvxnWT3ViJgLbmCpsI0fNlvYr3XwEK71ovAi3kTNOtrbQICE0Utgow/pyVbF5uIgIHSxCW1VjIPYlFM/PyyrfBb2XGVoxlAIGtzPYFRTHGsxgUzATIpucsBvW8+h4Txe1F4akBRed7AJWCqbQJgsBQmLQPVU7v8a04t4KS6leom5VfukMciZObetaCGnMg4iYCJYUtxFpDd9GhqFJCgcVeR64HfxEn+qiy6O4PhBT+/6YNXIZjKqpfunlATTuVrTM8a8k9bx0V/Wq8zkSBGwIqLGVu6VVUBMretV4EQvs7c4RjRIVt6WErTchHIgy6FWE3LxArj9/NXLAV/efZSWs67ZqYz3ra5oOy9STCm4HVEac4YeMb+pUrw1MDCgAbVEH8SUxFFwYPPsQeiJTy97kd4vVaBy6iWVlaYh/Uz71mWo6nkQJA22WMNnFWYRpysPXmhkJzCBPRZ0VbSa0sOWvrBseMHFNJi6oBqoMjs/qgv6+BsjWt3q1scETY16soY3R6FcMy9aRdEHctexFI9SgU4/S4bzJGQQYmi95rm5gG87Lvoj3XfavXsZXst2Lu+0kM0udWRulp68+zrTxtBzHohFNcFoP6e+g7Of3KheG5AcWLMyrKANhkKm6uqjWtF8aRwRCMlSwBWBjerKwsJrjr3xs6sZqWgwjUPEg7W2kgMQJL8c7JXb81VtqmE5C5+agE5bBjKm9iP0AYQWM1kbGYA5yOSA/Iulu5sgAtvWjTwWS9io51QhB5gmmZ0UBCzdGEbSuQ5Fe24ncukyCqP2dlZl4edi9L84+67nu/lVGXkkzMtroVbMVAZn6YUxaDsjWoOtBpZg2q9SvXhecGFPRVzg5CcuKP0vUAKmk+hkXX36V8XUHbB6KZlWfK2hWjCGQKW91BTKIh5O6Yxjohkgg0vLxjKQtEnyJq12XZBhWvcFXfFHDfqRzEoQ4ewazMvh1JNPIgInOF0Zmh6VVSHqMuSxKBtqxAWjW570ZSmfOwPWpe9pYg7wx3xG9lb09Q5RAXdjGnfUEzMUid4rwYFJW1TgzaMDP7k+JmwHJleHpAsf0f1Jldt7bJ6rX07xdFHcmHEVTMsZBmOdsqy2oBQlfWEqEd2DSUrWv/CpD4r98diGQxCHDLLvrfyqSswc12klsSMGiLTTJpA05Qtl7qfwflrLyrTl77p/nh2IBj2x4weiktfxKBGACtUQTatAL5HcxeYbsgmp4Pmpd1eHhLUP+RsRaC5EjYFYNC92a2Yqgalbbdga0WgwanOKdfqcSgM2bmdu0UtxeF5wYUHbxy8pf2fWYqTQZHn2CF8tq+tYgvbVJwV35TT9Oluf3sqVPOirKWnThktDqJQG3Vk/04S3NQsyVf2EoAFiCCi97rpSpoNagVaSUYUbbFvAAVoE2+NyoXOlARs6/MfkB1LVkpywxeometkSyZM6ZXCWKQ1JFFIO6n7A9WoMoRbqawdaxFmYg3L/ufR/X7gfJxkwvx9FiEK9hKtA6NnrZ7YtDMKS4yF5gYdMTMfK/OB3lFeG5AAUyH0gZCzVSC+KPa/xlTkYHeQDzzi5CzvF79sYxEbZeyn/ho01F/WJxXmLerHlTtLT4lsBwNzI2dqBkZylhIdDdLAkzhwRVT0X5cFJUyc7FK4ZW1HcRcDqc3tDTvSSfihi6WpRVIRCD7TSCblVKhU9iaExzV5mWg+6qY/wrF3ctetxJ+zRCPs5XB8lNah27T4xG6g1y0Bg07ma3TazFIP619FCu/+LyvDE8PKIEmswzmFQOotBVcQAVz8cc60RaOHVAx1oK+ShKLG35bgpnZFmLTq+h3wyJer26rv7KVElj2OsS1VUQc1ac0C4hI3nI8gk14PVP3peVrimHE/T/WQYLaqshVtmHNdsraZGSA73eK38Efbk1a5SL9tbj+RuvztrtZ6rC+lwJVXPMKWwXCDfNydeJ+9lvxh2O/lq14MWh6nm0Wg8DDj5BV1qCpU9xZM/OF4bkBxa1Exkw2xJ8BVLL4oxM+1+FNmuQHoIg6Tlnbf0yM5RS4tmoqcylFIFa2sjqAafEzYLHmCXPhyvqjgQUWzeENps6DiV75paVcUBPjFpjvipqViZvw1P6S5HcERphhEHsMPDDoVbwIxOD+TUm/5cQRTn1WCOcUthT3A6luxbOVM34rM2ABVkvbFIMGXcp5MSj/bOrsiIQt/UoGlivDcwMKYIOj/bynAxV3UI8HFW+RGBwOk75K87SBSjaRR87iJqBYR5jbYF9egDBbFzQWIOBFLx0fTGG7yqlsjHa9rpFXO13K1JHRu+t7NwNjYLISL4u0F4n9RFAhg4r2l2RCqnJWpTpi51YCiLXmmL9KFI+U4cGYSji4yYtA2WfloMKWEP1YCHBKWpjrPnDMb2UqBmHRL5u6d660NbZyVgwCMJzfAYTrCCZ5n08Uee6YDbDHwpMDCndavB4DldaPjoTrmNX+9iwUCIwEa08ZQEVYzIo2qFc08WR9I/4loM6A7CQ4uV51hXQKW6eoDUrbPce3KuhJcCyTa3EOcOjOdqO+Yw4qi+gvVDlru5WTUlY7WVljFI0Q/VWcCNTA4KAIJHnNZ+WswlbGgwKGspX2WaO7wLKspqCt/FYuMzE7tlL5ruiANqc4jOeuZDEoe9tGZW3tv6Kn4l8VnhxQYDtQN0FFByo6qARW40EcaOCOztojeExAhQHbxayjX7m/KRx11ZVBreerkC9ZJjlTZyvr2g55WmkUg0JnuPtsWlZ3fVXSLklhK2dpn2Uqjmu4jsh8xHVkFo18NZVpeWnvzeBwyn4QgVT3tMApoJPCln09tcLWi0gztrJlCTrEVuiY0lYn/sx3xe7hnt2xBlWn8Lf6CyZjZX8Oijy7oAKnU3FjS8UfY5UoQMWx7s5anFlZVzkvjuhEX+VJYyjc9Soy2ATbehniCMeMwFawAkRODNoCllnwIpu3/AiYqHXKu8wPb+82SZr4mM3KM2WtEyHsStJtDJOr35gKgnetVzUY1Vi4x5cKW3S2ovmJwCzKcP2OKhoBpet+ZiszS9AVbCV2/bbSdiYGVb/HnM+13TUzXxieG1B0AIAiqHACkSz+LH0wM5oYEHQnsiDY4HXVRdbiJprreD2LNiv2/ObCYFpWxapT2LaDqcW8rKIPFgOSElhAx8EFiACjrzEBFa3CDvJW0ACjbwdI11DFbRJl5NkOMu4VJiLQYAXSuEVYFU4obD1bIXGrEyaSLUHZdT8qake2MnPfv6sMZSDVWIjuYj4jBh0GFsyPSDgDLFeG5wYUoM9yz1QAGyjhR6Q8qOhg1YGmolFW0iKxQ2TWoowDfaByyL1x3f4aAN2TIOCZz+rqNkWtvBP0RbhPyL1uc6JPK99f9/c2NwY1I9/rd3AcOV7LBLRHLOz4qxBqEUhoTDi7lvw3nShsFWTyfiD3cx6sv3SodRa6FTiWteVlO/vxMZJ7ZTC6i/mUGOQpWsFgwrOTIxIqb9vWyU708fcXhc8OQDFNPkamsh4AFWUqTvwxMcgDhYaBtSj9RwQB5fBKuSt/lbscQ6BLZNtg0R5b20rXBjIDKwdFbRSDtDrXlrwPSCe27hWCtPUWAWbw42HPqHLnR1BpjEQ28wmLsI2GZmlzHclA8FeR/i5FIFe/P7vWwEffx5v5GU2EEeYRNhkqoyvMyyYaO90Ko/ZbmXnZbolBWtmlYlACGmUr5REJSb9SmZnNf+XC8FkAKDKgVTY+y1SCGMRd/PFpxoCkzjxPAfQDmNz3NopP6aHEUBbx9WBNS1lznfqdl0oMGkrYD1m3ort7ZbKpWz/dO1Npp9bX76JK79gSd08uiYo0/4RO9GRaVrEGJuKgOzl6ESgrbHVsyDjpSMGBtTD8MRi23IjOi0y3Amz7rbTPVR+NoK96VmlrPi0liFRHJrT0am9QZy9Rv+Ld+K8MDwMKEX0cwPcB+EfReuLTzPxdRPTlAH4AwNcA+N8A/GvM/OvUePF3AfgmAP8AwB9j5p/ergSmiIX9DnDBVNaToKID0i1ynql4JS5IBrIqYHWAe6ZSpAW9yorm+KbWJxOBHF6qsjgzlkKfosCiVp3DITvAgZqL/m0JoNJffBR/aOXmALf0OF++shFony6TNO3nJV0rqzR2qeymcIRTlPEKW8dQyiMRknk5AJ+mu5/yqNgKEP1W3oaJWYO3BuVzV2ZOcdXPe+TfDQr6lQvDaxjKC4D/gJl/moi+FMBPEdFfBvDHAPwoM/9ZIvoFS3nEAAAgAElEQVQOAN8B4NsBfCOAr5N/fwDAd8vf7eAHwYypnAUVWf3DpsJRNG0TXEUnmwh9RS8a69BJ7v016TooIpDPCrSK7n1PjqKW+U7c3fS9tUy8Un98C1y8GKT30hpTcidQ6b+v496F/HslUMlsxN9J2kyvYtdZr2LikPYf+kKj5a9O57LAmEf/xu4b+E+jbEW/sTEe6sB2AVs5a2L2okwlBpnviq18SQyCUtkuBlX+K+Uu2leGhwGFmX8FwK/I9f9FRD8H4KMAPgngn5ds3wvgx9EA5ZMAvo/bUfN/jYg+QkRfLeVMg1eqAq9gKtqfykp04rObLr6PPXvxDEIbtQIWo4PRM5lKr2KOcxoHG02dBcGcu9p4kUaLWZOZ5SR+JAsQArhsfLgg+gDoPioFqGSmopYW6x3xHFZdhlQCRYRs3dGjFga9Sr7WNhjzQHSEE0ZjQMBp5zIBfpNh+0YPsBXCpiVo67yV17AVXd1Uh7K1k7kSgyoz80y/cmW4RIdCRF8D4PcB+AkAX6Ugwcy/QkRfKdk+CuCX3GMfSFwAFCL6FIBPAcDtKz5iA4LtvAsZrEpzUZiUPYhA3c7dNHCWHr//xxBDRQqh4KZAh+CPshkVT7wy3oCisxN2A9BMy8zh4CZSa8QdzXeCBDi0flXGOh0K31s8scxaYS2HgzA1YAdUPE7JRLXe9F7JKhYxbANh6FsHLApGXuzxdVn86p6z52u20vJKm7T7k4etLkIlW6G00dCzGAB5TxBAw4+PXQ0sS+iIpF/ZEYM8KG0f6nRdeDWgENGXAPhvAfwpZv4/ww9ZpaxF3DD6mfnTAD4NAF/wez7KSpVVUAjiD/plUNQ6c6sp9JT+Yg4qwcJGrhbqgz6wREMQtheM81lX8XQPaZipApPC1rnym0WGHbuSey/2lL2+4VlL3IAshJXtWIfGjoQJSGfQnW2XchMRHVPxoBLKVeABsMacplDPXYb+3Yy5JOunjoNBYQtEZatX2BKLblL3AyGal9FYpFmCxGkyW4oICF621U+lzkzMZ8WgDiCjfqUCkSwGddHIyfIAhv1BF4VXAQoRfR4amPwFZv5LEv13VZQhoq8G8KsS/wGAj7vHPwbgl3frUJkWG0zFa/WFjWDhbg1gHZAdVAAEx7YMKgCMqfCtD+QgmjigMM9an08Hm4pHhD4wpf1anp5LqwpbEycgz9xloCgrUraiq6a2RZW3R4NnKWiWn2BJubOzxFD3U1Gm4h3gPL0IMCF5vN7D2Ia8l3jeBnMy3LVaoZbOXkyUQVLYkuKNjAOJB032A2XQmLGVyZ6gt8lWVEcDa2bUr+RT+Gc/RuZ/N0jNzHcGbs/iei9Wm+8B8HPM/J+5pB8G8K0A/qz8/SEX/yeJ6PvRlLG/uac/afXAVrIpU3GK2vZQf74zlAgqPuSdyvp9qq0R4dqRjxbv2IonJtqoMNE9e5F3uDuFrfqswIqEir7GhLwYpLoMA+A4pY8Ga7f8Zy1ScFVQubX28SKgkvVDkYsMIJN9rWyDpT6pIOauu/iX06T/NE9S2CqYG4vxVi4Cwu7lgq2QAF/YEyQL2xZbYd52iDvCVsA01a94de6WU5wpYZ1HY3eSex6G8ocA/FsA/hYR/Q2J+4/RgOQvEtG3AfhFAN8saT+CZjL+DJrZ+I8fqoXY9AsBVDxTmSlqgc5UxKJjs4Up6kZ05ZNJbloC7uNsABK2b44unsig29CrBPaihecJuSYPW1UE64RRpW0FLJLQ6Lrvyg5og7hjjnsURB/r7zuDbqhBRXtLmYpOcpNHYWykNa07xVl/GlspXPZNlEAQgSxO251FIAURxyADW5G27rGVwXXfAVxmKwosrUn1ZsOzbMWLQVvnrsCaX58UN4pGy+mN7XvhNVaev4r5IvgNRX4G8CfO1EE2OARUzEzqmIoqM7XXZQYH8QcRZILeRFd9wmhWVnEJqC1A+jEy8UjAESw5KgLpSiNWIS4UtiSgArHumN+KKmlFDJoCS1LUllagvECxuqcXoCKWM88SOltQE2piKLZdgFx+BzQCGNYy1av4tHztrEBBBFKxSutU8NX2qly0cACaTbZSWIK0GG8J8sCCBeVmwyvEIH/uSqVfySfFVfqVIe7C8PSesiTiDNtH3xF/gHAdgaQAFRz0VfHiD5D0L25FtevCX8V/O9M7FPdeJ+EZlS9D61ZAFD2NvQ8gwOLqXB4cPNqdwgJNWamLepsBooOSv3dJ0Mnpz4yBS1tjFVZgvynEIylCATmB28BWFrcoiMgzZSv6E6meZekhTQI23su2gZaMRRW9VwS2og5xTQRq5TwqBqloU+lXSmuQ069M/VcuDE8PKG31QAeViqlkRS2AAVT0Q6vsqwCRzcwbviphMueBXA1y769CDowCM0FX5pYK23at5+laG5SWezFolQktK/oALMpgjgZlKfKcAbiAylSnkkHFFLIK/tqP7HxXpF+9eAN9d8cM3bWykMBWAGMfrbuiz0r4NvJdAlth7ruXHQN5DVthmbxNBHodWzEQkRc9620blbQt7srw9IBCOiiA1zEViB+C3lUHNQHmULpnVh52LfvJawwH1sK4nwbRPV1XQpvr8p4COkFhq/k9wVEAgWMOjAgsq9afJnTV4YDpudt10dcboGIMQUHlJqu8FqxtWBAWgWqTYGMa0mplkJLevh2kDR2wvcUH6F60Bj76nRW01bxMQNi9LGykNyixFeo+UN5vxU7eVz0dMVbZ7Z5/3F1L32Mrd6Zd/Ur/hqM1KLxCVtJeGD4LAEVW6wwqr2QqNuBVZMhmZriVEMBgAfJ/vV7Fr4KBtcgko75SBhO0s+q0eDdw1dqgoo0frEB7jslWN32nACxmNmGrZ+K9Ym2wsgOLKECF5QsIqKhIYJ2io95EHrk2RuKUtUuv32r1ehXPTtCv7TsUIpDu6TF9tbCVYT+QPed2LyvrqHQr2qWerej7FWxFv736q6h1aEXPt8VWshgUzlnB6BSng3jwtnUiz9MoZd9JIPWBmICKDNRSUavu4N56AmEqTq4POhTAgZI0AYgWoOCFi66sBYJeBf5D2SLXwcxEIF3ZVh1AjRFFsSixlT5SEbxskxiUgcUsPzcVoYCjI8pYiiMa1h9gsb4IqBDEd4eM4ZUWILk2MFDxyAOHAYbqozzS2GftAKQsZKaw9as1wUQSYytSjwKNbTTMliAFFu1oJwb18gtgWdaSrTwqBs30K5W3benGj2Pf/2h4akAhdIayCSqV+GMjX0vrKySvCkYwlmMgYROe/FNGr82sPFHWGgBV/ioKQhDAQ8rnFLpBHKkUtoz+Wz8Mezfc3UrqxnsJLPJOFipwyT/fYS8yxuvX0TXAlJdLS4Mz3ZNx+sYUe1wH9FoZ60QgJCDR9ylEU88+oExRFxLHVlQHZMCUNhp2tiKVexOzOr5pWYRwNIL/AbItpa1+BS8GmR5Kx/2OfqX0tg00TstO3/GV4akBBUDvpC1QmZmUtWc9U5EPw5x8VVSHYiyj5TWRSAedKdl01UUfAYxAuQcgcYujnq9iYo8OQBOXaoVt0+47/5U7hfaa6KSsgLX+PtgDsJhWMYHLXihEH+cGN4g/beIXTEXQRzf3adlYPHNBZy3SsV4EYjh8M0bj5o72LfQv9Q/izcuAnbiv7TV/FmMiF7IVARb/W0EzMYiIcV+7YeyIfiVbg2Zm5ivDZwGgAH3G7jAVledXbDMV7iuNrXX+uEXLLwNXCEMQjXTAHVHWqoJ2TRNERxc4KnZ1govC0xiJvG+/j9e2k9cmDARcdHWDKFK7EptchdzfHtl9f3CEC4k1qDQrUectulkTdxKRiG2GeOubZy5+B7ZXyAIpneLfQQTiDjz2Vy1SHmw8a4H41jh28xq2osDilbYElJ62Z8WgI962lZn5c0uHAmUoOjvgrmtQabSXR1BRpqIffsZUNA8gK3lfDT1DMcZxQFnbRo1jIOiv0/LLyra6cuHzk4vU+3bDzlGOmWxPEFbqdSuIcm8PcW+TMRZXuQeXze/jiBpUua1fYpV2Z6ayCLPStnl6odeW5t43sRHTq5g4gO4kRzGvfoMAPIwGaCRLR35GmGFmK4/qVtR66IEns5UtMcgDi55VecbbVoFl0K9cGD5LAAU4CypGpTNTsUHrmMqwv6cPbJY2BOWtDgxWFqErdAKdM3qVoCdB/CvvF5mKvKRDHz1NLehWvFiWxKA25h1jATpjw8mBxr3PhjBhKt05jkezsjZblbrOCS6mobNL1Z8gAYn+VUBScHffs6OsdCu577igO8OZvmvCVrSsvNmwcohTMcjtC+pjdRSDtH/0pz2I+JBTnLcG6drq9StXhqcGFLPMPQAqQfwhyG7tzkQCUxFQaQAhQFI5wDHchIDkU3CQ5yU9iC2u6pleZRRhXF5jOJ2NdMYjnbTWbCU4xGmXlcACx1jaQA+L14ZD3BZLUaGSPahUTEV9VTIzsT+ZvcBYS/vLxjgCO8xmaOrfzNJtssqUVjahUcpsNHLxeZSJoJuY/XkrChoo2Ar5urfZyhXWoMrMHMSgC8JTAwrgZMMHmUpbqcnEoDAavXkZHUhKXxXPRiy9g5V31zdlbn+N0V8lsxB7JTJnKO/PUipsw25keRdJN9RygGMgsgkscrHqaqk9PV/JDEyUpRwBFah+gbsD3OL0Igoijq1k9lKKNXBWIDenvf+KfovAVuQ9KvNyYCuaMR/iZIxDFhXPVvxwrcQg9PgPA1iuDE8OKG3ANbHzFaCiQ5g8pQTgr8OlWI5Wu+sDTnOoMpZRiDquPh3Aq2t14a9iAGTgRH3V9ekbjMbAweLIPeiUtsLOdN9KK0Umv4xw0lVWzbYeXM6MQXb9jwJUgOCJbH2r72iet/p93EQNQOL/9v4HMCrMC7aiwNTNzDVbsVGXD3EidAX6ishWFOS9iCMNPisGlWOXtvcG3ZlKYOnG4+vCUwMKAUbJLgEVR3WZEZ3e3E5lUB/4OqhNhyLPh93KCirGYoCgrHWsZFcEEkYyMI0ZsxEzsTGYPbbC2BWDRmDRvtKqjyGKnQr3AKgE0CiYScvjgSYChS9jEIEqZqN9LnmCedmxFRC6MxwJEJvSE69nK36xuZCtbJmZrwxPDSiA6uIuBBW/HtscScivehWdAt4BTnOJstAmCSOucEBX1gLDKgkd5BPTctfdAN4RLjObDiDado1vQNPZkGMr4t1qbGULWOSNO7DAzUT0dk0Usv6oSbOYYR9UvDKWpR4SxuSVseosp+bmrmTVT+qAqkxHBwntBjMbd+Zh5uVchrcE7bEVku/h2Qqhm5ihCl6OhzkVwLKIKL8IuKk7v8HDCTPzleG5AYUg6EpvB1SMccjky3SSUJqVwxEISVlrjWSdvzKJvbUFLj2Zln316t3UAEveTeevYzZdv6LvoWWQlKFxNjKhozSIQTNg8Q5w8iuEAEZw2Qqpe7dARama+ap0O3Ff6Q0MHHtxDATw9XU2ael6La8e0iiVIczDVg5lOQowR9nKWROztUUqUBBB913Jf00F58QgZto0M18ZnhtQICYwYBdUvHmNGVgV4dc+N6dMBdwVtFmJSZhbgBhhD5ClA1FZy4giEhAVve0VemA4IHFxfhA6hW1mK61reLAENXCEDCyZrF4M2gEWSLnmo+LB5WCIjKUGFXmL7gAH9128H4f1m3TWERHIlK5uPmcQUrai+4Gof1O94YXNeFN62eqHXuCAQlgWIYpBd9eGLWCBA4wzYhAQzMwZWK4MTw0oBI7y3wao6E9PsDABuyaZ/MC2+KNdr7qU5KsCRNCATgHvPetNzYyUBgOsrG8JIhBgQDVV3orCNopFKW9S6iogdnBEo+VeDNLdzoD1iT9wSMUvm/aMIM7shgxK2pU7oAICcJNUAdL4e0yAiQ5eBFIgSHmCz4rLC0QQGvcBdVaiYktQ9AY/JRlbPg0EOxqB5FtIuZtikIzTPTHoqH4l+69cGZ4aUADPUPZBBVBQcWd5ChNok1m1sjugAnRfFc9agNGsjAgQgGMijqH0SdzZDifA8CKQsRMPJPBpjmVUbEYHqT6k2ChxtoP5oBikbMJWeQcOkB48HVxxW6DCSGZlAOqu34950Ae0YS5uYCHKHrrCNgAJZGJqGhxoeFYy81sBarZCPQ7EZqIelLZnxCAPLOZZK64S1L1ttxS3V4anBxTgHKh4hqL3ylY8a9llKu1p9NnkQAWFBQgODPKxCAZG6CJOPo5SAQiarmUhKm8D45CVsFLYBobT8oQzcTNbATXnMmU3B4DFFMZQiEZsx8Gg3WvXM1DJZmX119Ef4rJBkoEHkQ0a+9hW2A75FfDhAMbAq7ONQXkrbIQwMphSaas6PXJlK6NhSj4+rQ26kzl61vaFtSNaK8+bma8MTw8otiAcBBUFjVW4XP85AzamQuzc84WFlDuVgVZ75QCnMKIWIJmkgA6+Tq29IUQXIDbmMLKZ0rRMGPUlJHkrhe2QPzKaXbYiwGJb+VcduNgEltbsfUQJil5fnumZtkHFVnugtzE7xclk9gNJdSIdHFo7Sl2Ky29xZsFLrGSDrZjSXtlKH9THlLYKLP7T77GVE2LQleGpAaWNmYamR0HFBqD/mCrmsH7s0QIEOsBU0nXnJpKSFbNpB/PDehWXP+hNgqlZRhMc68gilWM0M7ZiQAJGP5sFbm8Qev/caAAWwLGWDb1K2L3su9efEMdzUDGzMlHfELhm9gLTq7RrGGMB0DdqEicw6ixj2FCo4lGlW5mxFQXkCVsx9gGg3MWsPWCGhokYpGK6swb1cRzNzB5YrgxPDSgg2G7ICBbHFLUArAPjdWFWdiyE2U3YLVAhgFknsLKTzDq62FAxkf6MTmxEEFBQ4RivCxkb23BMgTnFwbESfWeUbGVwiHNsJYtBxoQ8wwi9dG7168xK9CnygpugggwYbkUnV7Cu+gMIaPtZdClkcUisJZuXGztyoAGUbMXaZt0b2YqCUWYryh7Loycr/QpamSwnwlXWoLDREN2IcVV4bkBBBw+guw0DOKGoBfro8Nf7vip2XqpMIFPQAugzUe5UWcuYe9b6OG2sgoab9abDU3CrRKAMOnoNtEHi2IpR9QRIUL+VkCc9W4hBEVgwMpb2sQxoLBxYDB8FFW8BGvQqFBmNDYMAAr0BzZ+kx3ngGYDG/5M8ma3o8wYwyoyc0taD0SkxyOlXShd+eyQCy+cmQ0EUc4CTTAUdtR8FFSCJQFaWlJ6VtbYKRoEo6FX6064lfdBny1E8KiFe2xEJGwrbyrzclcPiBaodx9qhAqAKPiz5rE7pKUJkLNLHJGKLsRbfbSfCqLDVLzgBFe1Pr1cBunJ2YDRwgAP7dvasNz87tuGPseh1TtgKyWggVxchKGitvdTj9G3L4xHyWJ6JQQeA5crw1IBC4IGRAMeZioaOwReASpho7hoKYM4CVAGIF4HWPvCGfUCMIAINoJB9VDjdE0aFrTEYOPEHsGMP9F0yW/HvWLEVqZhlGd4CFsjjZ4KVRzQFFQDdV6V3QRSB9DNlEcgzEZ8PorDN7MMzFCuzf5+BrVhdBVsBRhOzvkChtDVgOSoGHQCWK8NTA0oOWfzZYypmQgbcKL4AVAaOEa8DN8nu+j6X37HsV0lt4Y5pmar4YJrWgmQUub09NfMZ8xmwwcdNgMV8UuAmfwQWIIKL/zTD4C5+wmMGKtopA1Px38MUtcooeCIauc+aFbbOL2UGRANbsTJ1Qju2QhhNzISwL8hAQhW36M6GAeQdq8k9UZqZ2ZsUrglPDyiLLqsSKqayMm2KP5r3nYEKIe4BAkp3fQMVhulCbZJLnFCIQaHbJnJvvjIPfS173t97nYnPo023/AQv7gxKW8u7ASxajQKANTCCi+6U3guhDDPh6RdMTEWPDDCvUz+lMnj4FV4rw77CNuXZZCvCaEq2ol2or6SLCygqbSWuZCtaZuW7coCtXBmeGlDamGD7jSgDEJwTf6DxR0GFGFgX2E5NPf5PfVUI2xYgGWlmvWEqPWt18tmJ+9oawmhaZllZ7Lk4l+OGRHR2ke7Dira6pq8uD6FbeUzc0fQaWOz4yQpYDPQMRtt7MiIDaR9UPtg2ypArF/3LtestZS1hNC0rC/FxgTX4SqVtChyIeUq2wmO+MPE1r39WGE0Qg9DjLhWDLgxPDSiAU8rugAr7vIigoqLP4dPfWD6iaQM1ixu0OhC91acAlXZXe9baU1ksYoymZcD8DIIi1olACgzDmbbJ96WxHep7fSrmYwpa55Pi0pWpWd362zqIiltd4e0dMAKLdK1+8DwExuBFH9eRhO4sN1XWAn0lX3IcBhGoMxl/LbqViVI3iE2TtG5Sbi3z4pF+yi4Ky0KWnjskBhXWIHD0tr0yPDegyGC5AlQ0HGEqqiQ17SV0YpKtzCaa2ETsad4BKYAKKHjWZhFoEIsIUQRadcImMcmzkR2flXhPnb74MpDLOMdW/LI8AItnFgIK2j/h06dxPhOLrL3Ggo6BCiPtAzL24Cah05cMCltK5mXpe6L+HcySovdA2MFsrARu0jOSeIRSaXtYDNJvYY6P/fMZW7kwPDWgqJVHTcBHxJ8tUNH9PHugEhw86QG9ivNYLEHFwmgiHuIsp2ceboJ4xap7k8hGEJWxSPfevOzqyaBUshUFEf/zqeTy3ny9kbHAVWH9omzm7EB3L38KVOx7dvCArt6OZQzKWHOiwyAuZUYCoGQvZnJ2ylcEZWwHn1Jpa+UmMUjAw46fDN+nL3Ym+lwYnhpQgO4pq+FdMBVlKO3fK5W1+WjJpKz1MNPZyESv4iaINy0DDjw8aNgEiwBRKmw5es8eZiuWJqxpYceUqE/wBCyZag/AYgmJqhQh6FMOgorm7e31PiywydnEBEQRRtcIx2rMvKy4mBhNqVvZYSs6PP1+oi2lrQGLjmNQzVaSGHRleH5A0RkBnGIqQA0qAA6e/ubvL7IAVcpamZyDaTn7q+hA2rICBcBxgHBQYdvuFU0xgpEyEGUlHlgwiXdxHlj8D5FVjAWQz/KKAR/OtPWObYxusTFG5ScaHIPgzjJLVuEaS67ckOb+MaKXrbIVUqDo4GCTHjEPrN21GATuwLIpBnn/nIvCsp9lOxDRjYh+hoj+O7n/WiL6CSL6eSL6ASL6fIn/Arn/jKR/zamGUvylsya69Hs9OCbkSfHezZh8vLtX78F4r34DEge9bpWYFt7l64MoXWvD/Ee2wcourT/DC4xy53Re2nPxHiaHh7wk8ct4rzJ/uydLz+Wxy68TCCmepYz2L8X5/LdeBjvLiX9H/Xc4cPxrYCWgEuIFRPtfDve0yj+X1+KcVczf60l5dr/C7nVvVUjn2DYrS/PKgoI11+PjqImY7NqkoG3PkuTTPGR5rwyvBhQA/x6An3P3fw7AdzLz1wH4dQDfJvHfBuDXmfn3AvhOybcZGiCs0N8OuQpUFhLL3xRU+BSo0IK274fQnNHkH1xc+4dDoGIT2CYu98leAEN/jjfBYpz0CTB2AGHMswUeWicVdXcAOQIsQASXDDAD4BwBFZ38O6DSJznLvw4MYfKHfynvNB+2y7t3wGj/epoCTgAoyRProhpYFFTW3HmvC68CFCL6GIB/GcCfl3sC8IcB/KBk+V4Af0SuPyn3kPRvkPzbDSR+K6DS8tagouUeBRWEZxJbWTxgOFDRfMsIKgYgjnVgSXHoaQFEPKPJZSRmM2MrMb1gK+neA8VQB2l8VwL2vxFY4OOT+BFECJxgLxlUgO4Ap/FHQCWD0IRlGAvhBiwDG5mwl6qcMQ8lZgLHZCKAjO1zjIQ1X++fq8JrdSj/OYD/EMCXyv1XAPgNZn6R+w8AfFSuPwrglwCAmV+I6Dcl/9/3BRLRpwB8CgC+6Ku+BIAqZpsQvKI7sgHoXrIMgOY6FQUVr1MBRq9aLc8NP/Re1+vuAEdMzfwqlp1mmdnRq4SzS6hNXBvYkma/tUP61HgUArtSnVJWd0VHBzrUCluncwkUONzrYGQ3QXvZm3nDvzGNGOgHLfXJCuk9SG/3TnCDZTYZtkBGyrD3pgYSg6+Kdm4JbIUjnANLQsxrERkYN+4ZSH4n2jiyRSmkyWA3R2LVr8Dnq53irgwPMxQi+lcA/Coz/5SPLrLygbQewfxpZv4EM3/iC7/sCwN4nGEqFkecyuiMpOdBYCrxPTeYis8D4FK9iq3u7NL6M361zyv/VATyLAOJdSwxT31PoYxKVzOwlVy/G9hBd0Ou/Bv2GYvrsxmLycGLPgA2dSp7bMWLNQOTKVkHD2xiV9fi2UrBRLroEvNYGxjbYpDkuzK8hqH8IQD/KhF9E4AvBPA70RjLR4jojbCUjwH4Zcn/AYCPA/iAiN4A+F0Afm2vkjzBjzIVl3vT+tPznD9TxZuX26r2egtQu4v+KsHhzQZusZOZEiNZpQ1LtAK1MmFWHlv8HKMZvGflHbliGdhhK/40OMdWWv3cG+BZjIKtm/zs+iSYnWdMpQjD0ZMTpuK/UOmvYn85WIE6oCOYmm0hgDMvT8AxsxxH3qKJWTMltmIWoxWRrchi1S1KG+j7YHiYoTDzf8TMH2PmrwHwLQB+jJn/TQB/BcAflWzfCuCH5PqH5R6S/mPM+04Gyjq8jkSZik87qlNRXUnUpXDJVG5Or1IzFWCmVymZiiprSXreK2sXXfogugsO7GTQq1B7Jihxh3RlAT1fqWCtWMfu/QVKW2MyNDIox1gs/ubfT1gLAD8ZT82RzFQEqCND0b88sIZBCRsYTME6XN4cv3e/XeaotLVnGAMzGZTFF4a34Yfy7QC+n4j+EwA/A+B7JP57APzXRPQZNGbyLXsF+bHhj4JUncoq3P2MTsV8WdCZij8pPx9/sL3/x98f8VUBAHaHIR1gK/6nIiq9ilx5HUB7F7hdza6F/ic+NO0IW5F8nmUYa3AMpOs/YP4vA/tQr9yKmTC7HkX3I9FvIktg1rMA6CLNDqj4HxuzuNWV7dJjv3T+UvQI8i0AACAASURBVLIV78uyxDRrlrKWJW5mDMzG5WOSb+Hr4dgPXkfSyuAxrXVt/30guG9wYbgEUJj5xwH8uFz/AoCvL/L8QwDffLbsRb6oF3E8qDwq/vhytsQf4PUOcCYTsPuYOCEC6fGSMkFLESiDjQ4et2oGt/0DClsDDQcMHoy6IriDgTbft2345zYm5kkJcmWxT9wGFmACLkWYHZBdiT/x67Z2tU8zF4EYyW3fsUZ1TmzpDGVbpZetPod43xaXWOYpMQhA2Bt0YXhyT9n2sq8FlVW+VGYqyj48U8k/fbq9U7m3cQtUWuq1epUcY5PbH8rEbnXSFi6SIKxHQcQzEFvZfLkOcAbdimcLE7ZCQxsK4FAgsv7ioWc2GUvounHprZjJ0O3uPnjaooOt6n52QaV6d99W/XeGrbh4ZSvIcSsiWzFmIuUpsBD6ALkoPDWgEJplZ+XlIVABtvf+VKACTcMRpqKtHEFFZ6GalU8pawl9E5eNYvSfq/AiEAolYmYwgClsu1KWBYCysrcPVM9WKvOyL7/fn2QrE2AZ0sjViw4sNvEd9Qx6AfepSjBJIbznDFSsW9w31c63f/LAxJ8miDIFW1EWk9mKfWxfFlDvCyK08UfS1pQG95muCk8NKABwc/qSI6ACwDo9AEhahabijzIbvBZU2vWuXoW6Mo/9JNIdy4AkUhB5ugg0+qa0SczyW7gyMLmvbnGSc1PU9ZpGcUhffAYOiPcGLOAiPj3rwEPFtjKN26TIwNKqJpv8AGrWom2swgxnJqDikuAhvccdZCvGEvw/rSQCUQAWTIDmQTHoyvD0gAKcA5WsqM2gksUf5qqcDjgKKi2upSmoMOBk0AwqQBxSKEGl5dpgK/76jAgE9J8B0bNrZyWbmFIobP2bObYS0iqxCK3ewD4m5Vr5/pCmKp06sDSWghFYfL9m1nJw8ngFbQUqmUyqG+RUBMpOcsqAlnEZsr96iJOyFbi8hVgU6yvSnBhkwOLqvyo8PaAsYKyg00ylSpsxlQwqjONetQAcW/Gf3d8XoCIz4pBnbQUqBPCaQIUK3xS5MtFGs1JiIYxNha0CCbsJERjHzBLEwPQgp4GJ6L8ERP4Za3xLPwIsDVRdNz1oKt1iKtLLAVTswnCoK2ybAt2lV4yjOpflIFtRECkZiepXwJ97DMWDxwxUNN8eqAAIilrPRipQsfzu+YVGptIYZQQVPcxpBirtzwNOcDqrROQZXPaXJOrowM0MhjFX2DIK07RjIvqayfQcJv7q31zz0AgSro3j6t57whIcsLTzPnAcWOSF9sDFp4/dXzOVxmIiqPhm51EwxmN8ZmYJ8szmKFsRMAlaAdXTXRieGlC849kWqATGcUJRm0EFiF61lfjT8uyfqt9+tN3eBAOoANjzrIWWwX4iFmwFCS68qKMTiGUySBlBYQsPPDJYS+9cdMWuK7diHDLPR4ahwGfnnyK0ccZWmhm3tzWUexBYgG1wOR1CHRhAReMDsOosd0wh/xvMxou8v5y3O2U2GJ81tuLnSWYrF4anBhSgW3mAx8UfANaZg/iT0vJv/7Q2RMtQdoCDSztqAdpy1we5SbzFVjKoUDcZNwax7wjn40uFrQJQZV7mPpEC49AOKYCmP0fdOjMBpQpYjEHhOLDAfRZjLX5npXbCwRDMz678+KVZrqMIZOZ4HGcr5gxnvy44uu/bMJiAkgFLIQZdGZ4eUIAGKsDSwEBAReMz2JxV1Ho/E03LoELY3v9TnVU7ijyw65am0xoDqLScJ/QqVjYQToPbcoQTtrLls9Kv434gm/wq8viJkhW0ifnYpFkw7guSiZPFoDaZ9OECWOAKDiA866UELD4B6YEqDQlUikAMB26UGEwNKpawwVbaYKyd7iqr0REx6Mrw1IBCaBaeO9MAKv0ju2m+w1Q2FbVaIfZBpXKA03CEqXRxKOlVlArzhl7FJlVnD63oxFYCBxljOttIYAOUCtvD5mXPGjTjHltx76DiTxTVMOpvMrD4iSr/xUndm+M+NRhxRh113w9hYEH9fgAV10UdRBzzcGn1coS5biWB0JYviweWK8NTAwoAA48KVLaYSovfV9QGkHBAlUGlzO9BhdF1Ptg2KytDiWuUxAPbehVgm608ACpD/IytZPOygoI3SU/YSgCRQgHbyvdAiW0QsucFainlASzuCGPp3ddjttz3h5AnpwOZACrWpgIoMBeB4EC1rW6SOGMrQG0d8iZr34iLwtMDCrANKjkewPBxt3QqlgfboHLIq7YAlVZXHDpE6tLvhoDOHG5f/hK9CmG0Am05wuV4JLZiQDBx+08TXl9PB/a4BwgFeETmsQUs/R9JvxQWIaBkLNblbgzYkJDII561Vej1uE/rQKX4YgFUZCUawUDN9kAUJw+wFc9MYM/5l74mPD2gePaxJf5o/BZT8eXpc1nxmkEFcFaeDCoecDB3gCMggAo74NGhxA582op0gV7larYSgEAn/NwZTrHNRJ60B8hASidLeIP4hvMJ6MGLOji6qJER+DfthdoncL306Aq+BSrdQc+lIbfxhHmZ5dtgzlbsvQpv2ivDUwOKTqWFurhyBFRqXYsPEVQAjMxDvsbe/p9W2nmzcgtuiIteZfY7QJr7Ur0KOUc4YRBtgCdfltTieL3jDJfYisVltrLlEHdWDEo7lgOwOFbirUJwn8fS/ctqOAEwh0HFdU/Zt77jZ+zDGMdxtqJxV4anBhTA60GOgUoLxxS1GVTsaWUeE1Dx+RgY0h5T1vr7DhtuHsKLQHEf0I4jnP9dmcoRTpmGWoWA6LbvBz5VwNGBbAATxoaVx73cFlA8IAYdAhZjL52x6FfQ9tqX8TP/kbAFKiWL6iOhrQsbbIVHoDistH3wdWbh6QEFOAcqWVF7ZO+PF3+yZ20l/mSvWmujpAEIvirzn0AFdFjMPGuh8ZVeBRjZSgUqTpk6ZSt4QAQaatvxb5G4ga3wnAnFuA0xyLGpUL5/zk/c8roGFm2PfTF/cyYcBZUSYEYRyLOWEYjy0lSkndjfdDQ8NaAQgBtW3LGcZipep/IwqEg7jrjqE04yFSAsezPP2pkTHIQpTPUqOmBthgGy1NWgIvkfVtha/g5eFVuxa6QBPjsaYYjbYCsbDncmBrp+OQosvge1C314BGD2QAWub/q1fDFJ0E/p+/IRtnJleGpAAdTt/kMEFSf+7Lnqe1A5YlYmwEajZzYteOaikx8GKi3H1j4gLQMYhqaOREIUgSy8Pbbir/OkL0HEK22pr6rMVB53sAVcxg6KXqqv9eV4U2F7alK6jtgCld7WeO2Z6chGQrMOs5Urw3MDinvbt8VUelBBfzkOKk6UsXt0UAG2j0DQZxRUiBRY3JA25rK/udBYi6zIpQjkmctREUjLFRPlpWxlxbDSutaOSlsvPvnjDhR0pL1bilujIyzsi8b0OLnJKWzlW+XZmIfTwVCBihXnQQW9j9p1rbD1fanP+PSSrVwYnhtQEF3iHwWVFmpQycChZVYdfcSrtpfD/RnUFiBgW1lb+auwxFf+Kug5ENfhBCRH2IoAgoEHEHQhl7GVwQMWc7YyjZP22raDA8BidUVQyunjqt/f3r5WBhf/wJngOnEAkqI9m/oRudHhM2UrDwLhLDw1oHSz8etAZW9DYVCspjKP7P8Bal8VGxBOIbulrGXJa2/P/fm8hp82LUuZcLnsOvH5UwpbGe3GDvAKtlIBSxJ5/DNjXAdCX97Aetzk7HEOWFxv7QGL9o6GILEeDAZgQETmKo+uD/ZuLG1IClv/br5JGunYypXhqQEFiKIOcD2oABg69QioeKayZVbOTKVfv0ZZ267zPqA2Vk6Ylo3698legoqwm1phK7kXR9fdnBgH+L5uxROnYV+Py1fFte6IwFIxHA8WCHECLHwMWOQr2Yt7fcojylotZxB/Uj95UGm3UQQKYqR0zoytXBmeHlCAtwsqIzvx4HF8/0+1z0fzM16nrO37fgBlLspa9vYBtSczW4nsY2ArOj9IV/qDbAWFCERwDnOvZCsufS9O3zubmWM7MkvxcSR558pb32UtzvXTVeDiA7v2+zZZu+dK1wwgAWwuDE8PKDrRFUCquKvFn7cBKtZul3ZUWdtCHw5ReTvXq0DIx+bBTQDC0AszWVMLEUhGcgSBCYvxDnOhxpNsReMEpMJkmoJNZCu7+pVcZmYs+lwSP7TN2oVBbEngcihkfUrqmJmepxKBpNljn5Lr8IvCUwOK16EogICWoKfIoALEg5geEX/OggpQu+pv+aq0dnqflg4q+RcLs9Nb6QQny00bMGJaZjU5R1Bpr7m1F0juZyKQy3PavKyTwPQf/Bhb8a7+qfWxZzQuObcVABfKt57aZixI+fw9kMCFfcq5sAcqgblYOwsnw/BO14enBhQAuNGKuxNP9kDF+5Q8Iv7MfFEqUNGQXfUtXv6WRyB4hazle9xdX1nLnl4Fjt282gokebJ5ecpWfMkLwsp+iK3ANa8Anv04YRsOWHy6Z1EZePqEdcBSMAT/jtp9QMFagNMAcwpUXJ/6LjN9irbzYlR5ekAB5qCi4V2AitQEf/zBWV+VrY2F/fqYsraF6v4VIlCewolBlGxF8njzsivBcoNwjSVICr9CDCqPO/DP5PgAMjpR58CiEzzEhc94Xt44DCrWJpasc7ZyZXh6QOkTP4JKyPMOmMpZr1oANsJmoMI4rqzVcmZsZTi0SZYjZSuPiUCI9x5UZCncU9jqag7G6y1BGYR8FzDOiUHK1FjFgzE9MJbc456xWJtjjwWGUsQB6XO+ImyBijEqY1exb64MTw0o+sIVqDTTAXC1+KM1ngGVHPbOVbH7E8pa4JwT3CERSEbWXAQCxmnpv0yGEHS2IywDYfAWgIOTbMU969mKtre75qNgJilOy5qZmRHLGsUff62TlYeJXfeca3vvuvPBfZ4AIqi+2igCXR2eGlAAJ+4kUPHBT/bXgsremSoVqFRHTp6xABFqUPHK2iNOcPW9H0aAF4HYsOOMI5zcVyJQGKUzlpEAByfYSgk86MBFCK75vryK5XiwQX57z3x61x0DFmm31p97UrphiEzEuwSYnCd32p5IVIlAV4anBxSgBpV+3kk2HZ8HlVYOdgFnb1OhhhmoWLrGT0AFqN31h2MQADfqNkQVBxLKVsKvF1qONvqINT6PVMTRWilsE/Cw1DGyjA2/lS22Et7KvXGa3IeYiWb1QJHEoFwWcv6i7jPA4uNyQgkeB8IxPUtYZi4LTw8og7iT7y8Qf7I/yllQAYCtHxUD6iMQ2vu5vCeVtfrMEREoTmPYiDvkCEcoRijCRPdspQ1YsolYsRUb1I6tGJBktmIg44ClYiiaXyfPCTFoD1hyOnJ+e6dzwOLjcvyQuBU8wuIEqFz8Oxqv+d20tx7MD0X+3uTor3zvg05I/XuTqbsQY6G1/bPnNa/LU6RZmWBXVqzHl+tBRa/Jle2fp1QWuef8Lye2fMBC7RlKz2gcKfMIcfEaPi/0HsY2iGSG2bPtGpaHx3vA3Teg8vegxlZ4QRt15Ca9pNmzgIkvvCCmVflduXatoESzMlxcqifkXUj+xXSrI92X7SKAidrk9Wn6sSm1189xiulnQlhnOMXZ/VHEOhaenqFMmcmD4s+WR+0eU2l11McfnPFVyemVspaxr1fR8LZFIBVlXqWwdYzmCFuBsAfPVqw5BVsxhpK9chNb2RSDJiymFUPhHTITgbu35yvG4jYh+l4LPefZBYpP+mhwbcp1XxWemqFoB86YyVJ0iWck/u8Yf56paMhMJDKWVu4CLtMzU7FXTazGFk/HJiJr6c94luPZSkub3SOyFWtIZyvWJvLxmY2MTMSnM3H7PZ+CrURGU6d5tlIxgE22soxsZcYitlhMZFU0ZyXTNrqyqJfjGYu2L/QLUvwDgfIUeRso4sKrAIWIPkJEP0hE/xMR/RwR/TNE9OVE9JeJ6Ofl75dJXiKi/4KIPkNEf5OIfv+hBspE3gKVG624OdHkSlBp5bv8Mnn3QEXbltNNfHGgE+LdP6CDSutDTgDTwcI/60HFizzLsm6KQCZyaZ4FoIWjCLS0fwFIFm7/KlCxSebzt2d44UF00PIsTZ+Hy7dk0CjyVyCTASTlz/EekCJQNTFoCkhZhFrqNrS0BCwJeCrAeQ3AtILk8zgGdlV4LUP5LgD/PTP/4wD+KQA/B+A7APwoM38dgB+VewD4RgBfJ/8+BeC79wrXPjsCKrC814KKlr8FOBVoZFDJehdyZWdQycBCrmyiDEBRr+KBYQQVTO5ho8vrVQa24gDDnslA4gBjYCvLhK04MIhMIepd8kSLuo4RWCrQCJNzI8+M6bwGWEpws/bTVM9SgYu9ww7AvAp4HggPAwoR/U4A/xyA7wEAZv4tZv4NAJ8E8L2S7XsB/BG5/iSA7+MW/hqAjxDRVz/c8iLcEhC8C1DRtFFJG0Glx9WgktPPKGvbNQYRyMagyxdBhSOoAAFUyO5hoPJ2FLZAJbr48rIYNLCV8NwrxKACQGZg0OMjsFQsYyZSlXm3xKHUlz5kgNkEk7ck+ryGofweAH8PwH9FRD9DRH+eiL4YwFcx868AgPz9Ssn/UQC/5J7/QOJCIKJPEdFPEtFP/t+/9lu4IU5iE29MHJmwlgdBZQ84btT+nQGVbAHKoHLGAkT5uXA9ggoQQWUUebxIdN4KFNiKTMjAVjzIAG7SCFtxYBCAIE/+nFZMyi22Uufp8TM9yiaLGeKdRWgZ68nAUopCW8BSgcUEXA6FtwAqrwGUNwB+P4DvZubfB+D/QRdvqlC98vBKzPxpZv4EM3/iS7788wBgAJUcrgQVLWcLVDQcBRXLv2F2rkDljF6lX0ewyHoVzVeZlkOagUXSqwyg0tPOKmxLtqJAUIFFlebKO8RWyjytWXNFbG5HAoYhP43gQZgCy2HG4vsOBQt5DbhcFF4DKB8A+ICZf0LufxANYP6uijLy91dd/o+75z8G4Jd3G6jMpGAq7QVqfcrbBhXPVLKvSqUzmTGVgZEUehmiEYgqUJnpVawcVMwEk3sgsBUoiDgR6FGFbQIRA5U9tjJLKyZkZDlbCuCarWSg8Exl91nVr3hgKcp/lLHMxKEpuMwA5i0Az8OAwsz/B4BfIqJ/TKK+AcDPAvhhAN8qcd8K4Ifk+ocB/Nti7fmDAH5TRaNZ0Pf9sECllbHNVDS9SquYSOUAl0FFy9gClUpZO+adgApi/EwE0jT4vNB7eWnNa/dJBApAku7R7xvzGPPMweIAWxme2wKpka1s6VH2GMbALgqwQi53o7yQH4U4BNfuCigywLwFMAFe79j27wD4C0T0+QB+AcAfRwOpv0hE3wbgFwF8s+T9EQDfBOAzAP6B5N0NNzDu6I5nw/0Bx7d8lsoZ5zcArvPHIw62jj8oT3grys7nrmxtLIR08JFjELac4BQYeiBECdTfTzYYklxLDhCKncu+AwUw2N0zxQmhbm9afXaGI5R7gkDoDmuxxvQcQ51bLI/UZc+ryofdRM7xGONnbvytHJL7yeZDcuUileHexb8bpKf1C7nIACrhM7/l8CpAYea/AeATRdI3FHkZwJ94pJ4PE1Ty/p/qiIMqrb30tlft3sZCAOMpcFz/DhCAEXTs+sw+IGk4GjvxZ9eCWA5ogo3Yzd8FMsDR57Vof98nuK3I1UZDqg9xas1KoCPFNvaUAUgnqgMW7uUNoOWApQQKjPFTYME2sCgoGiCkMgw0Hdb3vuh9tQUu0pVvLbxGh/JOwlTc+RB0KmPbONWRnqG5A9wRszKATQvQEJefo2N6Fc2fRaAej1IEOq2wTfGleVlfhHBItxLFg2K/UCgP20rbI2JQjqf4zFZ8rJvGOtK1PXfivrWzVuJqKHUuF4Wn38vjwzMwlf5xajaytTco17N4USmJSFYLb+8B8scgaH4Ts1z6uX1AgKMTxX29F6jdp8ObZmzFgrunxFYgoHKErRgTKNiKPiZ5Ribi2MpQXs1WPLPwDKeM92WFuslRHH3PyE60vD3xJ9+3OJLu4rHL/XteGJ6aofRT76tdxR8uU9na43PUq9bSCgtQT4tMpVLWPuoE94hp+bAjHLDDVhDih3sgxB1xhhvYSrbsuDK3lLalNUifmTjFbfqppHzZUuQZy8BqHmUs8O101qHUr1eHp2conS10VgLgQ2cqZw5qqs6q1fAaZa0vQ/UqvjxgW6/Symzl55/u6CGvgRrHpmM5pLCFYyugzjIyOznCVpLGcc5WWq0lW/H35JkIS9X1KXHDM7NrfSa3x7+my9PaTXLP4ZmSsUy+zhZjaUzHsZYhw+vD0wMKMIKKD88EKtVv/MxAZcsCVB2CXSlrZ6frawgnwaX0a0QgQDl7FoHan4nC1okx0wOcLHAAlRbDMnHJNSlae0JJHnQ8KACjGKRN2RGDhmfk5UexBh1YXJ4SWLRtFbD4+t1zR0UhH9fi3wI9wZOLPEAlgkRRx4dnEX+8snbLVV/v/b9cfiUiAdj0rB3i3P3RfUCAsGInGmURqF0jiEOHFLZW+In9QEfEIHGqmylGSxEJKe9EabvpFKf3mIg1hFDGTEyrFLfBh8XnK8rYV9Y63HbxV4bPCoYysoWRlQB4OqZy5FT96idQW9g5Wd8pawFENmO1zP1VLN2uN0zLgGMrs7Uv8hDLeUBh29Nkbbfo4r5gK7MDsnfZSnoTfx8ZxoYYpM9k9qJNyvG+uwIr6fdjWcJY+IAotMNYQlwmgxeEp2Yo1bt+tjIVn16lzZS1szyD+bhgM1ubC3N6ZVo+v8Gws5X20KMK23Nshanwsr2CrQwMo95ntLU36CHFbS7rSsaCSdxF4ekZSvXbxVtMZapjeQtMpQVZ43l+pOQRBzgAkWUYY4nlV2zmiLI2xKGDilMnD3oVTs+fUdhq2mmFraWdYCu6Op9gK+0+sRXC6GlbMIyu2yh+e0jLSGxF6y/zhTb18jyTiWnU249YNlz5JWNxfXMxlgB4ekDpzOAsqJTWoAdABQD8z562Zq1S9uOu+q+1AA155P6MvwrjuAjkrUCMzox6g+I9qWiBbYWtTqxoK5q47pOfaeh1OmAZvGwJ8O77edKSlHteDHJt1gntAMJetQAW+HwJgGbAUqdNgCWBiG9L0XuXhqcWeYAujmRxI8bVPik+PCr+VGEmAtV5t8Wf7eMROP0971mrf/f8VezZJALptX/emLTL+6jCVvOB3LOWFxgVtpN7DUbn69PhBjGI3ER/UAwqRauJLwuQxJ2hvPTMZINiTEsnx5XvNntnXBqenKG0oMzhw2AqAOB/9wfAhgjUxZOWX9/guFdtxVSslEIZnMFsU1k7EYGAuWnZ+6u8TgRq1wNbIRVuDpiXfR26ZHNx7/puPHm/x9ZM4CIxCL7Mgr3k3inaMmUyvg0u7xnGkr/SVeGpGUoFnlus4G0wla26H1XWbqVtKWv7v9cra4f87j6blpWteKZi6fI++3uBIpOBz2/3ka1YYsVWXFrJVsKKfIytRCZQHJ0wlOuujW1s7DXaMDNvsZKByex601LJRmaM5crw9AxlwYoVnVUAo05F7wGnhC2Yyh0U85xkKm/DqxZAYDIzB7hHlbUAhh3LmnZYr2LMpLMVpPT2HjNmkuNIXn9U2LZcB8zLtkwXHfkatqLRstJr/QNLoHSvzxIwOMUldtHzOVZCrk1VvvxMuh/TCKrnie80ZyxXhKdmKBoWRFYBjKzAFKiYMxVvYn4GplLpVaoT4Kq6fB17ebb0KkMcOluxZwdmExnItmm5YivOUU6Ywlnz8mv2BA1spdCDHGErnrHUz24cEFXdI7GS2cluRRmBhYTnJr9Y6K8vDM/NUAh9ZT/JVDRcxVRa6DqUt+kAt89kTlqAtvQq4c36cx5UtkzLSM8/4rbfrs6Zl1spB9iK3nOfVI11+B0+VvGoB7GV37ElZTOM+kfe4Z/tTnHGEHy+6jnfaxNWYv98W9Dv/XV7bs5YrgzPDSgpnAGVTe9Z6dQziloAeMRX5bWgsrUHKIZjytotf5VHTMut5gmwDKACjMDSp89R83K7bs8qKJR+Kzoj9d7ADlZ2m6wunrU0ihNS0itgOSoGKbCUQHIWWKw9CRwOAou+y8V48twij6Jp8DAtxB9LK8QfDVcoarfqehviz1Z6rq+qo1LoUlFOpYzVv7qoZxEo5kcQa/yzGndUYXvEvAwtQ/IGL1v0PNBn7Tke85AASxIjjihtB3MxRjGo3BuUvW03lK7AKKa0DzLWMVUGF21pcRQWlivC0zMUXe111QZGphKVsm+PqQAApLzrjpQEto6V3GMq1R4gAKiUteXxkgAeEYF4yD93hGt1zJhJFbdtXgZ0kS3YCrljETxbGe61XL0UtqIRh9hKkc5RDFLGMLKQLfGqqEcJlrbLMRtfR1C4uvo2GcuF4akZioabsZKRKWTHN+DtMZWq3tcylbENwgCw/6NjVX1ZWbu3Y1nLOmpa1rjMZrYc4fTZIwrbfF2Zl1ue3qApW6nYSWYhQIg7xFaKoydLhzlX9pyFbLCgancyHFvZMientIqxBCZ3UXh6hpKDV9ICOMVUVtO7vE5R2+q9Zv8PAPdRO5vybCSne2XtlIUkRjQbOLN9QCHNAflMr6L5dx3hgB22oo2wdR1ZYRvYCnXdSnbd12dLtmJhh604RgDPKlxzOquYOLf5t8oshIBdM3O+T+XOFLdDWmIs/b2uC08PKH3S9/0zXvzR8C7FHwClr8oMVABgtv/ntcraYcQOYVTWPioCVafBtRr2RSBfhmcasfEzoEkiEIDTfiv+ac/9LXAAlRbTy4hNOikGAf0UflT59f5CYEl5syiEqgsuCJ8VIk8lnpgo4MSady3+HD3+INb5bpW1TWSZK2v93yNHIWyJQFvHIeQy9Nl67099JIJXvJIr41K/lbclBmk6Zvn9feG/Uu370XvE+61nc9rnFKD4d10KsHgUVDyAVM5vR85TOXOmSp6IHxaoZL2Kb9MMT9bc3AAAGKdJREFUVGZWIA8MhBp4shWoctsnjCCCIm7mDGfgRCw/jQoDlUO6Ff/TqWYFKUDF/7LhEvOWE9inV2eoYJZf7zsgjWm9/pCOeD99tnjuqvDUgAJMvFsfAJVe3j6o+DADlSpuBiqxvA8PVKp6MmgEICjKqkzLwAgqPv9RhW1P78ykijvEVhywHGcrPN4DId/Rw5xG9lGAAwrWkQ9b2it7Q3E7mJOLepLm4NXh6XUoAILStMd1XUn2pm1xx3co+zrOKGp9PUfPVHl8/w/glbGtTO2NvfT5Qdhv07Sseaq9QPs7l/UFtuJ2nOGg+keWa6mDgfqnUvsTvRrJU+hXysOcCBs6EDYdj6aDsWlm7roOPq1fUbWQtZGrcnFpeGpA8T+pWJ8fex5U2rPHrT/AXFELJGvPBFRa2Sd+UxlAtgC9Dc/aXE9lKZp512oJlRUIQHjeW4GAbYVta4tP00pncQoc842GOtk2T4eT61hXApYMKg6crFkcW2MlSpq1dgY8hBIs3iawXBmeX+QpRJOQXokVG6JOFfeo+FO1sxJ/5mJOHe/repci0BG9Si4jiy9ZBKrEpLMK20q30q4R00VMyRsNNa9Gmhgk6d7nJYgyg8gzF4Pic9gUg4J+JYkkMt/7/dSfpN54OFXkSuCNtCvC0wMKUINKBIHu+JZ1Kl6BmhWlMe5xRe2RncpHQOWGNU3o59KrzHYtAxEQMjBk4DmrsNXyox5l2xI0uO6HdMlvu469QpcFDBCAoV3D8luwCZqUtg6EglJ2cJPvwBOUrSjAYUO/MlXU5mcRgYcvRoDPCkABjoOKD++SqVwBKrGODx9Uqr8KKhWjme0Fys9bmoEMLG3Pw7blm8fp9SG2ou25mK1s/WzqnFFMGM1QPgZgGhS3B5SxgKv/wvDUOhQApU4kpAcdyP6+H5/vEZ3KTFHb6to+/uBdOMABcDR2X1kbw3m9SnUgttZ4yBHuqMIWiMygaydSXHzJo1627bo9H0/ed3UR9xluVbEruzehVNrK88PeHy1SyjP9ihYt/+3pV8L+IGzn9fVfGT4rGEptEu49MRN/8vPVAU0+vFb8aXXVTCXETZhK3ZZ9pqIHMj2LXkXTBwajfZSYyBERSJ/fYyujyRmBrVg7DrKVQyZmV15v6DZbOWpmzmyFEfPXOpMdx7jMYC4MTw0o3srzNkHFT+ij4s/bAJU8AbdARTcOPote5cgGQ68bqRS2XgSqfnAs61ZqPUrtDLerW5FJlnUr882G6Pdet6JjKUzc6kxb9Imf9R0+vdK/DOUf0K+U5X8O6lDiRD0OKj3fuwWVrTNVthzgzuxWvlKvUnnEPqJXsfJmoHMBWzmrWxmBBoGt2AIdgAMGLH7iB7ZyVmnrgCXm68/XoNDLy8DCW8Ay0a9sKWqvCq8CFCL694nobxPR/0hE/w0RfSERfS0R/QQR/TwR/QARfb7k/QK5/4ykf83RemagYukFqFTetP75twUqPpzZ/xOe2wEVX98joDITkXy9/d95l/3qHTJbASKo5DyVwlb/eraicTPz8hg3YSvQOL3uZQxsBXrf824qbV38YTGoVKxOFLuIZdVlbIhZF4aHAYWIPgrg3wXwCWb+JwHcAHwLgD8H4DuZ+esA/DqAb5NHvg3ArzPz7wXwnZLvcKhAZeaj8mGDyhZTqeLOMpUjehWf94yIdLUIlNPzszb2izwADFTO7gd6DVvxe4JKtnLWxOzB5ogYtHWi24xxYFtnEvQrWYy6MLy2uDcAvoiI3gD4HQB+BcAfBvCDkv69AP6IXH9S7iHp30C0f1yUB4oth7Kct8d9eEzlEVCp2rENONugEvK+Q9PyLF8WXfZEoFBewT7y81kE2o7Th+Zspdxs6NL1eputuLgUX7MVTNnE1Myc9SvlMxPF7YXhYUBh5r8D4D8F8ItoQPKbAH4KwG8w84tk+wDAR+X6owB+SZ59kfxfkcslok8R0U8S0U/+5q/dAdSgUulTfF6va5iBSv38c4NKnTaCiv9JjpD3BKjs6VVm+pfANA5agWZsZdTFdLaSy3mMrSho1Gyl0q2cdojLcQDipD/IVkol7M5u5k1ntySWXRBeI/J8GRrr+FoAvxvAFwP4xiKrtrjCwuFtmPnTzPwJZv7ER778ZvGPgAqwLf4sWB9iKt6EvBU3trcDyKOu+vO0qOsI73lSr+LL2NKr+LIqtnJGBPJ/Z2wlPpNBYq6wHa0+xy1BCiyerZRiUACmnq8EFjooBm0oZaf6lazYHeoYgeXK8Jri/gUA/ysz/z1m/m0AfwnAPwvgIyICAcDHAPyyXH8A4OMAIOm/C8Cv7TdwW6Q5Aio97hqmEsus6tkHlSruiFftXprlOWjhCWLgk4pAoYzEVnzajK1o2v6xCIVuRcoalbL9GVBKV8BweadmZ/g8MGDZEoOmuhLqYtCgXxnqcPcXhtcAyi8C+INE9DtEF/INAH4WwF8B8Eclz7cC+CG5/mG5h6T/GDO7Ht1q5Lbu5Ij40+NqplI/fw1Tqfb/5PpK9lIAx56y9qhZ2YPGVcraKx3hXqOwfZytRJCZKm3PsJXyN5Xz/UQMqoDloJl5pl8pwejC8Bodyk+gKVd/GsDfkrI+DeDbAfxpIvoMmo7ke+SR7wHwFRL/pwF8xyP1zpS0M1Cw9LcAKrN2bcYdAJUQl4DDx22nzUHlCie4IyJQJeJkEciX+1oRyJeR2UpOq9hK+xuv24VT6sr9QybmDCKvZCtHvW339gddGV61l4eZ/wyAP5OifwHA1xd5/yGAbz5Zg9sX4/b0oO+piXtpqrNQ2ofye3JaGcfOUvF5F6oPaQLGg68342j/TBXfBq3XH9Stcdtp9R4gAD2N9s9WkU/RggzAvVP2t07jJ9o+Y6V9yxS/tR/IniFJ65Nz6/eB2p4h/3IaaHjhYU8Q2mT3Bzm13Fun77sO1KeolwfiTiNctuHclRCKA7GpF61lDnm0+mdhKB9GmOlTrmAqe89fxVQqV/1c3xZTqdqynVZbgELaDlOp8rxNvUpIP8hW4jOw+z3zsjcfbzMYBBHIyjrBVkqlLYo4ZTBAiH9kb9DUzOzZyoXhswJQpoBxAFSqvLN9P6/VqeS6Kp2Kz7t3pspZs/JMWZv1HPq+Ic1NcK9X2RKRtkBl5l27JwLl9Kp8DypAEm8MQLpuZcgjZeybl6+1BJVK2+wAd1AMOmsN2nLjvzI8NaB4NvYoqMQDlrZBpeV/HahsAsgOUznqqzIDDn99dg/QIzuWt8AiPHORFWhPYXvGvJx1KxWw9LQMNghspbIElQ5xBkYYgcWDSOXPAqR8O9agM8ByYXhqQAEOijYXMpVWxuOg4st9W6Di6z5rVp6Big9HQOUZRaCcb8u8bHkwspWWp2YrsLwOFDRO2+PK8Gzl3YpB7ZlSKTtjQReEpwcU4HWgUsU9K6iccYDzdZ8xK/s6H/WsPSMCLa7cK0SgPbYCjOCzZ15+G2yFCrZymRjkgeXA3qDSzPw5eaase9kzLMSHM960Lf46Re1ZUIl1FszhgK+Kj9tOqxTAc/FG08/6q2zV+TbYSgU+8RmE+8vZin8OPk46I7MVyZMZzwgK7h4uX8r7kJn5wvDcgII82XdYCPppamcc38Z6rlHU+nJnoHJ0p/JRX5VHNxYe3bE8y+PLqfUp50HlXShsz1iCjuxg3lTaFruYq8OcaMtdv2IwQMg7PzC7PfM5q5TdC35Pz2u9aYFrmErNCvaUwjzGbQHIxRag1zrBzRS6rxWBgG228hqF7Uy3ksvYZiZzYCnFIODdiEGOrWwCy+ciQ8H/1975hW5WlHH88+i2WvbH3aTYUtIFCbyIXKS0IqQ/ZktkFwZKkJkh1E1/LmKlC6luKiIkCP/QP4syzSRlKURM6KpNpbItNdcMXbNW2TIoCIPp4sz7/mbmPDNn5px53/ec3fOFl/ecmefMPGf2Pd/f93lm5ixxlRJD6RqVPq+SbLehKabVkYrXTwapuMelydoph0Apu5ha0dpI51G2QqPQhqDvjYVBreu3/KiJUROKdDx8MGzmZ1WkkqNU+rz+IHetSpo42nWxB7yLMFYdAqkJ2QEJ21y1oiVsN61WqoZBbrhzvCkU7YFsytdHKlu29ZSKi85FcZWmlbW8Smhfklfx+9ZJxbWJKZDYBkPNdt1qJZZbWXyn9gSFNr3Uinfdln2UWIJrlh1pYZB7U5UwekKBzZOKm9AsVSqpe+hSKp5tBVJxy9y6WLLWb1epS5BKTl7F/+S9YwV8UtF2OJeoFbXdwtxKY6MrmKFqZYtYDK0wSA1hnPPwBUqOKvGmmStiEoQCmycV14ea4Y/bXw6p5K5VyZ0BioVHsWRtar1KzqsQuhSIRirax8t3KLaQp1ZSIVDXupV2GJRDLL7ScIlFW2lbHAZ1vSkOvDrjllfAZAglxNTCnxJS6bNWpe/GQs03v05rtzu8GRoCubNAKdtVhkDNOd65lrRN5Vb8b1o20ZW2nk1BGIRTHytbnjsDUQmjJxSPCIL8xJTCn6YNTS109ZenVNx+Y6RSklfx64bnVUpDoLDf0Na9Zh0J21y1Ar4S6atWeodB2gud1Jc8OcRSEaMnFEiTSg7GqFQ8/3qQittHLql4fmvrbFQV5T/cbtsleRXXTiOVviGQaztWtZJ6kVNJ0nZJLAsbJQxieQ14CiRWVhmjJhSXPGOkklIp61QquStqmzbqKBW3j6HTyppSWXVe5QRHVfj9tEmlTwg0FrXSfHeple6k7daCN6JhkLqTWVsUp/0vhxUwakIJUUoq2W1VUCouSpVKCamk1qo0fZu8sqQa0XxTlMbAvIrXZ0dYo/WbIpWxq5VwhmjL73YY5PoVTdouOw0VjVuHTyLHYw4l9fAOmflptbVBpeKW5yRlh5LKkBmg2nkVr8+MsCZ3Fgj0EGgsamVxnlQr0KlWUu9dUZfwL2/OKauI0RMKtB+mPuHP0oZEWxWmlBv7YaTitp1DKl1rVWrOALllffYB5U4t+/2EhJAXAnkPf8I2pVYkYZcillY7GWqlT9I2Kww6oYNYKmIShALdYYZm1/eVBxpKw591kopnq5CKWz50BmjoPiDNLqVo9NCnOwRK5VZC20W9plYgrVa8thXloamVWLjjf9Mimd5hUMtmNeoEJkAoOQ+T+0NP2mUmaWO7mEvCn8a+LqmUvKu2dLey60NJXiUWAqUSsa5fue+ujeVLQrWSsg3VSjJMUlSG2lYGqYTE0q7PUSs+IQwNg7zVthUxekIJsbIEbGZbsXZzErWp//a0aaMslOvyo2sKuQ+pdIVA7baVuoAwNLuSEMi7LsO2JGEbKhVR2orlVty23DY1teLmTVI5l+W5o1YWxNJUujbEicVtpyImQSjhQ5RSKq5NzYVv2kuvw2u6ErVufyGp5O7/cfvMSuB2qZLCZG1Xfd+8imYXC4HCBz1FKjFbCfoPbcNcSEgsalvOtc05Xn1O0raPWlkSy8I3Ra2kFsXVxKgJRTyyKCeVEEPfTVsjUeu20yanclJxy0unlWvkVWJ+x9areHUKYXQthBuasI2SRmFuJTYTtLg2lrBdtOn1QQ6B1AmDlvmVQK3UwqgJBUKyiN98zsxPy64HqXhtVSCVWB/x8CKnzzxScctLVtb2zas0bXeHQLnko4c+6RBI818jlSG5lfA8JBa/vH/StnXuqpWQWJxrWmqlIkZPKCFSeYtcUvGu6RH+xK6vQSrtBPNwUimZAepaWZuzXsWvT+dVckOgVrsVE7aeosicXs5RKzohdauVRfkQtdKaDUqplYqYBKGEyiQ3GZqb2BwbqYT2blnuqtpYeRepuOVastb1LZZXCctSS/Zd37z2CsknRhRe+wOnl7XQxrs2uO8ctRKbCeoKg9z2VbUC+WFQRUyCUCAd7iTJoscS/bGRivvD98v9Poe8V6V9f6ZtGyGV8MHKXa/ijkPO1HKXXW4I1Hd6WbUZqFbc85Ra8b97Jm0jxFIToycU/0fsH+f8ZW7Ou0ll6GbCsG4VSiVGKp35k4EzQJ6t82DkTi2X5FVKZoFCu3ZfYYiivxVO+8Dw3EqKWGqqlb7E0jh6HIY8LvoqlV52EyGVdvvtB6+LVJr+80jF9SPmW9+8ilsfC4H6rFnR+j8BrS6tVmI2i/MW4QTta2FQc47XnzoTRJpA3PZSYdCyH8e/WpgEobg/CmgrFd82QgLBg3+sKZXUPXWutu0KdWIKxiGNWutVckKbhW2XnfaAh/3nTC9Dt1rJza3kqJVFf2q4BJ4/NcKgmpgEoUCbVFz0mU5u2jw+lEqqXL+X2D3GScX1QyOVeH13XsW9pjQE8soCwtD61xVNm1T6zgTFbP1zlufrCINqYtSEEsqxWD4lPM+dTg5tsxe1HUOkEiqVVSVra+VVQsLoEwJpasW1T+VhPCWyRrXifqfUSq8wqCJGTSiQrz7C8xJSidpJuV3ynSsjJZVWeSapeLYKaYT+9cmrDNkLFAuB/H4V4uoxvay1qZHKqtWKe232W+IqopNQROTbInJERA46ZTtF5B4Recx+77DlIiJfF5FDIvKQiOxxrrnC2j8mIleUOHli8I/WV6n4dvrDF7aRVCAZdjl7f0J/xkYqucv1XV9q5FVqzwKVrlkZuhhOUyCuTelMELTVSI0wqCZyFMp3gYuDsn3AvcaYs4F77TnAe4Gz7edq4HpoCAi4Fngz8Cbg2gUJ5aKGUmm9UKknqWwi/NH2/4QPpf6w+jM9sRmgvsv1h6xXidfnqZWSECimVmIhUNf0smsfEkvSRmlHUyspYtHUSEkYFBJLTXQSijHml8DRoPgS4GZ7fDPwAaf8e6bBr4BTRWQX8B7gHmPMUWPMP4B7aJNUJ0KlEqsLUVuppPxaFam0+lyBWlFtC5K1bnncj7YqyA2Bmvb7hUAxu1y1krJfQMuthG2mcivSYauFQYvvkjAovLYmtvW87tXGmGcAjDHPiMirbPlrgaccu8O2LFbegohcTaNuAP77htc9fVCzGylOA57btBOZmJKvMC1/p+QrwOtrNdSXUGLQBJRJlLcLjbkJuAlARB4wxpxXz73VYkr+TslXmJa/U/IVGn9rtdV3lufvNpTBfh+x5YeBMxy704G/JspnzJhxDKEvodwFLGZqrgDudMo/bGd7zgeet6HR3cBFIrLDJmMvsmUzZsw4htAZ8ojILcCFwGkicphmtuZLwG0ichXwJPBBa/4zYC9wCPgPcCWAMeaoiHwRuN/afcEYEyZ6NdyUfyujwJT8nZKvMC1/p+QrVPRXjKmb5Z0xY8bxi9GvlJ0xY8Z0MBPKjBkzqmG0hCIiF4vIo3YZ/77uK1buzxkicp+IPCwifxCRT9ry4m0Ia/T5RBH5jYjst+dnicgB6+utIrLdlp9kzw/Z+jM34OupInK7iDxix/iCkY/tp+3v4KCI3CIiJ49lfDe6XcYYM7oPcCLwOLAb2A78Djhnwz7tAvbY45cBfwLOAb4C7LPl+4Av2+O9wM9p1uCcDxzYgM+fAX4I7LfntwGX2eMbgI/b408AN9jjy4BbN+DrzcDH7PF24NSxji3NoswngBc74/qRsYwv8HZgD3DQKSsaS2An8Gf7vcMe7+jse90/nMwBuQC42zm/Brhm034FPt4JvBt4FNhly3YBj9rjG4HLHful3Zr8O51mn9U7gP32B/McsC0cY5op/Avs8TZrJ2v09eX2AZWgfKxju1j5vdOO136a7SWjGV/gzIBQisYSuBy40Sn37GKfsYY82Uv1NwErWc8FDhBsQwC6tiGsC9cBn4XlRplXAv80xvxP8Wfpq61/3tqvC7uBZ4Hv2BDtmyJyCiMdW2PM08BXaZZMPEMzXg8y3vGF8rHsNcZjJZTspfrrhoi8FPgJ8CljzL9SpkrZWu5BRN4HHDHGPJjpz6bHexuNRL/eGHMu8G+2drBr2Ki/Nv9wCXAW8BrgFJqd9jGfNj2+KQzeLuNirIQyyqX6IvIiGjL5gTHmDltcug1hHXgr8H4R+QvwI5qw5zqa3d+LxYyuP0tfbf0raO8wXyUOA4eNMQfs+e00BDPGsQV4F/CEMeZZY8wLwB3AWxjv+MKatsuMlVDuB862WfPtNImsuzbpkIgI8C3gYWPM15yq0m0IK4cx5hpjzOnGmDNpxu4XxpgPAfcBl0Z8XdzDpdZ+bX9BjTF/A54SkcWu13cCf2SEY2vxJHC+iLzE/i4W/o5yfBUfVrddZl2JrB5Jpb00MymPA58bgT9vo5F8DwG/tZ+9NLHwvcBj9nuntRfgG9b/3wPnbcjvC9ma5dkN/Jpma8SPgZNs+cn2/JCt370BP98IPGDH96c0MwujHVvg88AjwEHg+8BJYxlf4Baa3M4LNErjqj5jCXzU+nwIuDKn73np/YwZM6phrCHPjBkzJoiZUGbMmFENM6HMmDGjGmZCmTFjRjXMhDJjxoxqmAllxowZ1TATyowZM6rh//3U/pD+SiPDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(np.log(resid))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows a minimum, with some degeneracy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rf = 1.000, ff = 1.141, residual = 0.010\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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb65ce90320>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(radiuseff*rfactor[rmin], valeff, label='Calibration')\n",
    "plt.plot(radii, encircled_flux/np.max(encircled_flux)/ffactor[fmin], label='Our PSF')\n",
    "plt.xlim([0, 80])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "505899259895.6815"
      ]
     },
     "execution_count": 27,
     "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": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "### As units of map in MJy/sr, divide by 1E6\n",
