{
 "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": 2,
   "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": null,
   "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": null,
   "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": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf = (2*special.jn(1, q)/q)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check our kernel is properly normalized\n",
    "np.sum(kernel_blur*resol**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# apply the blur\n",
    "psfblur = signal.convolve(psf, kernel_blur, mode='same')*resol**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "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": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "psf_obs_norm = psfcor / scale_factor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "idj, idi = np.where(r<max_dpsfcor_2)\n",
    "print('central core for observation: {}'.format(np.sum(psf_obs_norm[idj, idi])*resol**2))\n",
    "idj, idi = np.where(r<max_dpsf_2)\n",
    "print('central core for theoretical: {}'.format(np.sum(psf[idj, idi])*resol**2))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two agree extremely well. \n",
    "\n",
    "Unfortunately, with real data, it is not always possible as we will see to use the derivative of the curve of growth to derive the factor beta of PSF fattening. For real observation, one can use a brute force approach to try all the reasonable couples alpha, beta and try to match the theoretical psf to the observed one. This is how we will proceed next on real data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Real data: PACS observations\n",
    "\n",
    "We will look at a real stack of point sources in the PACS 100 $\\mathrm{\\mu m}$ ELAIS-N1 observations, and try to find its normalization factor. \n",
    "\n",
    "Let's load the stacked PSF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fc2b1503828>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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D5UhBLheH0Ue6DBVpxO6YITX98t3CBS075nR/vMisFQdwFC6gLNAQBJH8PIaFJcH+t4UaPI2TxfHOdQ6Qt6E/DkCvN+sXokdpSbo6TNfjwPx/f8/6g1EJnUm4FuWkApAvvoBsPTU5XJRjWISMugTyXj628U5wVLDvyeFUF2NMAPdENNKg3v98x0WY5qFRvd8L6VkMXzU67jbJwwUM6+L9+0Qc93SBP6a9CkNhApdCQFZrTHER21RnjVvsSNKbDQ6h45zQtrLZMflJiPKz/PN2T6hWyE/ArbH7keLX0gqVO9LiT11gtPRi7dli8ZgwppGth0N0OPEZxGvZUcKv9t8NF06Jgq5F7DiEq+RPKiwlQeyLWQo0D80HDW3ZFWu+SoSpeT8gduaFlwDKvWjgjWTV2y0MrRQDSSSh1bgVPcASvo7ntvmgMiDdniMWbnEzgnx0nstyahr6F19kn7Hfed36HtaZ2Y9sRJwO9cnZsO+lGH/2J45poUzA+oMkbnXPpGWfEykFWVkQUe2LRuPhaPS7EPWIiXZ3RdlelH1BcjVgOKNLJr3XxYW04LCJpJc9O7BIZYU7v33ZxUs2EZmwZCFS62gBMN+/t+tyZwLSVZp+/5A0j4DAZxlwiH4YwuTgkk8o+gn4vfT9U0Jt6jbePq5kZeTDjNSUEF0BiXS4A+vwKM+AvnOXjGItGugg9Ax6BxHHcWF06OKuTYmuSDEuAIIDSeFYC3IvdCtsjsj0fl91Em7AIiHLDYcZK7XIVG/A/Yb5zlHbmzelb0oSmZOgcttKxGEmUaia0ujh/b6bNJ19qpUU97+rtpxTagpeaS0RUvBRRySXWc6Hz5Hb3ch6lPFrPYhRpXs9sIRpg9e6p3snDw+5KX0nOAogfMckeUoIkOo/bRC1CUcEwsSskOXWDiGc5yQhK+4LO3arM29BaMoJ1JtBeQ/HVZFMJEkV+P9iK76yvYsAD+15mm0bCfnHzGfnLj3Vkoaut9wh6yI7h1BFIvMTrZnbFqSk6TRSJzHNxfHd13JZSAqryb7rriUtiTZySg1h9IO/oLR5IYfd7WO2Lseu9RIm1hWFjBxvgKgDsduK7+j1M/Hd4qeH6wEYAcvFK2lQ9H5A9gF9eAjDvxgzErxzusH1/n6JCyD/QEQY40bUm8+YepFeNjHNMeZmcSLxQxt0Jpx539eY6/HB7fzSQNlFPESoaQRk321hUvPPxkUVMfhucJqhxoB+FqoKX533KyRTREkYR6cSsHb41HBBwmCgLzuUqhgZR7fGJ4owDFj9YFXMJ98tgZwcRFqqUBFIsxDxQpqR4VdNriS6sqXR5DsvEYsSnakkXegevA9qZmvrgMzVNSHfA5jBm2q+sbTMjfHxVpfCm0HLaE7457OtJT9qmj/1E0AiSOoLBnJ3PUWcFhKyiJYqAa0klAdl632dOxzHktGrNI58Ps3nO4f3lz6u6AxpBKV7yJf9QpTT3CB3WY0Br1U2iVQKF27tE9orMRQA3jyaKpILlynUQBKSQPG7b0Ym8vd1N28GE7FZ0pECsdCkTmpX/cVO1/fif1MFx8jBGso0/X+Sc0qWfN8B8WtePYHp7RtbdHMmrAUytr1b6jXu7i9Tmlv89VzALSf1McLVsL5ZCVq7ie9692JUe49763EEhMeYUL37Lrfnotg2W0DUhHBHPDH8er+7YlOi1oLebp4DIrkTMvavp4hEcETJxWTdEUljiIIKOPa9m5aFqO9y8X5liB2BnPR2B+CcU7yLj7W/kwK5mwM2NjTKTAHwJMZlngZg6rm5lPf7yijMvoU7BsCVmqW/rBP8OyfOi89KF6dG0s6u4Ee212EoQMvc0/pNhY6bvXwoN3uIZjBH1o4451UEq192EJRJwYWousI/9yGFoUPAeBGXQMtltwSrAk/Nv0ZGUzZN+DdphAqpVaHztpUiUGVHYLQAyIgKkG4PFwdzY5jJ2bstDhVTSJ4nB3cj3o8xfC66MzHoWpRIpb8zo7W6ZeU73FHRk9BlgtQZLlOtWDmZkeMG5MIOmO/ZnUpEVMPU/vzBV/F9ip4kn3PGwsLDw0qw8llfEihV7YL9AMCe7wL7Jxjy3GiANPQq1L8k+hP3Yd3AV61MndOVX+L7tC3mNzN0lwxhXt/78FPa6zAUitQP0D8Tf+kKATmIXGyhGyjXYgr6/W5Ckyp5dcmwHoeRPv1ui3gh0sQX/znaQj5DFx84ySTXePD5Z0YITHDjk+EcARkeeuQO6mHDTB/XnNTAigYm4faINHoBTG9QwnvixFwglDPZyUVVGXyG5WgcFrGao4HW10Sx+H0ZyxgXye+SL6riJY4dCpdRq1rtuxcX6kCf+d0xQK0Js1cj9b1qZyq3FGPdknD2+4qIhSyxPeebyLkU10bgrh3dyOmEZa27EXNmAnpAcck+2TYIjtVQVwI3+sZdNGnAUZAdc5joCsHRLjfCQHDfAR1FMOanXXVJxBnD4F/vmXTzxtlrndDrkZEQhu6Op8IxXDK5ynceff9k93vzaFoC1/GTmxCy+QFvW9YFAIAxMA+XyTrPoDPj9BHxGCOeTx4fgAeiBfch32VZO3n7Jolal4Dr4d+97BY12XryM72broIT4eEh5eDsW+42myE2EcF8ep/RplMYTe9IfQBFVHOYQRZJwo5zeQ6kOtJ9c0LgKh/nAqialIeHNLZby0V1u6cwSjUNG5DP7S5H8FGus7HOUwCF6B7T+qV1yI681vfeJkf00y8TSbpRkI5S20Ih4u5hjV7wfdnmBG4T0Nu62fRmLhjJUY4zYOPpYxal/EJotkO2R3vPrUGnaYlk3pPMvvnf374xXombGTeH85r7wPZ6DAVQ2PiyGwUsRRBggQDoihwlTFULi9d6iME52ASl3x2VmxjPLzkdSTROULNdi4ew6IkCKdLhv9EXARGfb0knD2KNhGqZPCXEFruni4qEfcUd5c1mGgQgIa8vjjASLJxClPHMf/Ydj3ksXVG1HBo6BmQf1fqQwIogfALLGFDmcjAngVoGujYUsNWdsF4zRF+68hIYmRtR7wsUQVm3ZLfz9YIs13wHuk77BuMqWvA+UecTW9aWYJ4MYO4ZUXHJ6qSy1biWnu84JlTKPA+ehHOiuJs0jKVOyuJWEhXWIkY9n32J4H1keyWGApDLxTrxOJxs8l/1BqDnzsnmE0V9p1pIKSYKITs0ohwkJu22z9lgTuhCIHKQoWqpwT65pLfkKaip8Oy9EG75swa6uN0xa3Wo3i3WT3/26RqQn5WS5M1j+qi3u5F2+yWLBfsk0qO4KNfbKq0GApmgd8j3vgAVfLFbU4Jc3Dod3m8uCeZ7EkpLnYxED9MrQnExVin8GObakxtwwlBrngY5CM8ClQ7grmukg1xIXRyzjJdLx7Xtxmsw8lURK+/J8fzCk+KqcO92dz4s54khXSutF0QkDfx92Hxm1OG9h7EvpnvhJqF6dyNi31WhuwZDnUUFnHPeo2dROW3P93ENTGhP7oclCJ4S4T62vQ5DAQSpqNxV6XeLIJR0hFk1NwNA5Gd46LKKhqJF1KQt6dxLBiFg0HMesYhqi4IwNWxaUYOIDU6Nf3MHpMhn3EBVJoZX7to6dDdizoxXB5ovqKomFTERGd0jGq/hhVGm8x0vseJ8/wgHJ6IIdEGYfkMijLaShfGdUrDGUED2f9xPbCxMHt88quKaDaWmwI1M0c9QHwEAzLqM76DsvLIa9OBctKVfTkRGYjNCk1ivI+JEsH+GSWBEe9XnDz7HUUUtWRBG61QuoOorONd9U9KK0oiSK0kJ5/CkzOcxrE/p9lJC4O+kY0BGNwNUrvOx7XUYCsU64CyN9tJn6eNy0lBCXYU5p05RF/IAZbcBXCPgA1JLmPF7jPWzpsMYUTRHmGNRKx2BE5Tw0Q1NLWRSopRGqppWQWrNBb6qi3JCH0ClYHUbnBeJWgSt53vVd2FYj7snF3qpU4lphWH1HClgmC6esfTTXXNhH0nK1Tqd4kIj1XtK7ynE4jEM1Ap4lEfzwYtx801D09BSykwXMvIxCNPnzGhCDaOLAOKG9u7kKjeYqAl6gutVng+saCp+2ByBIPsw+BnJPg+DUvgduijsM10J9YymFUKVRqvwN0o3pZKxZzf4A9srMRReJl/IXpOcuptWgbsZLS8LujApBsjFFItLAzZiaslM1aUiFACbpEvB1kJUjWkEFguW0vfdFc31EVFvk6Rr1XwAiHDqGFmFiztBa6ayBGwxETrGhM8Yf1T/AuwdPNFKn66IXIL7DfOpnDXCxeqTU+8W6QnXoElCWF8s8vYxIkuJuopPP3V1DxmW1GlopssaDqVh0+Q9wgizDwoClGrgxguoj5GHZihFiiEOEpA7OhcoSdkmUffU+u+eUbTLntfhu10usbHQeESInvOuaFxkA/Q2Uk3r/MjyHn6fMy9BV6jehzoVRXIbkc5Pg1vQdaCvMoet3smpcv0HttdhKICM148J1Zb8ASdcSIQJ+1DgccJz+3lhjEex6jWOSt6AAzFuqcvgYTc+CIE6XOkZIqPYIcruEJLbnhEYv9+yQ/VSZwBIYtXDv6qu3QB8oZX3o+vifI6qolFD4WSw+fbkbFr47DaxRroVbUOkIt9uyCSqlnoP5yJk21zbUA4ycqJNyubFyb70Uzv1Ve/Bj3BZRlGiEqpdCtf4zinagH46IIjvWXM1QgiFgOfBa5zD5gW2Y2urnsHfyYRYZVEDBvcrigGeXz+6xealjJ4bIrBoUZ7lZHD+040KifdaELpWTou+iotOZBbjx7XXYyicBGTKsQK5o5aQZrQlI46sMtIiA2loquaBrDHj3JwIo1wvOIWTT94EMrf8DBCLbElYgrvAy45BIVJDSJDJXwihcYPc7yF31pvVEY3aEyXrtBaapdBK9t30I+wrugBFymycgSRq4X/HAbx/MqFW7wBa7sjwnYqIjKRnZfhrXTmGiscsnI1GP2n9HJAaAJFAPrlAWW/E78vCu1wYPCVONb9LNys0Mj0XmWqk4KNGWrat8C6aocXi+oTWBy3uHxWsKpoBEBEXVlqvGg6OO3KDeJ6jMaDTjSijQvz89GtwLjAqQ8PEdcM1ovLcAH1gez2GookXWnEyix3nUm5diEyk+3HO0BwOJymhjWhA8Q+3Xga27BAilgwEQK9XzPdPaWTevvV7jAivaZVFxw6IfC4y35hgFacIy9Y8Dq9XoVv3RTUhFzMUNV1b6ZvSldo2g6EikZ0ocELYjYn2rHBUj11kOcGIiExXPHr9ijgLRTWPqwuXqNkufVfY4Ts+LtVnv16tL5ufwMVJXOP7TVBJRXXQGJOfpJ5D7mdiNXvwqIkRO7mjusjE5VjTXaWrpWoaFqolgaybQSNR35uLe0yQbIo8Grq6hPpukCU2pq0Uc0YW722mSLZ3HTknQ9yVfE4YfqLWfV9S16Mcwr5bhLAgmuV4hI9or8NQKNwVsF0+T1LSFJ+omlpuy3MkAKQclgq4GFQsrkFFE3bPspOqZioxd0KfcBTgUL9AsVVcKRbH8x3BxGIk0HJXFEghPd2fJQSnEekN7e1bRIQFiAVWlaRRG7OG+dwYUacQu98ZlRVXTVoDLpdFG+JfKq6DG8pKjA59XtUrdvPkV+JaVRTH3xH2g2NvbpFW/UsrfaYj+zoiDo62CtJKxOYRiq0nmdpw+pzzJnOkQal9sBWEeRxeXQopwycRXlGoo4ClSUFz/s6QNWJhP3YdB1EB59lWicu+GoMJTFVDpc7hmDt7fogPb6/DUAArH3G9ZUl+Rii4OOZwVpfnRSbJE5OK8WNWoFLNAY2Qa/ELKVXeN0MOcwB3e57GxXX3w46paSCJVRdIE+htAoPEaHGJ+I61hDpgxsRrE8Qu59+TL97aO5TFHlyOk27STKkXzY3dQl5xUcMnL92jojeAqkcgWqr8CGcXKC5ZrYmEIo8IKMpLeXCdB40w398eMmP9fGbC6zGzIphIHiFQNRIULvGa1G7cRvrwVdsBRMjYIk33IFUjNEzSlgpLn4usLlUrZltOkiMvzWMno4ASCudk/1gTGKUBGM8NdWvQPpM/49yculT8WgonVzJ1E7R9W/vVja3Wylgf0V6PoQDC0ocbUGPJ3E38vwgjcferiyGuV9SYY2SiFENhR0KR2EyrAAAgAElEQVQ9HQPSCOGbwXcuWp3L6ec2oQFUBSnrfM5rOcCoEHiahoktIhHP1KPDsyVnugLcUQ4eTKxRuSl2tK0jalhw926yZpjWxu8c9YCbFkSssfsAhhGY9p6VJLQdy1Bdy8LGsxRq4cIdw2TN3oeW4Qsfi1K8N0q72UKVy+5iqTuAtTxeQHBGvGIOlb4+qzm9ABLmAR50Daw8yTJGFYWFNuK06NRQjiLnrjDaBHcJxm3dVML1kiVSJ5qlCyKsv5WxBCCHIOpu1MZ+5IYTAjh9/swf2F6XoWDrZrGX49mA4qf1Ul3KJtZyrBsQZJ59D+sgsY2R8fgz2XMSdQXROnMgmYAWrVapOmcf8v5zGHRGt1R4EYi4+1PvyWequQss7Hu7pzpPnhug+Hz45W0JMQrfp3nNxkqoCVYuKAyhk3iMckDKZ/znUYyXaGmk6EgzTV0A4wlaTmSFFjLZ3Q9ySUSbtdHdIsG5ZHV6/w0ArRCVrLc5JX/PecLvbkni0q8PkrSWDAwZu8IquZd5WucSuQ5yOB7tsfd0V4iRnrLZxdhuabjDSNMQ1KgKkfK+r3O3CuI+oX2SoRCRfwTgJ7AuP1T1XxGRPwzgvwHwJwD8IwD/nqr+P9/oglF4pJ6aPaDTmXhCeU4aVmsCUvYKFB89SSB4jF8b/KzPosLrfanoHWjgNqGH1YfgDgGdENnMWCwTM10f4Vmf08/3PJFh8V464/CfCH8dmovuspu8+17CYI+P9nkvSmvnOzSg+SnYNZKjmgpDwH532YGjAU9XXwySrhj7SRUYh50nunXg8WGpoxGw3slCvbqOg6d3VVUi4IvZ+8m5gEBIrOkx1RLEnHPS9+8T7nNhzQLhI9W6I/Q1x5GM/93d19uAXHRN3CLJSXKSKIERIpe0x2HDpeRhuGoiUZfTslOtLoXOoyCzlvd0l4NcUIwHn6e2shmFu0yjS96pRATrPFzGiQjqE8VWwM8GUfzrqvrPyr9/DcDfV9VfF5Ff83//5W98NRoJIE+mKko2ZfUnEpfhn20rTHS0EDuJKgAy9BrRFYN+smb/FZfG0o57Gh/l4T/O/PszGbzGioDKO4URlDVyo7d7+MkRaaBwC+YGCXYjVWuuQtlha5p07ITcyRw5RBk2hvAOOzA42PCFb5kAHK5qS0PGIr2ARTzqc8SO2UxlOkaKhLzuRD0omi3qX+6eWUtX6enJCeYWRjaETkQPtdxfJM5J/pz5HqrlPE5JUpBQXkotlBMyXTYlJtTRZeT84U7PnBhVCI81kBE/R3eDVdTBlYRGp6p22DydLJAjiUTIP2ySRrUBaOXQKeYSvX0bFcOenX36ge3bcD1+FcCf8b//NQD/AN/EUJTdR/qWA0A/lM3TeuM7tapVX/UWlAdXeK40MG6VqwEAAOYI1IpOrG8gxwF9ukIuaucnPD6ARWmsstOA9C2Pq+fCuF5LglZHVVsu7+PFcKROThE7pQoXmwTXchJ3Df8BSIk1dzotWgIkAjlKqjSJSzbu9OMOfX+zif3972d/kyAkgtLpBWzL5HfuQ3i2BEOl3NmGZpo8NwL2++1Y+4H8AgvMbnBy8JpwmpsAj/xjmYCtJZlJ7cgYtsM2Ij5XQG7dKnRdj3RVxF1bViajlsUNUiR4Vfl9cEa+01+viVKdr9Hp3+XmNEb2XUU7E88NF5EJkQ7nMl0ioo8x7AhCanDOrvUHtk81FArgvxMzn/+5qv4IwC+r6u8AgKr+joj80je6UvNqyhNG3pC8ZBalbobDaEAAZH6/OunHt9rWyU9iTzXPBWlZ1i4Ip+bnhpy4AR0TsnuHlxi3nMmkeu/6nEAhKjdYRVgucJKEM2A/y8+hlYpNW7ckH5J9JBi7+9ylH3lvGszlKEDyKMyCvR/rZKS2gQufoqsaaux9dT/4vgxlt/I7LqQxDHL3BpFpFahVsyblXaDzffrpXJDMs6GvvRXdCMeHrslZcFRL/DNSoV6El2NQo23HAFrJ9K0uVIS38eLipcw9Usen2v1oBJhP47yWNuTirdmqdeevastQ2dp7heiO6mQ+024lBygMtCMDjufE5we2TzUU/5qq/rYbg78nIv/rN/2iiPwQwA8B4LF9z6yklCPQgBfYa+Qi0bnuFtQ/AK6Rz45S2Hmey0DUCV6FSAVZyL7ZzlZ1BJ3+n/uKNcHnTLhx0ldEpNMjJEjSqZJSwZhLvjef97KH/7xci+FhncZhuJRZ3K3S+3DD4q03PzbAoK3e7om6uIhqOLlwR+ZF+HXjGcirlNwQajccfbB8HVOqz0pBvd0ySsK+ZMRkKgC1A6lr4Vzu0hERK3oNNkdA0lqJSrS1f+csPAQQxXPPu7Aney0qYI5vr+du5PiHq7e8LN3QMgdx+g4l+1Qmc64PU2wy0hLiLM9pkcu+Ghggn+sT2icZClX9bf/zd0XkbwH4UwD+qYj8iqOJXwHwu1/x3R8B+BEA/GD/Ja06Afphsu/QfUsZK5V6L7002XyXYscQqwLqVZ/vvjN6odw4E5KJQ9IzFLt1g4aMY7dmPjd3SsATvJLUi/MoSF66wk9+4fuGVE4hOB67t2T/Vf2DTxL90s8U6ea3Gnz2z/mOErsqeRtyHU3yeLnoJ+9rGgOWu9u2RByXPQrg6NPTInxbjLSaIjF1LoxgPBmCu1yMe7hY4WI8XKKqfxCIQJB0usjUx5r16VWvwOpj/jyL4ZIZgi1TrtaENOeo2OgazC0jP3XRivhJ7jMQqZGkyAUe2aJHvgefed8W5WToTMgpMZeHuTUwlKHXm0X9qDquz+S5QMupa0DWQ2GiH7/jJPynOR6fYChE5AsATVV/4n//NwH8JwD+DoC/AODX/c+//fUXw4IeqGlQ+vJV7bZtmQZNOBXJNT2zMoHc6bhzc9CYl+ELSu8UUrWAy/6SIcP2d17K5CucYWYGX0UycHJw2wJ2EtUE1HTCLgryTM26GnXHY8l7VqJ+qQv7aQHQb+fuVidsjRCwf0kWxjVmsOwLbCUpWo9K6FnSf1GSTsvQDDUki/I23/lYXxIAts1I45fC1WdtRMk2jlO9AyX0HHc2Xq9K0GdLdwoIHiG4CUcLIXt/6Nn35M26rLkzJDIrEiBKpZ5BJyDb6X00NT0iiEO5dVoknZxLNRrVFanJkacWFdU+sX0KovhlAH/LLdcG4L9S1f9WRH4TwN8Ukb8I4B8D+HNfeyUOYkBqknCEkoXo2bzs/a1Ie9nBL0Q+0sJu0K7rpKskI0NjsWvqShp6izJ2IlnIlBOwEotN3HBIhj7nXPMM4hmLq3Ge4KPUbiQcnS1DhqWITvSllpBoRAxI4NnP47i76jerBnezvFcpy8Z3U3IbTJnnO5eJTbl9IDBC+ok1mkXyuTU/JQtAt3vq7YYIYT96zskchi6irqXzR14WT/ne7MPqIrBxEW/bOr+8EZmyujmjXGGsQ2HJ65lbKtUtZGW2MSxsymgN+bESNdF6Elwko/kG5EOvWmq0yOn+8c7D3KcSDFBuWJ/QPvrbqvoPAfxLL/z8nwP4sx90rTGjTsPiz9WIR7cdVSjxVQ15q95uWY7Mf5dirWTisyq3k3xnBHKUsnDSMlznE3spZlLgnex7MtiMdQOIvJUnCysu+SZMaqOR6B14cF/6oO+pcU3z/ZvzFIcVBibS4RkWVVoOxOIX6QHDQ2E6hpdtE9u57iZHRu+G5LgrImF1e3gIWC3+fti3WMBRo0JaEKDayuQu70IjXo/oo1uCsYcLpk/XFMVdr9lX/szesUYcAumKUKhEQ11l8IXIjqgY0UnwLd63b9/6JPWfl8jPsikRndyNxEzC1+9zzXNqJIoOzwhlxri56lhbh96e7NlYv4Ju3ZK1C4AFnMo14J+LA7F/nhzFz6ot6kKqCN1i6/AQ5WGDp+xIVVBsw3TnqFPJwSswEsexioB0ogpWFm3+mBYe9IUTE2JJ5kEc+mMHJNPdKS4DkAalXptGLnQAxm+EmxMToWMp9ECXoebBMGWdIT0SqD7Zo2crbwMkj+E7mITU9wDacGFXA9QPyK35GnQJN1mR2KKstNwLuWiiBKoYpz7z18tkQFSaopG5t9QHiJjB3Db7s0R5IpHwsrvx3kx5ej+8gpm/+kFCcOY86d2L2JSIRk/Dq3x3PiMXbR2bogES/qwaEsr82f80mAWlgrUjlloZevpchrsjZLuR2xmoldUk+v3Uzx/YXoWhQO/GEdTJyDTownyrHgbjDt/VuOu0hyV+rNebRT6++MKu55oIq3g17V7czUieMdtuA3QO6KHA+6coVrP4f9ypuBt5pSVbHLcM6fKIgEdPtqIvWlCTlLwKAPF9XHZPTbbPRKjz/ROWE9CdaJO6Q1X4CuTCrkrJlso+W1QH5pfv8kSxksLffvEH8bwROmb1adaDJOHHfnLXRK/XIKNZY8FyayZkKwKq3lOodWSEJCb7cWA+XVOL4e5OFP+ZjkqBRAvTeKM4NgCwvtZrJgyWzcQiMsWt84hYaEDopnAj4RiHatNK+y1FZAqJTRSgtSo4OTJev3vBJIbIY9xWnsYK6Y441Fget7JxFGPE9vNyPX7mjRObk5l/Mv58HFmwg2RkLRoTRJAv3lmqLAG+27wQ8gIQsl3yBSQsy85caznETloZdUZQGGGIWo1tNTJ8RsB2Wi3cRnVblufzClKuYQjYDySLz7yV290SxpZJNtJY1L499z/TtJ2cE8Bk3G8fkRGAdIkCwfGZ3zyG7z1dC1FPna8JWkylX56JRiKiQQWJ9R5VtkKtyXobXIi1luhxAAeyrglJWCBcnHAbSuRG3MUlka3SEm05QRyuUA21Q5OwrcRxdaVrvkYlffn+4uhNyVuVsVoW/wTAKJsjI38/i9z4Z49Sif0FovND2usxFJUVZsyeL1drDAD58iQr2ai0ZKotU7J5/XbqbG3JZUzPvaCR2PfkKzgpqjxbxEvPTUcQE0scv7WT0dP8nT9rcAzkUqg/qLtJFRFddhvwuyRR65/RY0ZdzsjfYH/e1fQfdbJUQ3KkK0Nkk2enSL5PvIv3NeE2SU13LSIFnX3E5+zrWKUCkeHCgRe1EN1PR3MuJkvyFbeVHBQbjTyPLaDGhMZn340UZ8r8/QbVwnM144PkdofOLTeRhcCk69PwrB4J78PNrEayxrA53huAlme/hvv6giEvrhX2PEownok8S52H3Wta1H76yPY6DMUc0C+/tL8HJ/CCCAow+S+bqsl0YSd4GczTcFuWDMvLnj6th1f13ftcgHRj5syFe1wTFrMeJX3W6UlYJKgitHhk8VMfOJHCKXDB+U4s22ZnhcT7fBGhsixA65PWT9/SCE+O4vvKwjXo9VZCc9NDdheEDiMMhbkHgMP4h1MR1uOA/uSn6yIp56bwpPhwnSgprhmr5WSspS4GeaGLu03v31t/MhluznAjAQS6XAhERg2OA/rOTz978xguoX75ZZ69UpPCHOkJK5D17jqNaWee1FBkqxGXmQZ9z6K1ep+ADuA2Iv3fnsuNX5WFP3q9T5YE4FhIHg0YYVwWzCknwwEwYpfRDPIYNoGTKH58sD643ddqbB/RXoehUCREo1hl5GQIPi928zJheYkxLPNy+NFxOlcrWlnishMa2bMFGWQkle2IzIeQrcC8WSbQoiVwdyLudVJpAmEcgnxjGLhA4MyhYDHX0/f5WRJtsZs0RJHWMcJNs3RwyfefSOMm1Kp4/L+8C+Cf0+QjlirVdVKfw9lA4Vzu8e+AxHWBM1dGs8CNRF/YItNyveXIgC7PwrjqNSCW3bw+jy+YIGG3LY8TuK8hem4IS/LZgiJOXBDfjU3pYjihTeK5IrQjd3++uxUmsnvEczdBFD2qRCfJchLTBWVG2Lmfiht9RHsdhqJJZIpGTHxhaU96Cifjzqo1rf4yyuQCwCPtVya6GA8Ki2qBl2cTwHbS80KJf3u8XpbvIAlT+qeLPLssRD5HrUZU3BczYMVndSQR53xOP5Oj3jv6S4IHABC7m+DwknPF7eME7eJhac3JGdf02gxBXt59Bzzl2VDRGbuzJP/jbg/rQ+jt5rkfMwr28HkjwqQO2y8lGlWaiKwbRBOUSjCggC1SyEvfRX9P5wCW/i8G5CzVB3J3r7t8DRezcaMo9wp9Ca8ff848LpP8B1017+eIqIUkQBLN8roiL29cH9Beh6EA0ienbBWwlz1GKtXiw5KW1ncN4SlPy0VXQxBGxFPP5fJmXfQ6l88vPMHNFoJc3uSie//eCLUmIatlaDfKohW9R5zVSQLSyS19esrJV/UFQERcIkTp4rGYHEC6C3evrdj3RB9VeBRhVQnOJXZyTuBu76vXI90uL0sXrWoQ/L709aVrIJjIibgzU7cgwHp+yXAjPxUK10sw2gWkgSviM7qHgR7Yn1wk5JceHpID2DaIDOjR4qgDPOSYy/e/Bx4jGHVPfGHG2bTRfwpMM7LSWhK+fJbDDb6Pa83i1ffvF2OzlMyrpROqHibQ7QZ5+ybvQ1FVyYamixvX6h1y+S6ERwOiGaxSLbtOfKbuaC219WzMagRSMkx1HGsNAIg06nq9YKLLztddbDQmcB8RxozdZpaw4GyIQ4w9EqCbHxx8FGgM2K6gp92jSJ6t2jTsuR8ukK1ASBlJegJp+GhEp/Xh4rIE096Alky7oZZCHs6ZRKh6CI9wlv51feZnegPFi4RZ8b9rlmTszELep5xzwV2WVbR0Wj/OUlmbrolzM0t0oTVIVwstl7ohQaZy8ethknFuTlu3fjrGV0ufF9fCx7ZyHwyBu9JYmm8WOrx8YhmvQG4l4sQaHNRH0HgEEV/ek6pTZpLyGSrKJqpo3wVDAbFDawFkclCPMF1IX5m4BKQLwYlzoSviu8W4AYdC3pT8jlisfluKZmo6MmADuHc/nMYPmfVDddVJpEQ9rcC9BoynjOAQxtZip5VQZfafOOQvNR4UsBL+DzvksN00IDKNRcl+rWIyVhRfFIcNCVk5waNug4UcjfQ6fAduKyEZiMEm8WKoGZ5jKBswefzRc3FKy0pLPMJP2eeukH24gElWSRwXPsmJZ0hLlMYaFa0YD5YPIGIj91GMXAjIwkhsqcZk8iGQSXohmS9ycM1IUy0sXEP1sUDvd+B2zTl2GNpZkEEhmgMZeAUzqx42o75HEKOcVxwKur7FlVJMvGDCP6i9DkMhCSUVeFlLACSkF0nN/ZKi7YvwshspFHBxZMhO1az8S7uflHRecMJs6+Je8k6K0WK4jtWqYvey71r9ipEajS5GMNWQGF0fGpRj2OS+3VP2DCTE9HfQOdMfdv9Y6k7Lid0pmW5QHMFx2EUE8pA7boSePV8ldq1+Kbt4EqsSilc3Vq4tiUxVmUnWnmX6RC2MCs2eegq6PyQQIyN2xLPGdejH8/7AIp6Kkvhe0mBpo6TIi6RLw+tT8+LjweuEcWBeBp+3LuR6LWk5jqFULZGUkAiM4BkAmPy++4KnfsRdWymfXcad7q7KdwVReJNyUhR8sJuAmZ4ChJWW4/BSa/7dwuSn2u5MUCEHRRUYxwola/NdIY6zp7/HCc0/xzDCieGsJUuzLKTYbQpRVicS1Yp9vXaQetV9WQRVhfgDUgdyNoQ0QNWFOMuHy9F2VX368lCJFV/xUGMYeCoUaSj9fkKeiUpFryti4eNiVJcxKAlxJU/j2XOEFHoCsiVsn3MpJRcIK8RLq/sZi4xRBCCjEuf+jMS3La/zkkvLzWHfLerDOVBRqfeTkIz294Z6iYPeYvOzcOdtuT4NXBUXRsqBfdAqnn9CeyWGQtaXDq1BgYd7IccKyWP/zsFRFTuGT8RqNrC+Qim+y+8GQRQk083Ca1T/nXbN+N70nf4si2VI80xKcfHCDM4C2wvhKp6qHUlD9TDl7toF1y3EZFa1CBDlD6z0RWk2Ge+KXDhBb3eLNDw+GOkXCWljMRI80FjevkmI3/tSREYARF1Pnu/phr66L9FILtbxuF5zzOmn+7tzhybSUJYJlCKHJmEadTZbVtDy54ywqSr05gdQN0eB24Y48gDO49zfZ10LPc23yjVVQ0IRV33Hy57PUqtzOUphX8plf5Z8GC6MCPAgngaQczmyfT2ic55X8Yyf0F6JocBKwMTun3ByIbpqcleNG0uSmOqSX63QtK33kfNuObxM3iPMPeF1VRHFS/3YN50jd27G0v3aIaOtAi1yKc/i3FbVG9sW2Y8ouwErMz0zWNyZpx8LONyvfv9kv2/cgZ3E5LMUwZfe/GDmeUkYzHttPSItzMsIJEZDSPTACe+5NiYXbhn+ZKblSzUTnFeyE85nLj7ZABTylYjy8HqfTo6GsRexaE/VotCVKcVwKO9fNpmYS9UNLH3Bd65RJLZTOPPcnqG75qQpYJofH8d6qHOmtNN9mPlMoxiplxZ/oE5ZQqLnMPKHtldiKDTLzpPQcV+OJJZB2wrrpp06zsrMNXffQ1a47JloNBVRIIexedUksiiYivNG94weMOGsQneSq90luNUV6B2yO8l4G1kBqmciFmZz1wexyOjaRLiW/UAOpBCu86dfhn8v9SxVACF55u4JRL8qn7FUvEITIx/Lv+MEreOIvIwgEEkyA4CW3IKX2izRkOmiOO60vSVvwHv7OOvTU4HSdp2sP9GNCDwOzHfv8rvqitTHR498pWHUOe0Q5tihyzsSQR0H9O5GmovM0/cXApMGT/LM1xh7wOYJ3EgQPfjREovOxtGPMFGQruyZX9EWuUiVu4laqN1Vpxs3lReEbz/nmpk/m6bIatChehMjYY5isQNCJpEZFYAYd5ecGELhTs1KZQiy8hceJcB+gRDSznJsQBBQKxkZ3wcWSB4Zi0zUqUZCp73TyQ0Kxr2iEu5SPkkt1OXfYf5J7+shzJ51uhgOu2Ain7FCV+vveXqmsmOxdGCQcC3fBciFdtkho7iHFEmxMW0+3IuexYz5ztIAPcIwV3LZ+AzxEnNen6QiRPYdjT+fw314JanM+VWrofv1c6Mi8ZnjgS6JemaD+f6FKGS0JaT3iVDqeRtx+DOzi/mcNbGPrfcMuc+ZRoDzgSjQq6RFKoG7IHFQ8ncmKazJSgaSnLwg60M2F+WwpuboLhAqsLxqDAh3jyNqNirS4EQ41eHnMsHCGJ0gG3dlsVi9XegFX5C6gereNDd8TEPv3eDyS4NIiAznFPYthUN8Pxojnr7duh0o1NpzA+nXzHyLMhkpD/b3WmBtFX8R1fCgaFZA1xEEosrIXRdIgyp2DsVSMZzjwH6q0JrkYyELBVtyL9sWPj9zOepGQQOxjF+NzvAwKS21JihKq1JoP9mtnkxu1/ew7THs+ZmH0j05rYRTwcXP54sTy6YfRlV2fNU89a41S7wjIq7SbZ7f6s/C1PR4NrZZTrb7hPZ6DEXvriC7GCTz7E+wepTn2etxAO+O9DmH5PfZSEYJw1UtuY6tQ+cWMXgAK8nGVOnwawEr5iLxjEsIq5cdlMbhGGtIkwy3eG7FDvPj3RBJa8DDxfiAg4cW9ajhACCRTJCEPY3Z9WrP+NAz1bq+Ew2e5ybI4EHPLYvrNiN/GT6l0ZVeFpwI4FIuZZEXxvg9JGfv2cNgxPkTvmNSH6B+6PPiJnU/eEnz/I4qxIuitPd7Flz+4os8rwMApOXmQPRUC+TwjJaCuGJsrlZNS/YsaqtPHqJt3atLaRqRNj3rdEb0R3zMo84GFaLh8nTI997a3Hr3lDkYVddC7UbdQIh0pkYS4VK16kxisl/DmH4XksKAtWrTS3UWa6uEHoCIew/k4mHSVG2+0KKMHqXREetn3gQJLx9gWvCqs6hqN07I3hGVq0+1JcI35bX82Dsu4iU9mM9CGBmCM4kJH8cHzgm91wk1i2EoxV3V3oOh1lpGzupoDE9qMzejYpwl96TIqrOWJ9KY0D/fYO9JlKeZAHYONcYRDUOTbwph0pGTv7g75kI4hBfJA6j9d3TXohUfPTYCd3sYYtUxM0q0aCDKlkxjybnFYjP3O/CUUagcjzT0dcNIt2Su149OmTaf6+ZEBMb3LH0bc41q5BoqPZVp+Jj2agyFFr+OQxRWmWIshpIYIeDpTc5t2CTTIN+WAWjpSwYx5aGqPAbgKzrTia5nUmEgQ21cBMw5ccYfrFVA0q9oDPSOtPZ8HtZH5EA38VPAJ1R996Z/WokvtgrdSayOcjxiffeivlQ1l447dUxmLYtCGiDuB2sLVyByUGpyVZWaB1lr8vxnrmKQrBqakBQOeWWzbbPw8Gzm6jR5ZowjwSsWPOzznAvkUlpZrGNGHUpLeb88D8OfGw1MkVrbKWN+Ti3Pk+090Q4TxUp49sUWriWST+HPpYHCoVCbsvRADS2XUHxEgL5CD/NN2+swFJX4GdPK4ANg/obOuRzUay7KDjw+2gTdvLAIFxxQFHltzVW43x2qm+8farzpZz6y/Ds7lgPt6dxRpk2oVizRCgB4uj7PQuVztHIfLVwLUAi9FkRlGkpJw3MrR9ux7xi1YT/wZ+6GRBFiHWk89z0Xo6sJl2elUawoiobjdK8gGblLjwm0ubpwS7ix7Mae7JV5M5qf11P+CD+rM2B1nNcChCTaImHesVstmW/9xZPi7HmS2JUv3q5QnbJ1dysyn+gexs14I1h/qAJzi2tHlW+OE5snOoZmArCxWghmsdPpCjeizMOpBoFczFFK9pFv8uMMMWeWEPzI9joMhcCLbBS/m+3Mzi+1AUqeP/13l63qbaZPfNnXCSvNSNASo19ahXK8P6MJAELLUYQxMZiVUKJx4LM2P0TocH+dUR7AkNAJkid55dECtHw2Muy1GE48vst62Wg8phq66c10Ily00uxMVGDNM+A7sYYDkMipGI/YgWsORZUn894hf89kKJ2KyL1xrZZEdKJEHEIwVom6/LuqAvUgouoisdhszCWXNQN5FgfniSMcfj4iVrVRCNbEnscPcmb/hHvk/JPyTFQ3Kuw3tBaJX4ZwSnFe19b4hTISwzUQyX2nDUiU0YUAACAASURBVKm0Jfz/nUgzF8kyZWNADx5tr+mbkolmtSDxk5sBMC4PIN2O1qHv3llnHUdCW52x0y5imAaETw1bHFExaXdlHhfE03WFvK1o8sWkzdyZws/0hRO7TFH76bv35uvzfUkkKhWehRSk4Agw0uuyG7y+p2Iz0MZxpEt1NrhdDJ0Q2vdmVaUaSbzrSiSOCSXTz2esURgfR16fhYsjUsIcCH7mzaNFCKhfoA6mCdAukIeConrzQsPJT8DVoqan2ZYwKh4fnPOY0N//SZKmnnRWT39XZZZsSy6lFpO57LmY+Y6sUFV5DrqBdYMAEOUL1DgoPZD8T3V3KdkvuS/hxh5ugLnBqSKO1WTYffeivlUaftlj8/1ulMJTJDkYO5+kkQByVxyjMNBpWc8KOPGQog6vL3Ca1Iuuv/rSbgzEw2ZxqO05Ng4kgjm3MyLqWEOUhOmUC/dmBmX/igGthGCB8BZeG/kOqsE7GLeRsfulOCsThfiz69VCcvslQ74kWt1Iqt4tAgAA2jLMSHvZJDKAWXpwUUCeCUH2a33fghqk7Q6gnAOqknggJNxWBbsnsjrNA/ZfFOZl3wNOCLdEo3QZa6SJRrdESQJhEH0wfFne4xnCPOcAFWUtk/Ci+jbvxZKIPNphKUcw0kgwtKsKsNiNNFTp/ndHmckcD1rTGstvAlyPJPF6EcREPYjCK4zcEQRYkUltNE5RZu3kI5YYPokhuexrpxeIa/csk/RsRIITKAskYutf0TUvqSzreR8sr8br85rel1aFqrg4lVzz9Hw7K4TnjKR7YPUrJMObuKabE3yLI6m+rYu1d4D1LgiZgeQeGJnQtc/j3uwjbg4cQ8/8nGOESyK93rcYRPIp57Gn60juaffnLWjupVyJKNLr4xLvAxSUUhZmNZJ1XsRz+GY3UMoEFiKb5QOIyvgKTYC2Ld9/JiIMBCX57J/QXomhcPjpPqHlLqTMuioJl4y7opjUp2vCRGBdkOoqOO7I758wabkZVz/DSxFLgqJaLgarZdTFSTHZdzu7IxCPkU6snRB+7jmUxdd4uCQpdUYPJSy2FGqVzSMV91ig6gtexrZM1KVkYMToy075MLJ4L9PUSRROk0UDziOx+cTl6WJhTPgOLOzDVsJ9dDcCutPPDtHRAcXFDUDPsCjHk6KmOdMtJRcyZKmLKV+8XRZeiNS4iKvLwmvTJRxzdYM5DoCVAKDrxH4r0vgomOPGKsOUjj4uu/WnGzSt37vs5jbdT4iQfRcuUhF1EXF42gNUU9+imue1fGR7JYYCSZw5ibWc3KVadt528u2Kpa5htjbXa3OCjBnKN212ihSmny4V4cAC7RyVnEkjS3Iy9i0OpnVWPRbo9gIhVd2HWugVyF3xBBNDok2RF2A8R8BNby4FVy05GSIIlHAm5fiuHvaMXbU1YHPykmG3ipw0j/OzvIuCJspY2jv5PVmJuyKUORfhVs1zkM3RDcltaQBzefiZfVvK6y3vBHcbz6iF4+fCsHq9eo1Fzs33buXZh9X6DHEUx5cE+knMV49ytHEiYrH3i6Q5SWNYN67lVHbOoXDnylw/n6AO4FlI/yNa+7oPiMhfFZHfFZH/qfzsD4vI3xOR/8P//EP+cxGRvyIivyUi/6OI/Mvf+ElK8lMNTUVjDsXZTwtJrk/OMcy/vt09JbvsREWTLxQrcUdzGK3HYQq98/FyDkUZbnp2z3KfQBBMV/fPRDHeliQebvc8MCg7OD+39dy5qmtVCrLYDlm+f0Is4QoQWQw7TU393sKCNkUMpBcnb+W0+H1n1Nvd/uMYVHfKiUQA8fzPeIPyrDUMfOZoxMsAhNyenFRvJu1nn1SNTPSL1SPle3IX1sMNUu/PIkYAEkHaA+QvKH6S1WiHZJ66BfYBNTZ0985zla3kxCx6HrohRZZOFAkeaszG9UB+iC4y3Zf/H8jM/xLAfwrgr5ef/RqAv6+qvy4iv+b//ssA/m0Af9L/+9MA/jP/8w9uJNgixFnkqg6J1xoOAuhITbw2CPNBZmr/hSIXIBY+YXQItdiKhHZpVQMA2MImMUYCzLMdaUzEIw96vS1xemwb8PYhSTNfJAJHCC3FMebOONS/F9fnnKBWoHMsdqBMWrXKSKrAkT/nwc6WDLcv4VCwXiTlxzFGTrxN2GTk7vb0FBGZaFUpGVxBGs1YpBwHvguNIJ+LhxiT/CQReLvFYo2yBPVE8Dqm/tyBwqQlevRnDel9hfpEsnDUxMzeMm+tiG9xEah+LWX1AFhU7yzYu95iMQeqagLA9SCR3UrkNTPKQiK1JkKqQsRdp968wG8WNPqU9rXfVtX/XkT+xOnHvwrgz/jf/xqAfwAzFL8K4K+rraz/QUR+UUR+RVV/5w+8iSAnjyCtKCdCXdDFiMRCp4Um/K/FZ6hMC8g3ckegUEncr707YcQwICtOAYjy+NkvZSLxh6aR4Olki1Kvl7AVoa20lEDThye7X6MiHuY0SXcq/CInpO4Wy06Y5NYitmqynHUZqKTuhsNTmqvb0Rso5hHuoEQzfH4uzN1J1GWcC+rgnwxrV+2Gev5LKwSuiOFfrjPXJKzHShayt60HDtVckDhzltd1UhTHTHeuIKgQmHk6v4yySdUDlTiXilFdeAUiK08rt7NwR9FyFLTcJaOA/JOoazPuazlVjbxNia5ZIuFMQ/oJ7WPNzC9z8avq74jIL/nP/yiAf1I+92P/2dcYigKrZy5odUgfsNOTu/R+mJHgCVsgZ2ADHX4wADuVXK1zVaOWpgIQxp5ZoSl0CtN3VZccM3eE9zkOKxDjIUHulHoM6Pt3+V4URkXtBQW+fHfatST1Fm68lhPCVbHwNd5f8vCw3scXfIQRW2oAjDlXIM60LAlDVeEJhLGNKtwA4uAZuga9W4VwwurjSKXk7W6u39n9mWqZo0zIcgVshCyLAYlT3Y90C6OR1LwUZemo5QjLsQCthfBMiWga0iAdR7qHIhb9APyM1VFUmVhcFK0S7LN74O/KufLMHdvc5a3oq/lBTT6W+u5dGrtq0Lz+SrgpM11Ukql6u1stj31P1He7Q895Tx/YftZk5kuO0HMmCYCI/BDADwHgsX0vSS81uGyxYSBUlxSalBd+NhA1DZfxd9+JhWeJtuJXAokwmCw2Roi2ol6mDltohZgMEc9UxCljtVVyjwZn4RZ80lJr0HKix+QtEy52qTl8Evm1aRiqe8Qdcu3wnKyuzlzCqROmO2nihVQ0w9HwnJVtyzCfS4KjxqnvuALYpGS+BUm+qWDVrbrjChENSctKcsYOPRLttLI4ali4d6B7KDuiGsV1kmbjRMjuYxhzaOvQzcLJBtsdKRF5AYEEkptgqnqLxCvK8yHitVLuKzlPzqBK2Sleg88H8WefiOpglYiOM0tI2m5bpKs/SzH3dfHzCo/+U7oUIvIrAH7Xf/5jAH+8fO6PAfjtly6gqj8C8CMA+MHllzVrHvB/eO5azDysRoHwZWOy8vOanR6d3Bp4roXwsNuixotd7cQYKxeXMhQn6w4HZFyeCWwkLUt+QJS0u7EOZnFr2CrEpe9KNwVYEQfdqlIgJ0J7+fDJLbA5eskJSNeqFJ31ewW8dmnzs8xHX2BnI2XhYzcu41gXAX1xIHmC6HtJg0AVZq8bCBBJXnWcyXMQVYYrUohNvruHCylusiMZ4BxIW0K6UkPnvCfRxFYiPeQK+Hxa0BTnqpZyiDXUG8iXxkdy81Ab11pBbDleInJj1DmuMn/Jhziv9azq+Ae2jzUUfwfAXwDw6/7n3y4//0si8jdgJObvfS0/AeQkcFLTTmraTtaczLEfDsNYMRe3OmdxuaT/h2muAQklr/vACIidkeAwmXUo2LElWhHyYy4UJqL5rhosdBOLXdvNVl+YVZb2DeKFa6JQT8dqpMbMXZX/BhKKRoZqiXbQt66G5m4cgr1LnlWR/Eazk9/VBFBy44lm1SD1dF+AjJ7UIr8cO8CRihcJ8hoiQQzej1xU22buwpjWTzMN7JLW7igswrGXSxp+Li6Snr2ZvP443CVA1mnoPTOOgVxow08O4wJtspzDEjzQGbUVvcJKRGKpXKVP11zYDYDA3MY5XRfj3FOtWUK9DE+UI0Lze4qfEB+kfZMswsP+pBHm2rqUDeQj2tcaChH5r2HE5b8gIj8G8B/DDMTfFJG/COAfA/hz/vHfAPDvAPgtAO8A/Iff6CkU2Tn1HM4icokW0YyGENsAWBSKgFvXsljnXP9kmNANkBxHnhLeJAU/zBisijlC5cobFEsuxZ99Vgy4deAiWTKuulwR8i1JZ7UY790IQmnHioDOO+dLroj/eznRu/45J/TpWoi3WmFK00DzO+EnJ2EqZTYFPK6x/pPSEXTbqrtBg8JQZA1BEvaP4tbV9413UU9J11xMzl1YIaIyp86KRyAMqjhkFxwArB9iLMexRMMsV6flrh48icBu4MZCyFM0V8Pq6ptTTRtEpV9TFSGXLwiDbjWrtkeSWiC1ZghdPhYTWPsmUY8//xW/+rMvfFYB/Ecf/BQCQxJPV3tBCn902jHyVezjC10uu4WPuAhI/pGtv17tmUoOP8OPSaC1LA7DVlK6te3uR+d9goSKTFIXEr19YyjmOFWdPkHg2E1YMq7UH4AWnX6E9dwADpvAcnci9tEiKVVIFs0RybNiMtHf3mfXmzPlFkpbCuyKF4PRpXdyUWpW3l4R2MydjHxIiQDUnRyA3dNRir5/itPP2w++j1A97lbqnsithrgBmBrViclQzcL6U2hwWN2rNegNwPCaktwo4nM1LKlWwepoizsLwPQ3t7vPw1KR6kzM7jwHtmVo+snmZtSJ3QppWTizJemOUQyi7JmFkMyY3R1NbHl/j7Tp7Ct38RHtdSgzFRHCVFU0Fm8BzBhPXVni2FnI4nsoMXxhnwRqmaM1uxRAEJFswkgAIxOihVzz0v/8HpDx9CrK8rwQvd3z7NFtc0JrrMw4+ZKZRWOihfuBNJg0aqLpAlXUQD6jfr+Sq0RVqmYQApby3ycWnr58DSdzgbeWegwussfHLFdIQ06eIq7rixXOkVQFbuhhiLpOUQQbJLvmVJONV8gPQHUEvyP+DiotZPTRqsQfAOY1DV7vpvZ8fHReaOQufmrm5gLy5tGeq5LU/Luj2mWDYf8SqfaWXIe7I7KR0yIHUbQ4EXkSqDqnMm5QrZqYYqxCSfoVL/IN2+swFLCJE2w4mX8gtfOE+zVR63535hlAvzjCo/EoIafaqi6AE9Ll3kq41oDIL6ikGn//TCJbSrjRL+dEUIUd3VfIML5P92tRQQpkpIWVseiaeJUsUOjFRe73jwgP+7MYCul94SLsei0WdrgJ4WbQAE3gJfFu1aVUteFELAqhYSzJTgt6Y1WsOkbuaixCOUL9mfUpIqHtpefixsE+Rs+F6uO3FPndd0jNg5ASDWLfUgjHsHNvgTxYYUqAmL9WUn8k53CqXRJIllVv6XrNaci6VhevMnIivULimqum6aaqIpIbdzecqmt260e012EoxEjAmCCEXdyhRYyUZGSEi+B6dRSypRsSsfSSGDXdFemEYD3CawrkbnnkzmI3IkyGDcJUQEv5uQj7peEJppyRAtZ3CLcISXqJhLuyQEzAD8Q5zKft3YxE4T/0es2J//iY4d1adSsUobeE/oyWbI5WxlwVia1bZaW6KOcE2oRsXuGbiXBe/k2PI4u2UHHqhzrL2zfhAqXL4Il/FcWNAcG2FIpRKl6nuRD65nFRKy4RobMcm5wViVeOV2vQL95YHx8jF2QhEfXLdxnOZHMjUc8iiRAt0w2alKgFox3FSBAhxlg3l34/PVsSStRHzq6ibFZoe/BiT/CT08YpkuZktbgh+5T2SgyF/+lGwhjzI92R7qnCSCPBgqqxGKh2Y7q66+8XlSV3uBKWo7jHwrJlh54nKE8YeXyFrxekFQoB+bIVXycgd/iCUrhTLINejFfNKWDB3RqCLNdmkReZM7IS4zoMqfZm5FnsXC2ySM34zvW6fF+ivDEzHMrfnYq8qsvGAQS8fxYxqX3o/45Uf2kZBud/BUF5x5boRcuNA7AogVqSmEwvvrOEziVIRObzaPA/sLnD4aCIy3mCkGEzw7O3KO9v+hl3Y9hmKaFPvRDHjs/fzR3GDlCvsZxYX93q6mrwnShWlPGV8/BD2uswFHwPOSUFzVzMCcWSN4jYuzSzqFx0eyGjHBXE4b9bj1LxhI1B5gGLbx67CndQohQORjU4rcFKmTHEV1wmpGE7KywXQzRLXY4Sc1+K7JCsPRcyeSnSQYk4cyPc/0UlvJbIhsazR/EZwJHTgB6FdOMCO+d4cOLTIJ1zDHgf+tLXUmZesJC/0hrw+ADWjtA50zDw/hyDqC8hK3dT23GkcZyCRcRV0EE+50y3gKiJvEDk1IwM3ZM/cHQHkSiAhPc0xN1QYqUMSuasTFgBI4ZlZ08u43Y33mLbLBJDY+wc2rkpSd6fQXslhkKTC9B7hiJ7N7KI9QGu15DdBiNO9p1x/SYJvYkogNwhgYwqVFKThNG2AdNDX/c7dN8hUsKwUTuBhJQvXjLZrOxE9V/rAZdDTnyeyOHWTODqMNJ5Dtm21H5wcR8jcwtay1h9hcYeeoyaiZ4vEvVDFzLTk9hIkjKP4+m6ohqPUETSEeDuoCW6WRKc++kjDw8WN9Dy/e8lh8Bir92rhW+JAsMwjAF58yZk92AI2/tALjv0izemJPVoiPg161gZQvBzZZkjNEaS0YyK8Hl5lmuNUIwrtN0gIlGEN3KEgNTrcDevkS4pp5SR9ym/RwP0WI18PbZAON+WjaD5syP6ETDEHZEqErpAzv2PbK/GUDDBSLrDraqX72XHJ0m4bTnQNTQ41SYVFysJS1+MEZ/mjkRGOEQ2hQh7fEjhUVRFmmn9a90BsuaeT6BTVqb5nIVK7sRuluggjNgMDkXKDsZrxo4DAIfXt3QDa67bSDKSyUwlVBqu2nEgC7z6ri6SuyRJziAni8Hie0TI1P10FUAzbKsyy7GKLX3vcF8KJ9Ja7sK8rqfZ69TUJzjCWRacTiMCGUGoXFIdCx8/M0Z0SZ3TmG78XRYd7tIJCS5amb4K9GqB3TquIppzcTAy4r+m+9gkOI1IBKQhoztzSvgDsCLMeM6WKEe+C4aCrbVEB0B2vk9q2TZo1ywNN0ZkaIZkFU70TYU8PkD6tvquBZEwZr/EmDm56Ee7fFffP2XtiKpIrKiFhKEI5H53ZNCT1AJyJypjHeImNDvd7H4zoZArVNX7QtUL8V526C9+3wwIycRuBkbvhMuF42A0hnxD6W+mdkemLNHC03WpFGVdcw8jbcZkJJxnSJSk346FfCZ0DxKyuhd0q5r1QTwz+RcWl3V/XESChJanW6JHpo/XpK0aafCwd5DcYtXHI0FuTkA0++AYaOewIlEe36El8RpzrHzWnmHkqetAlAOIQ4ZDJ+Sk576ZtmLMUoIRALrNm3CxffnGcQWbaTpKTRfAPXuWYfjI9moMRUifWSuhhki5MHtfy9D7xNDTAmDokaXU8oCftPSEo7FTPjykf+x1OON4P7+mTc5ZtAwzLD+ALDj74gs6Uimhu2C2SV5xsXCC9Z4H8nIxkMylsIlhQ4bG7pmSHmo8hgbZl9SdAID6wjkTYi/tQtxJzwfkFP5kQTzu7skxlhoOqO9dKzoBZidUiqJWE9m0TNmuitvQdIgg8/b9kSlfB3UOBekxwlb4pqiKxf49h4yrK1YTuwAskuv6J1FXbZSHkwOhShgwsnffgU2TkKaqc7aIskSkjwl6vRgddrdvEnJGGx/YXo2hWCwrC5pwJ+OCrXkeTN0uMt84MYzXcN84IyDJrouUw1mA3NHpZ2MAN7PGAfN7W4rdcBBQIb3D5aigRG6EsLIScJE0dUDhz0qXi0VluEs7ByN+GG6E/NR3oNBbDIuj12Im9oJYSsKHAOsofjp3wBJyrKQun2e3sYiTwRh2ZDSmJidRH1KzaWlwzuSjFIKR/6YLoZpuUUm8W8R3XHhlTsSzS0M9yyUMD9GRFq3F5ZLohtcq60zLPAL6EiKPSAe5LBoTbi4wAlS6GvdEtTEQ1cLk4sStG1vBsRqACHs7Mj71nzLcTaFgPOvHt9dhKAQZXuJuCKwnPF9vuYMvRXRbHB6URXmfwFwBSy2faRgCRhdoOkcWWRkZHoOq6/1Hgd++kPtmVjosvu9s797nTvLwgKhfoWq+O6tWuSBH1YyTNPEQrfMRsgUJqi5HR+8RiZi/9/v+HG0NNW5vcvHw/baWmgLuwqw3UcnhSKYzhCfdD+gZw4RJhORzLlW0Q8UYC6ivUQhGR6jb4C5KQ3W/I0VImi4i34HnUxwHtCR5hSiuiI2iYhhRRu82tgyxRpiRWo6WUH3MTKoTsXdyEjHcXfZfIDmx/g3uxM/K5QL2sQvEDDhhWyJ8jlzam8dEDywzyPR+f2ceVBThbnJPbnD0/fvMlSGJzjH5hPY6DIU6ajg/DmsvSNjFMAALWdVKZmclBkP+ikyrFsmQFgmgAhFrTcxICqNOAIXUEoE87IlwqqgHiOjLUrb9cno/ulOxq5VJ39RyErgT9PJOQCIZMuRA7lxBeNU+1hRadTt1W4u4LEuyOSLwbMRQMVIspPrcSLQTgerqQu60C/G3PM/I+3mx2uiX82cxnYNx2fjlAlzYN30Z96Xu5OAcalHW38jSspMTnVCTwO/zPflMlXQFktcRSWTAa5FUZridLheRjWomwfHn22ZIg67WcnRCISV7A0aib21iRaLvY5l/0tqCmj+lvQ5DAVgoEnhe2j6ELOZrVpckIiGRWPU14hIO8sysUf5c6gIEMkmoNvqwsXtvAesXhALYQNN49GSsF3+1Wx0Frc/OBX5WffLaDp9l3/JeJK3cRYsw52I0GSYuLgbRketONIznZkVcppqfTPQRhCPymlSu1shICQ/XhLpaLDr6hc9R3TMuJvYDd1Yx1y+htqOQMDbkrwrhei7YEq7MdGNW3Cy2+5FcBnU7dBdE1mzgQmrXs0JoQGTfy1m0GkYivsMqWm8eEW7MV+RlVIk+6I4+iCM4LxzMbFluQoBxYd8J1wPuZgyL28v3vx8TQJ/e2Yu/fZMLtEYdalGPqPxjQhQq5J6pCuG+JFPOlZWtep5dUYlULuBeMhMovx0zw5ytR3oz9JTJ5z5jhG4ByNvHRABPVwDTUMfp+zEBG1JTooVko9int1NI09PsqcgcwzUY0Qn2Hg6L47AgnZCfvlvCiwqYOpbvc7dq1gGR3zzakYTUQGiZ8AxFVt1K/R35D/ZLb4B0aJ/AcTKUlz0P3NWZNWIiGlWMJIDIyyjIS3qLA41ThNXDJYpSBIAbsOYoqYSzqWE5hh/nOMtitOey+1xszrA6VmtWGfzpmgt6zxPJlHqeuiECq1G93vJdcIMcPVyOyGSlK1bKAHxKex2Gookt0CC3PN06IOBIsY37kWeGN2LXY+2YCEUCK4ys5J1IEKHnsxoJHSPBp2ahcqeIlPARx+oByDDbPaMVC9yeZYdpAhGGcgFoIqslX4T35fsy3o6yE0eym72n7htEysI8xgq3q3vkysrghHrPYjGB8kam1JfdfQlv+nGGS3Yox4UuFluV4rdiWOfJiNyv+RnPu4nnqkjuXiJRDy+EBb1oj41HvZ/POapGWUynSqunI4bqHtV5xX5g2gBLAvI9RHz+Hmu0ScvzA4iiRjWcXT9Hl64S1N1OB4vkNOYDAVm49yPb6zAUgCEGJmo9PZluIeD8tH8DvqjNDYkirFpqFdJFIYsNFN+V6MCh2JwZZiKUZx0LRxdSkQWw+Ns67s9gYhimmxNLFGFx0W+baSUAWywMiV0uWOpYPl0tIQoIIk16L8RmAw6D0VEsWFw1yNOzGWVpDcpzTVn6nzvpVOi7p/L5nv3OLM3ezWU5bEIaEvNEPiZ9AaHpMMO36hOCxRcxyH9yG7jjB480C1JzcpOoLzirkqgXSVe1hJ9vNLGoyRvd75DhcyKI1DyZTbbiJlUXqksg1Hhud4uDi9IJkS3OxuUxDuFS7xtke2Pv8PQUSCaOexjD5iLTEoDohyBUKdmuhiNSGnzs7zdDLbvXbTm70R/YXoehUBR23gnEWo2qhLvs86eUaroGgnW34c59ds+kgVWWdQybNL6T640GoZBa58etPiqfjVGF/JAV3dkVeHxMJr05H8IoyTilVfcWZGFMFJRJsiReeYLT8GPqqDNxf9WSvewgY21WE1MI5eu1eCDxwKKKXULWjp6Co3m4JLlH9MB0+TGAN1vyBN5f2tyYiZiLJZJIh+8EINK2W3cy2gxUaGuqvz0KqnIUEOhwmsFaFJrOewUyLHwCzp/zuRZz7ATfowKYiJHD7IdasIgIefg0nD37jYa46C6if8+FZohQIrqSEUHrs548DbNVC2L+1PY6DEVt1U+l0dDT2QRUotFHPCdI0R2o+RAeEgtjUs/ocBmvbK0YgCJy8rZUw65qTF6LTDaf4yxRpsXvsAH1haXdIwkRlmNfnCZLb1EbMRSfNBIAIipQowwuT5cikqJhjTqLR8tnOpGogaBmqeRMcVh91uBifLLPXGg14zdJVlkNayGWs/gNUmlKcVQ1EqzZoV7XgkijEqIkW0/uQSCXekwhiUvK7/kzyquDPyiEO9GpEqUCS6m9knei0wv5UsRHxDVSkCb9tDmx9ufww6SUXMZcxmlpFXVwA/rE5LDXYSgElnBU6zJUKDVz4imJx1YScoDkJygQenyEeN0BAJY4RNjMnbwQXeLHsAlzSIA0CCQca0jPfx6H6JbzSJZ3cChIEjOStGruxntb7DJ6PueY4Y4sOSUUFfnOo72j1cOD+Yy8d83tOI4oXCtxZKCkjJtEKxfYHLAIgrsdnHSqwPunDNdRgdkbVD3EpzN5DiI7Kgm56/UL4pAjIH3uiNBsrokYuWPSDfH6IhHCpnHY6g7t+hsanjMEZ6iUXJO7Xks+hWcn1wHYLwAAIABJREFUP9vh2ddHbloRjiSpCiTXBRgBTGFYJSv5d+pM3C3U283WBVGG+Eb07r1d25PTgl+BGxByXg85/5e18hHtdRgKSOzetXDJQrK5/ykThTmfq0XlbtYzZh4EVYWTEc8uNSHr5yrEJMfA56nW3idB+KlVm7FLcgCEz1NNgclirR631zEh3C1GIRprIZ8TfKznWcqp3Fue4EVFZUuSt8bjpxr36KgnwqTs9/+Pu7cL1W1LrsNGzbnWt/c+p38kRbYstTqRYySC7QQZhPPgF0EeQkxA+CFBfnDiYCI/SCQGPcTWS/wi8IMtYwgIZGQSgRNFYEOEEQQ7JAQHy0YWIrakGIQlpI46kpK01H3vPfv71lqz8lA1qmquvbv73nPozqYnXO4+e38/a801Z82qUaNGEeMgIHaSbFMkOY7hzpRxGMU7aeUEBhLo6/n5U9q2pvSUHknG/qHONdga0jJORnAbsXamnhgla6b+PeHm6wDaJTwvY/SuYbQTdyk9PKb7H5PxjmcR896T90HMjOX8xIBO7FU8XvNZPjwkWXB/zHVZPTtmxzjngefgaZr4I46XYSjElZBOOMR008tiC68jb/62mVvpp0lQqnszwOpqE6XblgpXTr5BR6aSAE8v1R6ShiCHi7w5gzBcZN98ZD16qisVpsQKcWoRU+MC9Bx7a9C7O7RwYRsov24o/xbzAwChgzCQhm9ZnJnqn7Htdgq9eTTDue+QfcnPJw2+uKKMqYMyzE0a4UTJPgDhec1GocTkhSAUoF9wX5xvsN3MFb841lHDCi/EM5DvmrU/ZLrikopa9CCPA9hL/QyQ/JvIoLR8FkzZxonMcLJ4HPQiixiwkpQV82/PM/RQjpFdzBCRggPavp62LbwY9eu0UvslPxu2rnkIyOtXU+VseK8MoQowHllBGrn2DObxEcfLMBTAnAIcCmAUl5KnS5/xiDoKAj3l6unq0qUG5liTbiV1LQ96BeWB7QhvYupHCuTpxgXq4CIO5El3KcI7vLZW4siqJl68mZSNfwqyBUeDp9F5Pgn8EQVnJsEra7Wmg32Ba9eiul0Mhbu9cSqJIGT2gfx9FRiKOHmWtY9R060ErflvuuCRwi2n9nSPBccCfO4KNiQtn7V7DbU3T36Qr699T72Nfc8m0xzEv4p3F/oPJfTFWGJ+Jpp21cdoMnlTOoZpd4pkXxMPa/M+JX9P5Rt6ucSX1kscRuHh7jpd89uMl2Eo1BFabuhxepqM95j6BL744iOnnQi9x39aPicXjgAobmVv3vfBNoWiUGz9YQTG4IQr22Ajw5N1SY8grr+4gTQqdQHx/0Mn8DQGT7MxzMuoKdelfG54VB24a1nmTc+EBDHAuQ1lwTF1yEvGOhuKE3057qFSltd1vq+C6ygwC9GyPJvpYVWgzfUQ4TG101zV+XVtzmdZuZT3Y4r3GIAW0hc9DP6NB0NvUArWEnMaanOl5VkytITOGhLlEsLY07uCe5VuyNlbNTGwMcnq2fWUUJxGrdpMYj7AHLr7PVJc6V3GyzAU0HTdouWeA0HLXTyocOP4gGjdtUFqKo+DHgWprNyMwRwsEnnMcgDpqrHHRkMuTAJRIomO11PmjCc4qBcSdEC+nkDae+/zxvIUZF9LIBHufY+4VlmKLJKLS9WYgPwdTxp6TU4ZrydsSLLx2uhxcJ67K1+tC8arizl67gXIPiyj0kaebDSqBSPQYLGWxVqrK4Eo5gqyk4dJVJvia+L5kBa/9KyWrEaqhBvRrHnb/Jn6mvAOY1kG74Vvty20R6Ly9G7JbFp9NgxXuR57z/CSa6N1sM3PtA5QPMOlG2azbZbpOcrfDie4FSLghLc4U5N6IEIiHFPvz2BcH3W8EEOBeAhBqgGebnymr4Di9h75fz1ZTk2Q9AlAWYRkwPoBLgQAU9UeAMiI0yTAwNI97FnhkkivAaH4RI+iplVLjYNcVlNuGoV+W+6p0ti1dcjiSPjQPKnozgfRyUKgyPiQdVhi4aisZKjiXA8sRhLStWPcr3bJYlwQ2Q602wLcXFzlVjCeofMJX7GDoTPgxrCggnv1OTJs8ms1L4CA4JEnPzU+6VUupfs6x7JYE6aCgwQofGdZJmZrat1RyOvv41ksI66ZWM05td3KtXhoNQkDaZmP+rkE5FncWD4y2ciHGZgx5gpcwMJJ4GuEcAUgaNDPhRTPbT4gJxLwPpAtkV+mnCrngWzAtuZCpPvJ8t6KkJ9qBCAlY9CMzYfa05P34Z8LDAcwC/GIJ1/hi2grfSGDm39YbFnj7aYInIajuJ1oq5OqjvSagARP1c81EQAaJ7zwM/vFXlNOLV06xv0Fetdx+8QKXQTaYVDApmi3gfW9DXI90Lei+cGQ47nneeKxJE6kEfNnXUZPLMcbIEEkPUSvbTHiXE8Nkor4M51Mw1/B0g8esz8p9SGapCJUPaxohHmd1E0RsZ3kkgNT+MG0bsw7prAlnmH9e73OAIs18Tm+3slxSuwMSIrAcSQwXrMpbzlehqEQQag5O8114u4DJT7rAKX8NRd7Y6y6LOFmByZReBBVao8nUKhddUeXRYyOfLvlpnGPITyHUrk6pw0ZViT2EQ++pGn1dgvhXCGnnyXUrfn3ari5Fn6U+Vgv2eOizKPsRxDSJrq5Z2z0ts36lX7/UjIIAKxm4OEO+voebz71GrePN3zwTQ37AzC4h27A8gHw+rdWrO8NPDSgPVo6T957k0SrouZ9FllJXMBDousVOrJIDyWez8KvwmkBvOfLktT0JTf0VEB4f2dVsdtunIbbFpR99G6eRM3Q8HpL2Bs9Z4AEHT3zxaK4Wgwo4ulubl7qWGjxAIGg68dB2MQFiZqFXhT5rQptLmbExsXJxUCGKyTcvUpOxduMl2EoOMiOJKpbPQzG2pc+kZWEXgUp1BPt+AiPYcoqTACVD3IKOM6uGt3NE28DB4ws1TW9EmYhxMGlSBuWMGUcM8WZXovH6NKKFF8Vopn0M0akFicB1fpzBYlRQhfJnhlVDDYwhcsKfbjgeH3B49d33D4pePMHFPurAb331z42LO819Ktg9IbLF7wK9WqgbxKyEvxjF3oSmuLk4wYoqmF6HFbivnh7RoZOvEcgY3ACg14S7g8mnmUY8+mUPlyfstTzuATiBKqLJJbTT9KKAMh/ifmtlaeq7qWVxXXmm9TnSvp9DdXqa2DLUKpRp/fsSuBMEQu2YlS/wulREflbAP59AL+tqn/Uf/eXAfynAH7HX/ZDqvoz/re/BODPwab2P1PV//HLXkXNe3NUY3FOefpr5f6uxPd0zyURcA9BFEjDUHUMqZkZ6S1AP3gMSy+XS2lB76g3XUmma/cd2G/Qa3moy5IcDNXpgYf3UuNZzkFdOGT67Tvw5hFk58mrhycxfHQop1GK2F9PYK4Ady29IDokzsikapNcVhyffI39k3e4fsOK9z4tePNNA9/6b/wW/tWPfw7fdPd5bNrxm28+iV///Nfj/12/Eff/d8Pl/RV3h6IPpPGuGRPdp++IbmW2cAznELXNSw+DJ78rO0U6lzUa9443qAK7rYcEpnuEjrpbQ2ahV8EqZAc0qdUKwIuqPGt2sbL+UA0HbEMCZtRp6GtpOtdbNcqXJG8pRikrsJ/l7mJ/lyPL+W8bgM3WINm2TGk3N7pRZepreLlkCEJeDHGXdxgfxqP4rwH8VwB+4vT7v66qf7X+QkT+MIDvBfBHAHwLgH8gIt+h+mz2eh51kwNzCojxfg0bzlRvDsbsX4wHX99L46LH5IlM8Sfjem4qHYj29g7KxSnYyAiVzHufLLm05sVOBZnvLRfr43VGt0eWTEfsywVJt5o06Mo94GneG6J3h4i5yWcE3N3pir9gadAuOFbB/lqhn9jwR7/hs/i3Xv8GvmX9HB51xa/e/X7c9x3/2ye/DvubBcNrQEzXwo1RMZQkBamwrL9wJ2qoyBASAI5m5DBlIyTXpGQqssxvckvaVGtiXA6vFN52e0/1TIhhsNJ2KNA1Ae9Ie5ZwiTR8GoqKA6j62p3xGt7bhFkNRQgML65LwSxPxavORYdV2i7C8VFaWBxeqerhzVeawq2q/6uIfNuH/LzvAfCTqnoF8Ksi8isA/jiAf/Slv6T8XKr5lBNQ6zg4CQEkWZ44BHBptXV3urd/7sRraIH0278FQWUGwEKroPOGwhaSxEJjUZmXtPA5eQVbKacLkAsXG6BLLtjtBoilJCNWLqeVpcFmw6GLA2rbXoxHebT0XIj/qBaMpRk7shqYKCDzt6/A+rDhO179X/g3738D/9ryAX5vdFzkwBeOe/zs6z+I47LYeh/lnkkdP3lVsdloSLV8N59VqYuJd5YCqyf3FiEoDWEBx5ltKG59YCWVQt7zeVtHMHhma0CoD8J5P3uCvF9Vz4xkyFzT/RMBi1m8fSQew0xazdb5M4l+tAQ1a68POHPZcZzAeGqq+B3Gu2AUPyAi/xGAnwPwg6r6OQCfAvCz5TWf8d89GSLyfQC+DwDu5bWBSmxETNeaJzMA1nFk/NdSMl8l8++LcwWuV+Mv0LDUdFwvaDUA9HQLQyPyOCyfzeFxYKRuxV/DMuMbkicw1Frl1XDJgdSgSS+LgaXefyHaGzJV5t8hvZkqNIDkd+zpNvu9TO0KCebdtgidgnNxvQUvg/UwerfaKcvULWDAbLPwW7uiN8W9bPh4u+Hr2oJ7OfC74/P4xvUL6MuRSvVNoCRVeSft2qldgejqFfckJdTomO5/ek7+7KnyVbGbAPeC7m+bUFYv9uOzcCr+pApOg1LAS7isnHSvgaGyGD2Yo4QDpXWArbNMuzJ1jeMw9fLWy3z4Wrtt0MdHM9j0VI70oCA91k+EQQR4uU6WDqirZ5VrtPKFdws7ADzX0/5DjR8F8IcAfCeAzwL4a/7753z9Z02Zqv6Yqn6Xqn7XRe4THDq5q3CtRHYIl8tqbQbvLsmQBGzz3LY8KZ9+X1rVWlADJCDoGydYjxzHKNWtHibUk4gFZnSfGWMydtUCdHLQY2iJfMfJF3hLAWnDI/HrXpfscF2xjnCHeZKUjcSFU91uT5/puVdHa9ClQRvQboLbmxW/fv1X8GvbN+A39oHfOQT/z/Ex/PbtE9geF7QrIMfsOVT3nz1JQsOBww2erGseEqQt872Vwl2Zraf0oe67t1f0tcT3EkRmiFdJSIWHMRXDUVKPwCPnEJgzaKN4LlE8dro+iunUcNjnPepqeK/VQ+F6AKKuJdfkYd7nbZtFeh1sDc