    "psfok=psfok/1.0E6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 160 micron source, e.g. `----`. We can see from `GAMA-15_PACS160_v0.9.fits` that it has a flux of -- Jy. Maximum value in our normalised PSF gives ---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileNotFoundError",
     "evalue": "[Errno 2] No such file or directory: './data/GAMA15_PACSxID24_v1.fits'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-30-ac54bf2cb4bf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTable\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./data/GAMA15_PACSxID24_v1.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/table/table.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[1;32m   2548\u001b[0m         \u001b[0;31m# RST table and inserts at the end of the docstring.  DO NOT REMOVE.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2549\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2550\u001b[0;31m         \u001b[0mout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio_registry\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2551\u001b[0m         \u001b[0;31m# For some readers (e.g., ascii.ecsv), the returned `out` class is not\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2552\u001b[0m         \u001b[0;31m# guaranteed to be the same as the desired output `cls`.  If so,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/io/registry.py\u001b[0m in \u001b[0;36mread\u001b[0;34m(cls, format, *args, **kwargs)\u001b[0m\n\u001b[1;32m    500\u001b[0m                     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    501\u001b[0m                         \u001b[0mctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_readable_fileobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mencoding\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'binary'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 502\u001b[0;31m                         \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mctx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    503\u001b[0m                     \u001b[0;32mexcept\u001b[0m \u001b[0mOSError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    504\u001b[0m                         \u001b[0;32mraise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/contextlib.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     79\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     80\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 81\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgen\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     82\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     83\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"generator didn't yield\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/astropy/utils/data.py\u001b[0m in \u001b[0;36mget_readable_fileobj\u001b[0;34m(name_or_obj, encoding, cache, show_progress, remote_timeout)\u001b[0m\n\u001b[1;32m    191\u001b[0m                 \u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcache\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshow_progress\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mshow_progress\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    192\u001b[0m                 timeout=remote_timeout)\n\u001b[0;32m--> 193\u001b[0;31m         \u001b[0mfileobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mio\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFileIO\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname_or_obj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    194\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mis_url\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcache\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    195\u001b[0m             \u001b[0mdelete_fds\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfileobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: './data/GAMA15_PACSxID24_v1.fits'"
     ]
    }
   ],
   "source": [
    "PACScat=Table.read('./data/GAMA15_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PACScat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-31-c5b280bad8ff>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    }
   ],
   "source": [
    "PACScat['HELP_ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'PACScat' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-32-f66b601ff7a2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'GAMA15-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'PACScat' is not defined"
     ]
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='GAMA15-PACSxID24-1-69605']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 21.6068 Jy/sr, off pixel Max PSF = 19.4609 Jy/sr\n"
     ]
    }
   ],
   "source": [
    "cpix=np.int((hd['NAXIS1']+1)/2.0)\n",
    "\n",
    "print(\"Max PSF = {:.4f} Jy/sr, off pixel Max PSF = {:.4f} Jy/sr\".format(psfok[cpix-1,cpix-1]*0.0185,psfok[cpix-3,cpix-3]*0.0185))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mc741/anaconda3/lib/python3.6/site-packages/mpl_toolkits/axes_grid/__init__.py:12: MatplotlibDeprecationWarning: \n",
      "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist, which provide the same functionality instead.\n",
      "  obj_type='module')\n"
     ]
    },
    {
     "ename": "OSError",
     "evalue": "File not found: ./data/input_data/GAMA-09_PACS160_v0.9.fits",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mOSError\u001b[0m                                   Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-35-82d57bfc87bc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_style\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"white\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcubehelix_palette\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrot\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m.75\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mas_cmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mfig\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maplpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFITSFigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'./data/input_data/GAMA-09_PACS160_v0.9.fits'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecenter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'GAMA09-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'RA'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mPACScat\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'HELP_ID'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'XMM-PACSxID24-1-69605'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Dec'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mradius\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.005\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mfig\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow_colorscale\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvmin\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m0.001\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvmax\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.002\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcmap\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/core.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, hdu, figure, subplot, downsample, north, convention, dimensions, slices, auto_refresh, **kwargs)\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/decorators.py\u001b[0m in \u001b[0;36m_auto_refresh\u001b[0;34m(f, *args, **kwargs)\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0mmydata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnesting\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmydata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'nesting'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 25\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     26\u001b[0m     \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     27\u001b[0m         \u001b[0mmydata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnesting\u001b[0m \u001b[0;34m-=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/core.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, hdu, figure, subplot, downsample, north, convention, dimensions, slices, auto_refresh, **kwargs)\u001b[0m\n\u001b[1;32m    215\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    216\u001b[0m             self._data, self._header, self._wcs = self._get_hdu(data, hdu, north, \\\n\u001b[0;32m--> 217\u001b[0;31m                 convention=convention, dimensions=dimensions, slices=slices)\n\u001b[0m\u001b[1;32m    218\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_wcs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_header\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'NAXIS%i'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdimensions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    219\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_wcs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mny\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_header\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'NAXIS%i'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mdimensions\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/aplpy/core.py\u001b[0m in \u001b[0;36m_get_hdu\u001b[0;34m(self, data, hdu, north, convention, dimensions, slices)\u001b[0m\n\u001b[1;32m    297\u001b[0m             \u001b[0;31m# Check file exists\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    298\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexists\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 299\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mIOError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"File not found: \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mfilename\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    300\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    301\u001b[0m             \u001b[0;31m# Read in FITS file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mOSError\u001b[0m: File not found: ./data/input_data/GAMA-09_PACS160_v0.9.fits"
     ]
    }
   ],
   "source": [
    "import aplpy\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "cmap=sns.cubehelix_palette(8, start=.5, rot=-.75,as_cmap=True)\n",
    "fig=aplpy.FITSFigure('./data/input_data/GAMA-09_PACS160_v0.9.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='GAMA09-PACSxID24-1-69605']['RA'],PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']['Dec'], radius=0.005)\n",
    "fig.show_colorscale(vmin=-0.001,vmax=0.002,cmap=cmap)\n",
    "fig.add_colorbar()\n",
    "fig.colorbar.set_location('top')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fb655627f98>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rad=20\n",
    "plt.imshow(psfok[cpix-1-rad:cpix+rad:5,cpix-1-rad:cpix+rad:5]*0.0185,vmin=0,vmax=2,cmap=cmap)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, the PSF is within 10% of this source, and given noise and shape of source will add additional uncertianty, as well as non-zero background, this seems reasonable.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "stackhd[0].data=psfok\n",
    "stackhd.writeto('./data/dmu18_PACS_160_PSF_GAMA15_20190301sr.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.hist(psfok.flatten(),bins=np.arange(-0.01,0.05,0.0005));\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(psfok.flatten(),bins=np.arange(1000,1100,1));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1213.4483909939188"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(~np.isnan(psf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (herschelhelp_internal)",
   "language": "python",
   "name": "helpint"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