1Xfn5/263uj+lt3qSqv8WfReRvAvh7/s/PAPh0eem3AvjNj/DBubGqq0rgkMh9qW3QIvFmqUta0wJaMub3BxiG4GBj2DE9FJyMClShNycUrSvCHjKMaH6NE4EK6UXQM/D3xHf4vQXCTVdT9XmTC2RVrJjakgy1lGhFyeuJTLWroaa9QFe/ZXp0ypKIkZnU4iO0A+hvBPsXVvwfX/gmNFH8zt0ncN82/Or19+GXPv/NwO9esL4vaDeFHDafQo1IJ24FvuLAHvUnp05h8VC9JqOlRmnUVExGtdm62D375UZy6r/KeTkOr8mooaDMsoCc39697P8IDCpa/p1G1GjorIQW68O9KAHA1ohRJ+NerK2DzAylYWSWw7EyZUtB90K8E51gsZ3cWmIXomkcaibuLcdbGQoR+WZV/az/808B+Of+808D+G9F5EdgYOa3A/gnX/YDWdA1NJvClr+hNlRZFqN181oqLRqwk3/bLWVUFx+r8HpLBh9jTdZHLCcv4raZQtWyoK0mzU+XuXLqBShEJiQoyjQo+24cB/S992avo/fZKBa1o+la6FJzU9226JgNID0Jxv2s0iRz7wzMLc6ErCnmlnRt2QbWz29ou+JYL3j8fMcv4F/HL3z807h7tWFZDrx5c8Hxexd84l82vPqdgcvv3tAed8jNS6P3I1ONOixF2LwPBb2Goq9RlcOq6hTnUUunMDOGxdNQtbqPOEyWDAeupRcIsRGGHqunlo+jlM47dwV3wc3QtkY2ZVJcZ0hM9SlNWTvL7LimRsgx2udna8py0jOr4ZwavW0pjozFUqI0aiSheUOoKIV3mr+tyyUPw6+0RyEi/x2A7wbwjSLyGQD/JYDvFpHvhO2PXwPw530SflFEfgrAL8FqLr//Q2U8qqGuBJwADZELXIqbXQ1Ba+lNPMNCmxSxeTJUmi1dxzKhehypTXh3Z3Jn3rtC91EUuUtYUAlYTL6TJLSzKa7an9YPYacZC3uqb7q3GqLRi6nhVA1Jymko5ZRVaZk5KHG7bAe6n+L3v9sB6dg+27F/oeF2f8G1K/pjw/37gvvPKe5+7zAjsR02j/VaGQbAnqe2Ymhp4INJ6wg0jTmzXHThKbHvNRR2b8fsprsXZ4I7SC+V9US96JAsPUNJivsQLHyuNLsyJPkM6vOI52JNlKOFZF1Xtw1z9/mRQCQco6hSdwTyI0vSELKRxHZIzed6odekYv0+vtIKV6r6p5/59Y9/idf/MIAffpeLmngKXACtR5pMXZR0Qq/hG+DhIeNOMjR5EnPyt1PhmRbF4mBRGl6iqpDbZhuqez3EDletepOLMvo/rhGuhKANAa0maK9fcZ5mifnp/u1kmTQG/D3hRRC3mEhpI9mFNayotTPEP0LTEcDSDaMgPrTtaI83aG/o24G7Jlg+WLC+v+C4CMZiYU/fFMvjwP3v3NAfd7SrYUSyH2F0ZIxoKGxzWtKmPO1qtoKcATc2we70gqeYs6FAK2fQUBiBA55udqNDT2zbwqDIsmT2Z0u8xsDFsqlKunbe8OkdQCUFf2rmiODq/Z39V/EQru1WyFDHkYV4/v4K7Ot+2L/X4vmyGI5zDNicnGtb3rHOA3gpzEyCb+0ZCw5EXKes6PQRNN5Jt6Kc5DQwrVhopowmQK/5QtInxsfQ/+YVeQQgExwKKfpWTjO3/lngNCzNW7EAXjuQ7vfQuZKVbjv7jfLkEAFqfUgwVX0z7mrZGHoRp3qF6ONKvki9JnXMYz8gWKDHQHuzQ/YBORTaBdoFowvaoejXA8sXrnFqs85kutcKLu77dG2VxhwbZj9mPILYEpBGh3NCo1f5KpxbppWHs08Z7vCeuXn5Hq6Hc50IN37FRxzb0rqmwlA0wOt8ntRZtBZpy/Bwyj1yzaGCvs30Q+O66vokgOlrSHVAJIWbsV4QOrHvMF6IocB8I88J0xDQOWtK8C11ksl87OvTCfIFkqnEMgUsOSePQizVByDifD3jAjQYpSR8krILcK09764OouUjDAWNhN42NzZrGsO6iItEW1DTgTCOetb1GEkqAjuB+fXIMQwcPRxb2DYIH43fa7sd0O74y9qhImjbAXlzi3uyz0CGcc2v+8hrmNz3M5BZQ0g+VzfmUbvAe6wdzeXIz2QnuNMIrg2Qm5HeTQ0fa7TM9CsISFaiU5ulFJnVKOC7tcrE/D0ERmngdEQGL0Db6cJnQ46BNBicnyK6DHq5QAnt/n/IenxFxnrJU2foNDmqmjJ0PTs0TbgDBye5eA4K5Gmimq4pT50xkmdAMOjI3qaTGAg9mApmrmu4suI8hYoDRIPfJsZj8AepQEr293KyupHQx6tzAO7TO/GO5/p4jWsRIE90dsBSNRXrIZO7bgK6I2nffC8Auc0cASL/wiKzUtwFMU0MqNrfxSpNM9Q5nvInjiPd5mPAFLQ1vSX/OXqcEOuI6/S5v1usy1oJlcy4eDhamK1RbLVeggsBFtid09zMEF33Uw1IZuKmZka+SSO09Hoghlba/FkOo47H5qbA8boapZ7rjiB03eQ8IFwnBL00+QEyxGQatxaK9UuEp18NCvdXfigQGgkCkI4avHa63DwxltKwhYalzV5Clo57PCvD0ktnt5hEK6bFrrdZCSo2KFmSdKOlnG7pWUSlIDU1gQxXyqJnabCJs1xSAZxxb6T/GHot84YiqAWkShJBMD2nl53xF6Ai5lPqnPbrPRbzdMJd1vQYtt2zF+klyVAnaQlkRKAQ90BSmNJYS0tuRL0ueiGVxh8TN9KT9E0X4KA/o1lQ9xnwN3Q+/JnwGoBURpMEpZmCfyIaU/kdfM4lNKAqtxQSlRG5NoQmazBJEVTzyUBgAAdyPTIMK98ztQ10I2F9Xbp5o12Ad8MyX4ih4KhklLp4meIjMxFApAGZj+9rVkH6xpauJgLjHgKkWUFOyXac6yikN+jmi6LQvOOECuo1AnFWbGnZWZBGzU8++IKTcLNIb1Cszsl3t7iKv9RqR16PL4YJRQ83u2WFZYnf47P95EIxQhG+nGLyLG33LmxiwKSglc2VGam4t5Fg3BRi9T6fxsxQBNfiyOfaT2nQynhlqEZvQzXXBzdqxV2CRj6SIeuHkBC8pnH1YrA6omNZO4VIp5ESiTJn0zxFLL424juoyM1sFeeEXkEbCGnAcZT1KLmWJm8rweKsiT9d3zuMF2IodFrc4RYHOImM3QHLUNDjIIrthS/Bw7i/gzw8BDXaXO4DZ5UgANnajtTo16/te8j2PA5zB3u3NCkLz7ioyOqj8WLhz7oaTbtyQ1yWjbRgypYFeMn7Zp78stpipX4Fad7UvqizWABRXhdDLwnqOungdFmPbGcHmGG5uzOdDPd4LCM0Jlq6udsDgkum4Uj8YiqPoZGLB09ZizXd4sBnwpC4DN26ZiFZ9fAqk7E104FgCHEUQ3lOJZ9X3TFMfIgb9Bge2tr8636kXsVdoWlHlulInY/1YoAjQ4AaFrusHlm48nrNsIn3PGFfftDd39n3Hc3VzE4gaJVUcI9cHrw155GGN0KjdxgvxFDAb0SBVioPSZABJnfLyob3tOJA5o/5ELcduBypcF3JPOfsAzAvvjoIxHER+QIww6D5vrh+yfy+Gwwt8WVUC/LEJZpPd5Wcfd1g6eGWIBmQG2KU+4gwyzadiM2JAvb+w9rdCZBpwXqfx0D4+FOFogBo2UF9FO4IF/m+W/oPmArNwJJtQXH1j+nENjwBeZ8n5S42pY7qXL+nKHaiZ9Ssa73sxSuhkaghCDe6z6VMYGu5f4ZIrTwXXj+f1Tg/e+T6Kx5gpFyr51CrZmtGjnNa1yI9tV6uP1KsluGaroGhTMGzsH8RpbGPMF6GoVAUy+obTTzeYoct13dg9RxdKb3eDFdgr4RmYBh5+BYiOHW2F4vNk6+eDsAsKsIKPREXXAWiahUerrCq01sbTjn1x6t5Dw+lY5OTrqJFnAjE+1VEeEHX2rt3h7aFf2bKxGVoErL4ozT+XRbTTKRRdMafvTkXp9zfZQex3hLkLViHtJZArzcgVlUDlb2B9MRYHIZDsP9pGBUP57Iy1/gtihF9O2qcrzKs3Fsk9CLIKK1ov1yt2AuuGkb8YuqyVnApAIaZMItQBq9BgAC99fHRjVTLdPbuWIsLxkyU+Djp/fXeZwX8zEqv5vDUKTGnyr+R4s0YtuH8CnZjs4cUa6viVdKbzck7jJdhKDiICZCIQsvNtCQXDyvrSHc9g3eRP7fFQuLU5FHUWFVKU5g4pVsBSFvgH9OpSu8gNjhOJ3WRqWcmomAiT4C60zCCVW7oCI+UeAub9aQXQGyBgJ7YDedpxQ0G5MlGmjFP7Tr3ZD3ylDqfquNAMBkBRMovKnV71NJMqWXeI5mXNLIMkYh7OLaEDq+zKaEi07lN5nkHzBOpYr2l6jjXiU5hCr05kvOyUFGMo+K8CeGucVwk6OY1o0PsJ+pFDkBLQ+TWkjDFZ0QPzg+1wNyGY2t8DtXQ1NQzMTxVVHbplBZ+y/EyDIUg6cx8ePyZgyW9lLYDkt8OxuDltR4Px4RVsIwvHAfQlnJCPCNRxvdQk9GNw5xVKNkGXnsYueqKlpSqpx/RMGENVecy+mpyaKowRcduLah59XZGAW3JNXA0/wnF/cQ1eUI6qyg+f1d5LARve0d0biPRrc5hmxerjhHpS8N06nw3YHNDRUWr+lxI7+fre4Op/iKf5W2zrAPnCgBUIPf38ToaKqk7gSxMdeIaMzpxL83ut84bn3eteiWORFyG10rjVJ9PzOlpbcWUFINHw8h1yc+cng3B3fYUSH6L8TIMBQoNloAk05b37o5yE59rFhzkrNLq0Zg2UOYtXfR1seIhINrSRUeoICAxppQoZIqHAkzGQHmCBv/iyBiXBmvLvHx4Fy3Tp+RNYIwpfy8sJotMxAK8emWb5LYhKhslqxCrt6PjSHTf+SdYF9OJ2I9y6jlJ7Hp1fY2TIRnZswJwg7TMsXVgJNJ8YofpedSUaFUop9G6rAHAqheSyd4cTHQAsOhLRFgT11auYd+TDt5LvYjfQ26uAl7Cr3VHGqQ+spiNqcqH+9D7tPDjkqCtr1t4p6/QFolQpMg28rVRX+PPldc6hjVf4qFDgSRqj9QDSNWl/JZgiFp16ci5dq/7a6NJMRcaMFlVk2AvlpF5Yi4yp/FGs1sHC8P61qKjMVzjsCDCHMHk7HnqxaZHAlGCOcQI+riWpsEjv5tglAuWRI2Dj2wU4wuqpuYKa5EsSZJtAuBjlSoBLiD1QSuvpHoRqgn6lRHhFzcGPycYhOW6GuYUJAG4Sqffc0MrQdygWQ+rxmzNjCE3m6ciddCIFbf5OKB7Q7A2WQlceRi1XoKqX66DMQ22Fajr4ASkRsboGJCl9Cylce6Jx0Q20gFtlSP/3k9AbRTMyfx9KEbNn5nR60tGbLT0ToHJI2EVtYk7Va/Z5QW+JrIeqsmgG3kKhQhrz5u2kvQlYmYzGFJSXMfUV1O8LiNIVRdLuenVAZ+7O8hlPrnNLVzTc2CsHmgzcpGRFBWxp4TBidaCpcYgSoD5PQHK1ezNMLVxIMucA1zr+b3sU8LFQUPjIj91A4pzOfSNpZbl3lKgETY54DspXbduRuFURRmfV/49ZXWGhodUG0E/odNX3KDWvdw2A3ulQZHkO2F2hc+ptUyVl2eBzYxDgKgsCKzP88zIpAp5IUDZZ21mINgxXll2Lulx1Owb4OlaKvfzAAAgAElEQVRQ5LNwfQxpzZiYQB4oXHc03vtu4SXTocyK7UemcpkurirjBPoBS29HxsPlBr42eBQlLm4F8OHJ7GkyAMmSpHfBk6UOGoluaTMAVtfwTA0J3XGL8wq41FqpwPQQ43mxLlCB6wkwNVDAv7Iwh/erZLizLLNbzVCegBpPKuzZA8RxgUnMpG7Ec75/KIAjcRa/R10Xo2AzPFE1rVKCeECmWwmkHpixinb6bh0JKDtvpILHMe/8TBpiPjPiQUDK2/WekoDP4Sxky9JIVVCVn09DylOel0xWsFaBHTPET2nbLY0qilfCQwuINUeDE0A4kNqYDH0IHBPkjr4su+lhuGdYDdjEOHZPLtZJzaaUz33X8TIMBXPOkLKIBZGeBFwVqMa8R7jJCmNhhnEpG1a6y/XX/D03NV9/duWeAzOfowRXd67WgtCt3fZJDDiovDWNyHsddloFQ5QeU2uJdZxHLA7JUOV03UqDwUKnkRJuIffOzyqZEt1HLsRa3VmAxalUH8jwkQafuIqrhIvziFWzI1hs4sKsNMbqYmHIzbMFQMbZ0iAX89BkXY1iTfZkk1MpehrhwLJovHitgGcZEIcPqeJSUunz1Nt163GE52i4ssyYSs0I8XC7t3S3vLnOnhTg926fLwTb6ziOBOZjDc3GOrI9vgYibHqH8UIMBbKFWwW8gDyBimtnVYQjrDuAdOGrJ0D0WiSETQMnYFn49WaMQ7fQUbzjGzqJUMa0rCzBTMuNGbeogGvvYSy0uuK9AeqALUla3XU3W1mcmgAhOQ7qIBZPEa2hAgcN5rZlFepldQEej78fYfJ+U8pwREwcRCeKvtKg2aROsvMGGt8SVK1EtyMNb5yGgNdBdIQLRSwiwOlyUAzjDERanCEYsxqVjSkyl9mTvs3XsziMzMq4d50NJwB5yAxJsEeJxwxNnVR/vw4XSr4rBWinQ0T2Yy6g46YOb1aM5uKHGzu/Vx5GhBqc7/v7kj0ZySpukgWQ7zBehqGAZKztKO8Td7XeKNH8ulnoMvIErUCbyFQtOdWEEBNgLMv30EhwsVV0m7/zzROna2xYekNu5CrDlGHR0n3T7AUs9RBLBoiQaVk8Ec8OBS5L3O+kFh758+IWc7Gqex/sNeqZkUgNcr5DNm/GJsLdHqZQHpoRkfprECnhl8/XpC1R/mb3VVKclV/ANn2dLnkhQPm1xuFQwsXIbu07QlzNORURclSKea0jaQLIkuJE9Xql+XMpc0LxoDM7mBkKPs/ImqW3G/yP4Z/DzJkzgDHKBdBLIkZHA3MMw0wouExvVZ1sx7L8msp+y/EyDAXXDSnIbU2Qje5UFSaplp8fUQuoeBLXhR6AaJ5oFts3WKyfjWWjg5NIsjkdiIy8ey8GzfPU2dy3BdiY4GebUmLToNs4mnW0gjMqG1WaEddgJzmSin3M+gV6wOLhIDKpeTH0WsqmTozEsi9RhUliGufMK1vD7fWuWVoenYhAL6vdJ70gL4irZLnADvxUzAvXMBZfrIApZPOBYOIK9qehI9PizOB4NkouVuqfRiLXh4kgKaQfCA+HBiIOrsIjKQA7gWkloCu5ZgKLqFIFvF8+e3pJ/L+WcK8x5SkANLIu8NAn57QQ6Xjtvbmn+25GAngphkIJlCWgIwtAYZBgJHI4+KcfvAlw0yjUG0gP1sPIPJFGre4X03gFz6hl3VxEyg3iI9x3Di5IuoYVfedGGWXDbDvklUvhbSx8WiIcsTSWkapEhxUa9ZY6CseRtSuP18g2TGw/VVsc12vMjXzsHmQ6RnbJU2bRRo+AKnkg6314VGy7NxlKSG5uN+o21+uEEU1SfsFYzLJ+uxQu/MSIwliHjiam1zPc0n2kQWYYwRDBHop95OXyFEfqDezpIjLi9A06e2U08uDi9YdxOJIl2huiqfLEUzmgm2ZRX50fAFauwDlwTZH4Pv986mQON9YEyok5vcm9EIfXugJLKsG/y3gZhgJ4Ctb5wpmIOi1PHFUBGolP+QAN3EQAWioSNfxTVyonolDoBF6YpMx8HAewy6xjKJKpNJ7I2w60Iw3DmcrcEUbCFqgbD9LQmdmpoRX5AAB0OJruoZAwA3K7ZUYFF4v1S+FbUKGDC1HCJSCyK6wtqDhJntCa1afKDSX52bz28wiMSADxNO0o8w5/X9k0gV1Mp2KLcELGiQTF0JGvJ4DJ+a9GYcoGubeDAozzecX1fZkRrn7Pg4wZOIYXzPr4tWQjqjHXBfGwUk3MYenhMYZnVIlwLe9NYw0g6Pq5dp7xqN9yvBxDQcQayNQZT8xlySuV4joCGRdyQyAXRnAw+NmUSbsVZhwNQJd0u/nZvrnDpTxTqsNlJKjaUnwm9BCbAYjrBaHQBCCa7h4H9P0PfA6cOXpS5+bCgrTMi4dX1PI1/AxZjJ0X3I8SuxOcI9eA6T/iJkPylOKmGaYoDSBJbjUu5+c7SQlVvJbzzfRnlRDgaesch/He++ZhLYs1Y2YD4THsBPUq3CzkIyELCB5HpdoTgK1kOjIhSbm/3lJlLPAP/9t4Jtt0Nrx3F6N3e/Hik5C3/lwzWder4TfkngD2nTwAdoKmIwleggzNRIyABpgh9UKxwPb2wxoEAWmU32G8GENR+zjQpQ2MoKSoJkKQj4gvn3OvhiKakPI0G664fbRcQF6h6AKRccLoMcylXVfDTgQZ3ozT6RcgoAZYCKCg7KU4zeNePaxC1kqnZT454vOIKyDBzGoAIzsiie94tgNAuqOVf0Apez+dGAqEloG/Vv1+pPwc80KSkrvokSGqm2uMnAtxwxmg7EiyFpBxOk8/VdswNIyeGZMw9sUD0WFAJON57osTN6XWuuhts405Xa95bHnNxJgKKAnDgqQ0n4rrB56GDSWtT1AzWKN1cM7p4fF+RRLwrqGQk/hMHd7Da6aiZYduvJ+5ydHbjBdiKOZYV7ctN4tb9YoVTPl98QrLQK0JXvHhF/CO4QAHTyC+jCQcLuiq0+AjKwUXK7oq+XjVZwxVXHMhT7m2YhjFUhMQg0aNHhOp03Eh9WTZy6lZAN2K6ANPAOD6WefrpNENXQZfaFHez7iZJCX+PUIBejgFiziGkcYYqws7n8MA0/2SLQ5Ujf1JgplIsE11CGTbk4HL519S2ZEtawK0JYxqBa2Dv8HrBJ4Cf8RhDgc5l+6G26+jHmplDqewYShwQRrI1mzn8fmfvZZBL+JpSjO+50hA/klGiQVyvUOPzQ7Rs1H6iOOFGIoZ/Y5uXJwEKgQRhQaKIfBRiUFbAjhMW0a5du/GlXBB2CxY0sxwOFdA7lxlqJ6yfC2NRJxONwfCigS7A5+TghRp4LuJrgYIVjMkNQY/3WOkYatGZ1C33dg2r5CkW6sjC6YcNCN/wMDSQo2ugycikF6NF7UFT0IkwyF7aPa+D974HF4QxXuFcIVHU83iASCtAa8ewihW9e1zOlVUgVcPuWmIE4zsExIGjdkVcjSckh3vrXMcDN19/puyTNwPpecK56IepWxIZn/ayBaA65LZNXp8pS4nSHnAXPtDvEkkGk9DJLUwxGuCzsa1ezZr+1oCM0+nVmyeoZGSm1x8jsqjKGW1Wj4zXNrC68cxLJZ3TgYNgZLpxhO6uJyR7uPGo5sJxEYP0Vwgw6bKGDyQp7ZK3mcYopHuck3RVe8BiI0XCzyyOGJSgL3PvSMAREcseinsOFVL9ot3x3uu9xfPihhACafyeXroVr2TImeIzQ1roT5XAd4pi8Pn99zz9EF91KhXqUPK8yNAuzgBzz8jesRMdUXu+XGQNMfnig5clrw2zv9+2uBoUdEsgCmvASW9afc9gcPHkYQpp5OT9xJhMtcN19iZWczMXj/Nx1uMF2Mo1Et0IW1maZInr+oRQcksVJ59eAw166DJBaAbGsIeKQpTN/zM1+Bp6v/m4gyEXcLNZEpKj8Nify66jpTPEwmUGoCj7Q1yKeh9SXlJbW9PQ7InzTs29uWSrvO+A7JGRymhq342eKp2Y9oStK2lz63Z+7tLuQGBZ9ADs3Aj51tkSQPzTF0N6eEUgLG5TcMcytdAhoQEY7nZg4+hCaT636QagygZP5/8rczbmrVAtQaGz+coFO5SuKbbbtmnS5nPauz4/dz45Frw377+Jk6LtAmnU27yyq/g+ihz+0QRjOC0P0foF+elfJTxQgyFzkQmCq/urMkflg0QB3pETVdh19ioAJ4AROket5n/z9cONdrxXiaSwJAI9M2b9A5evXLCTnuiNxAqy36qmAKTAZXCDEYAXi1DDXo9DjYq8/SrQAhUDm8tV4rOznEq6yYixag6AYrZsFeB2zUEYeGpUXiYEBWSx5GyciJJO3ftCPEKR+W1icn5Bb9huFwbkB4EvTM+r2VBCOH2BqAYS57KVdMhip2Ki8+aD570zCqImHH0kGcanhql1ySk5YuYd2ATbNd2u5kR9Wc6keiKhzmFSHcXw5yn8FmgDBHqnCyntUFjIgJZAXSXUDxSsGjyojg/1EIR4kdbXttIA/Iu48saChH5NICfAPAHYGfrj6nq3xCRbwDw3wP4Nlij4v9QVT8ntor/BoA/CeADAH9WVX/+y14JUeIN6dpt9eQ29BbbZu5pzYH7+7W1kIKMkKUBU+enqcjpSBo1EErVPDGVVZXinkicACfXnAVB5GUwz+5jUrCidwC7nQnRBmIxytKtDHyrbn+N1cUA2KEW/wJ5ijG/PrEKfcHsRzb+XU5xa7jdLQhwcWJFis0R/CrAA+R8jHnRU+yFXIonWatimHOSnvm5GFp6LFWn8kl3rZh8/z3BZP+deQsZHgUu4htVpUge1hoXIGstjsLopQcpMhHkokdI6SMaBp+pYnoY9fu8sheqxj4txLpMlxdvptZG3Vh7QwzkhPO8xfgwHsUO4AdV9edF5OMA/qmI/H0AfxbA/6Sqf0VE/iKAvwjgvwDw7wH4dv/v3wbwo/7/Lz4IgHEBHavlpik6wgrKOo5sdAIgQ4zeg59gugbld+fROmQZSYiqRgRIb8BPcwJ08RqmFClA49cVOorA7M2gWPbqCQFQ3OXnTJkQ8by6GZzQC40wTdJTImmKRDAaPt5QSUPqtkN2v19yK/iaQuPWbuk2DGdT0gsom4qfiWUxz2bfrQSBc1XBTqYcWczEtJ6qaUvQSF4K3+IY2Qpg6cByl+I7TQAkmEf9DgDmJRA/AXx+YbUx44BeT7F7X9Pw8BAaZGvuGWb2ZvOiw7xeriVeKw2meIEivUECopfLBIoz5FO4Z3gdkCXDtMggRehb9gK9mLZnawOut3WdxYDfw1uPL2soVPWzAD7rP39BRH4ZwKcAfA+A7/aX/TcA/heYofgeAD+htiN+VkS+TkS+2T/ni3wJ3L1zcGllXUFptrM6w89PtojxIh5Nd5AP+ZzmA4GuWt25LA6gldMXsO+ofAfvgB4uKDc503+HNdc1Qk8H2jqFFsF32AqJp57ITJn6dWPfJx0ELoKonuRnFJwmRFIAgApLZaMEPlPowpAMZ1LMNcFc43pspli1L2nQybkAkN2ueE0DaBr3Y+h7jxy/GXnLelDKL65VD8NNeAqqX8s+0ohyDsiRqCFPtx4YARRWHCC+QzPWr/frEonJ7zgyM1FHLaevmasKRNLYcq0cWalqYZl4Nq9kMNDj2es4ZiFmHmLdxYp4AEZIlkBmGIci/Buhy1uOj4RRiMi3AfhjAP4xgG/i5lfVz4rI7/eXfQrAb5S3fcZ/NxkKEfk+AN8HAPftY6W8u0z2eRBQCszi4v0jWvxNyQwsRsK/kN87icaYloWLpdjNTG5a8OZVEcVMd5cwDE/wAXTLJPj1WJzcAG12wpWFFz02mUajC+qv0fKgBbANsALBHiXoKWK4hp/EsrucHDdSQxiJyL+zjuGcqYisS3G1udALCj8J59bQqY5yioZITnOjvhyp3gXkdYQn0wwwJG4D+OkKN0LluhjOsFRfJKs/a8aHz2lzQPiUfQ6vj5uXPVcjo+Qn/77DatEIMvYUubU35FdWfUyurcLEBIBQQAPyADwwhY8Va5m8Upbwx+HTUtuierrvOD60oRCRjwH4OwD+gqp+/ksUmTz3hycBpKr+GIAfA4BPLr9Pg17Lkw2IWHgC/wI4aqCEez4wpKFp3U5Vr6/QZ3Qig/rNHPVxQLcD0WaOQKcbh0DAnWYt7CJWdAGAI9N0JRsCGhoaLPI5WLVZTnCLQ0su309SWRDutT5mER0XqY4R3b1MlFYytoV7YRXzOClZR6OfqjClrn0BpNdTQzTVpKAz5OMzLhkkkb0QnYaf/KvRssktKcBbdFX3LmuRETjXxIRnJLPRYzaD6lxqcota1Lym0Kmwf0nEUtUQvo1w4TiA9z+wz1MFtmNqDhSA9rpO2htB/AKgb94gmJ7LktW9LC24uwMLCUG90tD+0KxjcmA3rt+fY832RH3MVwGjgIisMCPxt1X17/qvf4shhYh8M4Df9t9/BsCny9u/FcBvftkvGQegtb9GQ3T4LukdWYt6UF1Y0p8AY9NJxe+odGECV9U9ryk25tJ50nLU+JLeABW4/MFoLwYiNh3Tjy0Aq9NEu4fhGYFxAEdxwaXI3tX3MBQhiKmKEOkpatkRHIwChHVkCMK+GWMkJlS+e0p5lo0RmSne45lhehT9CmaMxDUj6gLneTI0ZQlDyKhkTch81PIsafCmOgu1++e9k70pVXi4hJy8LgcMRfayFsrnPty7t2N1Ohbq3aZDgL1vMeZsTxUFCrbxGIBK4B8kTMVeqB5IXYfH4dhai9DZPu/Itc+1d87+fMTxYbIeAuDHAfyyqv5I+dNPA/iPAfwV////UH7/AyLykzAQ8/e+JD4BgMUuBgwuT3L6ABJpJzjG0l4gT02+l70+qWZEDEEH9OYn1Oqut8frJoIzA4Py6mG21AAqNXpyKy9rZiGaP3j4qUpykWr2mFgvuQk5yiluix+huUD8QBZvaHy5lE1U4m+GJRd3iYEZSAQmcFiCJeoexVmqT7SkHEfiAAXrEZao81rKggWp6ttu1ZX3HoKEISjf1fza9x3QSxonJWbgmScCoXeXfOZw7AOYwiKWA0hvtsFrlakbWZbRhzo3VbOWnh4cP7AUlemOwNamE5tGlOGdepEWPQQAQi+lvp7p3CbAIQnQ79YBPchzy2LrZzcN1ZpuDVIeS9H9UK3CTW8zPoyZ+RMA/gyAfyYiv+C/+yGYgfgpEflzAH4dwH/gf/sZWGr0V2Dp0f/kw1zIVNTCQiK6o/3EpefD4SDICdsU0SSnWQm5RLm6zmm8wVi1pXSaKiBItJqfD9gmIuHp7MqNk7Wnm0i9AlK+WX1Jqb3iXioQpcIiErhJaHUcRzIXewPFZKfvXHpsdvbJmMrim8msDQdGtTWL1YdnZ7AUj64lSLwskG2D1iiSn8tULbMuJYyIGJ7rdHfchqnvM6Pzi41zrQI9wlrWHX9zjc3ozTkAGK4SWBRddBZXnQ+CGpJUz+aY42h5uJ8PuACLR+Bk+e+RnsQZj+PaVAWO4t1WzKwwigOnaZKv9/dErUvV1nzH8WGyHv8Qz+MOAPDvPPN6BfD9H+0yBLi/Mx1BAPJYJsrrL6Z8NYlUVcWYKbtRFJ2APA1q9sNPdQ1V5pZWnTLpF1Zh7pHyrIvJPrMFsE+ehR4HpF8QJeE1fVua+9i1ZhotXPQT50KJbfB39LxADGBeDKHVcb0+QfYja3Mezh6sMvzhAvOE7z0W3xTSkV9CyjnrFvqp21h9LZCkL8bqcQNtzurUwq1zif85zKg1IszYuJFluwYzjj3vsT5XZk+KIpW0kkWZjDJDlgylmB62dQCf85w/M76cB6QRKCB9/C4M1IxD2eQVz9GvO+a2YmLbV9FQfNUG89fsvHwWgEGx5GTh+Zj6dDjwqKrW+Yq8g7s780zWNclEfPBDM6NBA9GagWnXm226y2rsw+IOmwaAg0aPVz9BWoKjFwNi9XozA8LvAgzVn/gWtsD1WgRpuGnCsyroetSXlEXccNK8VKjuk3EIpimRcTEvQNY2E4XIl6ArTpBPMruCq4vpskiKSl6AgdBSjIUbdoV31OLvK9vxOEwLNNxnTSMEGGeEvyPGs6UxnhiTvk4yjN2Mb1A1J+Dfu+eJblqTb/xaMIvaxCS6l+vrJNsS9sQ53NPRx1saUaavXXc1QGwfUj5fty0zZJc1OoJV40jtCqEQkHuR8TmlbuVro1MYLIaVJtPpaX/SfKinxTipTjv4I+KFXkCcvPQg4rQB7P+XNeLn+LrbFmEBEXCWPKufMMwiYF1swx8jTyqmIoeG0dEP3hjlWVrSwNuaJ0eNUXvJ7TMrUYE+IBH9SKmN+e8AWLVoUhwd6LBCuWM8nzKjx8OF6NWdYbClhBWVDAYk5f2WKcVJOfqJZ0G3uSfNXtXARn7uF3Odm0B3jRAtP5MZmRahSOAovCeCiYVPIrditNbyTHjdE9O04GXFC5k4E0B6GEBS1f0a6WnENdOzKAB4MGnr/JNExkxaa35IKIASKnnYFLKEwJR9etvxMgyFIrn9wdlnNsJfcwzvntWzqo7pVC2L12PBAKtKWXpUhfKUXJY8uWjtrzcD9oCMz/392PcUdwVygfnrZCFOkjF6gHC8tlICnRumbDwWVFXhVKC4+ub9JLnLO5HrFl6FGdRzTO/uNpAn+FYKzOBeTs0knPZpXDf5DL6Y1RH7SCnS2PG50QOQlpuGXhcxAtWs+OU4p/74HMrGN8Tfs2UMEfm38cz88v69yXBVC7P6ipb6oedRcBv2S8lKV8zf0VsJK3ktOoeqezEEnsanVisAKyF3wxUqYYDxa/gZHq5K1Xc942fthPG9xXgZhkLgPAdf/J6zluOwk4kxZ6hJt0TyecpX0Ah4xl3MEGZy91qzmgpPSdnfe5ywUg1KIbNg36HvvQ9I6Ua2ruYmbsaz1w/e2PvWFe3hIeJexuYWZow8VY9jFmB1tJuGDE2M5sxNQFfbM0E49jR4TLE24iAj2HpB0wZygQ4/XVmC3np6bMNl/asKWU0N83OWBbK2FAQeA/qF9xKnqSm6urBp/Nw9JjGNGyBO6puzY51ar9cr5OHBSur3xefKvQWGTWB45YYqPAT/eWNo0IGthA3unRi5yuebVb7EInwepg1awcelT+Q8FL6NeqEXT34RCY6HHIetPYYbvWUY4p+tPFAqFkdD5vc99VB5jsD4EcbLMBSQiH+jezNVnuHWvrrLzFwwHmaVI0MCWvwzYaWi8SNPwCgDBhIT4ENv/iCBOd6me8yMAeCbzqeU4U64ozKRlCYeSCkhnnLrgG/WIxcEF0xNyT138nrq10A8AJU6Wb47iEetnPZ8TVUZ43VyDsrJHySx6g14iXMAr5xL/84qOoM9Qc4IQ3brsiYjjckTcJRgtmd7pLI0K7ZR555YCNOuTLVq9v5I194zJZzjXfI0j/XSIswRvi480TzMIvs01IxAzzmTbbN0dy00JGB+eN0HywLKIYIuJqwcWIRRAGJ++X3HgXG94l3GCzEUPlSB/QZ9TKBoctN5SjB9uO3mPnsXMAC+OY1yPR5zcsKHGGoLWMSk3ql3AfNWIt/sNF2i0kHKYnYFMJ4FFwWBsw/ehDsql8tcW1KtuuMGAGzzE9Tz1wVAJ3maZlalh+cAYGaGOicCsVBOCL4DYFNlbEXQeT/VSBxHbiBgdtedn6BNINct+m2AjEoHloXZE+dmzJJ0vlm9s3nURNATAAzPkD2fgxgmoNdbqjppvY+WQK60XB9MRcIModzfI5pPnVifselpvFn4VfkupWBQgcwWUWx3WSIkJW5krNnFwPQoU/eWmh6yRI0TLIqUi3M9RKxVw7ZBLpds3OztH0LBrOwH6NdK6AFgUp6iPkBVdiqpohCrJRhZgbNRrHKpBMzTtlBtK4JO4RWeaJ5OAzDHh+WklbueOXhuumNkD0ofqTOJ9JyATH8yrGmnU1nV3kQQ0jcs1uWZ1/o9V/IV2a1MG7omhd42qx4NFuCR6H4tVx4+t4eBlMqahMI3gYiBcK0h2icAeWp7FsPAzi2NxijuOjc5ELF/eEwnlqcMAnoMJbyuhXMozUDH44DAsYYC/uqeRg7NU+nLEmxUPrcnhL8qqXdWkgJOv0tjFaLFqjNsRFIfSVnERVQRXcKq10hcqGSEdD9Cs3Niqdb1QGzqcgHe4K3HyzAUnG+q+gC5SdATbY6qRvc2yikwIbs0KC60EoNxd3VNg8qdGz6wDkkDxP6dlWylTSBI1N6+Q2JTRtkvuRnOtpzcdgJxYeSOp26zh0ZKYk+g3UjshTyJqpYVKH125Q66dW+2eCijF0VjO0JIpny/Hgdku1l9ATMyInCrmOFaDSnckMR/vtHzupn3L8ZnlFDQDWJ+VgNwFADR53P4WvE0LecKgO1ZhqU8/d88lpBlmdOJJeR8rqgwyH30IisgPcYc5tAb6Q26JTaSnmDLtKkLBzP7I7E+AehhXgUbcRMgpfdIA86Dh+s61lB3pu7bj5dhKAgqLRlCVM57WuQ9FwkfdDUsuy2YiNMcFA2XrMHVonqCS60sOk1hXxqjSSSFJCrSn6/X6BQWOXTqCxBI8gZBqsvExFPf3HEC0KN4dPfdDVJ0uKoLt7a8P59qlWRVwa7b5mlUGObiLvc0l1WBCvD6FQ2hIF57gH+AbcKd2ID/vwLJ7lrrfmS4NTRPUma2SHbi3HP4xogO5wXniL9Dw5vIHrb+O90R+IxkC8jQU71eo0pT7u/Mvd+PUBUnbTo4NMeRayTkFzva61eZuuSa47i5TgbDEFY3A3koVVLf5joqx4GJ8Qq45zYAdOjtEVFJ3e/Do4XrZNT9RcWxtx0vw1DUVBZHnBotXXWe6LctHlqATjyZh6a7G3lzgoeHpT4vFyfWyBSXRpzaBEBLsBMI95DiLVribcgAuj8InrbVssctOS1bxFSLCtBa6dK6rrZQqztJo1i9jQrAorI1PYvRHb3vbgj9VJtKmukhtYCqaaMAACAASURBVOb0eYZbtxnA5TUcsIV60l8Q5wPEae7zEC3/6CmRkLauDixyrkaWinNEzUQLryC9L+I+9P5aucaRz8Bfo9gx9VI9r7sosedpjPn3pOAD6ZE2ySxSbRrNgwJIBupQI7UVxuVTcNbvd9sTi+Laq+xVYhu8JmnJPKVWxZFiSWiCd+VSvAxDAaT7T5epYBI4TWhltAlgm4sxPONxINloQwP4lL4bwrx0yFgQQqj+ukijSTLoaNGZylI5nLzkbEuegEw11kF1IeIaFMQBkjV6FJJYAbWiNwVdUDiuIWVzABliHC1EYq3mwIA7We7tNXRpuXF3Td7AOX1GUluEGcUjYv8SGsr9iE1ET0hRQgnuff7MGg3gKcGu8EcCz2imgfnkdaN4mcFPKM+zYhx1DbHIjQdDIfIZQNnTKPh16xiZDamjGqj6PcQcSFOf3iPz9ZRrZNoUAHB/h6qnGgbISwOiLOC5EInzF1XMXwuGojfIq4dsmEK1Z/6brpO4gMvYkTL3yI1aAcHx9ETX6xVjKPrDPaTd5SnFhd8kFcABRNqt0qzD9fPrY4kvOQ+U1Kvu+VDguEHVc+N+Esni17zd7D+CcX4t7f7er/uWwKuTcPR2gMh9TXUG0Esj150NCkxGMSjnl9Wo4gzDnj3RM/aHFxzp42OGha9fzZhM2aBSOCpKzRGnx5tX0mKep9CpdUh3EPW2QYba9xzmFSJk85bM6vDAuG0JEF56ZjpqbcgJVwLVpW5b+eye7SxrNozXzffWLBWfP2ntANhcOESYe7lXPww0rsOAxxBdJm37eo3+tZHSf/0QWTo9ioK8G9swEsTl3mG8DEOhQFZ0ltNTXPo8GH8FcXawU4eYyAkHPwPIh9mLkvTNOfQ1lvTMiQFCZr3tlCpAJTeNp/noGgrrOfzh2SmlxfX3IafUIlNr/BtPpduWbidL5L1qFV4G/8RlpZFZltBfwJZiOBMz9HTCPteRyu6nZHccJJsWYgmNopiM2RHVmYTE8JCPe4zAAM7kN+Vzp+teNzMVv4OuX8SBCgchPL1lrhth1mbi5JTnH3NEujQucUCl5FxLTMcNS9V2xRiQVrZVZO1GeAwRIgY+gclzxeqpU679agRYQOae71TJXMOtwkjGyPL2tx0vxFBkq3nU+Jn8eXe/+DBkXaM+P5D8KP6Bpc6ACQ1Gb5DbZhL8bAR7iv2skMx5Bk0gr1/Pf6spVcBKjJfTogjjVLwc2gtpyYfQEgYEySqzEqoKPD4W0K6Fq23/lnkxuMBOpHKLZxOnVcWBzmk+knoYQz8+2qImazQAYTNoUgV56UV4uKO3Dbh3A7NtsWmzStJPdxEgiHVpRJWhAJCFfqyZYEbL1cFk+Iar7Md4aIaRRIhHzMS9j1rKH2lrZt44V5QVeLiHLi6JSDq2jmRTLjU082tqCqirsp+uKbGQNm/iJpDLfWbzVNNDcA0VmegA3pLxnC2L9/qe+ZoAMwWJ6kvPU5cLs0tYY7S5cjQGC8DO5CH4CUCLvCyY1IAqqq46G5F9z9Ongl7kJ9Di8xpIta4xLxcgU49NgLZk5WqT9EicyRjaGsew11XPxO91TvvWWLwAfTQgJJkBASaKtnMZWXov/v7AevYjT792mQlKcdL5x/cOdE9hOlipasBoSvuf8YZTvB4b6JjCsYjdh5O1VknQmxtKR4nd3SNi7UTQ5zPDwH4kub7E5qph3tT7XP0b6+Dhvpzifh2bQverff7lkgdFJUExDOy+RksdST7jNIISadGeoSS9uAMBgM7YSgFiz2voI46XYShADQPG9KdYcnhdvyqA7hZUI2Y+u+7hxpXQIsAraemeA7M154k9NA3E2c0n6MpwYM8UmV2vXwvdyeB5HXlCFz1L3mNkHvidw4zWRC6qBgHIDUfAtF4HvZaB58GsZbHMC5CnH+e7S1Y9BsdipAfWu3k7IVLbENR7pqWLIU1ORnoUijHPsW8GktWUjauZsfF7ykyGhxsU6akud8cM8DHlLqVlYc26+IhsUC+vP4aFuNuWPUpKxkPuagq+egEjcZIApIvk3nFAyZis2T0tAC2Qz616vzUD489PazjM7yQgDszG+C3GyzAUnCxy5kVMP4KlwuUh2OiW4mp3U2wKLgBKlb3/fk7UmXzF31Eu7nrLB3R/yVOIqdnzKco6AWIRHQFqxWlaMxbSUvWZNShucKKr1braZ3FBBijaMlOx5akK4GQ8NCpruVi1NQ/FClHKU7JPmu1WajJ/PuDpzJL+LWk3qfaH13QpwJ/Pg46RtGayYP090Y8jXP8CMnusrg3pEYDYysjvOY40wOQtuNGKkObq1/PwkN7O9Va8WfHQdkkvVDfzMN48Rvd0yyZ5tSnXRAkJayFbaJY8U6MjBdfgutHDgcsm2T4gQrHu4aWHIhfDT7RrtHKYMiHHgIhnv7avolz/V25oAkRAWljAFtcUe9mCCHVrYLauSzdNxm2fN+c5DQoAWMNyj32PzkrWgarPJ18vjY9pJFgLQCzAsw26rhCpJ0A57VhncRxebOZsQc/oRCwPTFyQqZR6lBN0O1KHkwxK9AQTjxmvsPkaCYB2ZKaErz8DYhxMSWpLctBzFbs1zOEchLhMTym4UZ4Hwz3BnJGoylJseTgOC0sOzqd7kZc+G7KOAFEViIZQumzAhkyn17Qn6ykqJgVMnlquEUlsrBLRaLzPmhYc+57pVh6GxxGG6EnKM9bQkZ5ayz0irOcRfy8QXoZda3/6LD/ieBmGQk9goajnio+ygMoCUBc2pSbDFNepFSeNkSfbICDUc8L5kOOk3hz0uZtKyQFYxeA9iVIw9By3uQhoFJq1h0RWW7BDr49+uq0ev9rnNieN6ZvMm8vDw2Qc6jDCkYuqVjA2FrPH4zUtS6PGxkMiEPRSKbnOmRiK0yy54CLd2Jt5R6Ep0XPjAtCbA5BDbe67zBvMU47oPTe3bpkNGApcnDNRcZbAXVZXjvJN0XsogukxEsQuGy04N9zEBYOJ5cfKz7OWxcH1tQArvaJSjHV3sVO7D6s3kRK+LXnfQc5rvn6qYK+nL8N4qgL394ieokMB186I+WBoQSO17wnkUziIz5evLeJMbzNehqEAMn8OZLjAqkCy3yJWHcjJK5gFP4tWug4uDm4wZ1jC1ZuNg7DMxuUMuhHnABI8jVy5Z1aOPmc/+NpwbQseccYOnNhDw6b+nZCWhWYee0axkzjw5htnKmoK4BUp038Gu5iGowt9vm8Sd0i6smKV/DvDGlaqAhbu4DTKtU0eogOIFKedUtE1hUxjwXul5Fxv0NEzncg5qdWvnOLLOnkPuu8ZqnlhGAYQgr1SsLMSbrH6UxdWkyJ7sQI5x8+tQ+JkYpW80RXdQfepZWRryEOtzDdTruStHKe5J3eGHAot7RfecrwMQ1EAQyEAQwBtnE6AiY1XNrXLjAkIJhFV7vlZdIV9wehxzSKpdQHWS4KeOrJisCD4QQhjVWWlYYuxJucaipZWPchUBf2XBXJxJqVqiNtOZKcygtnJz4qUZctrpwdVU7liitvneSdVO9K5vJ8CzgrZlGe1rZoBCLk3B/JKmfyE5p+ed4CCIqWGQvMEvKPXZJ6Lbm787vz6eiETcb1QSUrK9zLEqF5Dvd9W0sVHCX3Oc8asQyXh9Qbokr/j3JC67T1PnwDjZUxrVlsaTbI7Md8PRZfDk6CYT83uOTkOmmI/bztehqEA0i1lTHnY78zq3xDNgIA8mRgHHiP5F0XZaDqZmKmQ0pnpzZvEGXwj6KMv1mWZY/fy4CEjTgWQyt27cQmY2mRbuubAKx/w6JDFMQa6+fBQyVOtJsC6Z968kJeCls6uXMfuG1vNZS9psqo4DjFiGtHxZDIeieKvlzQwTBuvtjh1P6AffIDgDNzd5cl2Ncwlekw4l4IGciYFaXID6AEMlyks2iPxnlrgVLMsFK+tYVANwyoXgxyHw3u+BLuy2z1rbq4pE0LP09eStAZcltAWlW2P9GU8Fz6vwuuZNEmYLu8OmkpL8Pi8fngNdfC1vBd6wnd3yTWqe8Q9Prm/Bz6Htx4vw1DEJkoXKuJkTgrRe3f7EjgrSD5PEYxiLEZ+Ft1+VUy9EE5pyRjVDaYrWL+byDYQuflQtwZmfgXjdRKG+Lljvo5JLi4W15hSi4GAx2U6ecvVmM3QHl7TsqQitLpwcIi5SGZZaDDjVBO7ZmHjnyO8BTIfJ2/LKfWi7m4za1MHjUQNPSL9Os/9pIDFsWZJuN5uGWKw7JrXHnKAEsCvcDOHTugp4xOsxhI+MIw5X8fZMyC+5l6AVo+Oc5M3lka6FM+xunni5ZBbU79v4siUbnqO7U0gdgDkLUHOtxwvxFAgTwMWBZWNHdMkpWt0ZCBK3Ety1mjxvHk6BusQCLYdpMRygYOUWK6yPeXIxePl7KatiRln4IZj/Ozl5orqCcl04gXeARTsBLHRJgMKhCdTS94jjl4XoC1mVGkkagq5pOdsk51cW/jpR56H6LypeY/7bmXf/DevXSUpyiekXctpmB5eS/yhxtHtmc1VZAKtVuUwj6CJYQvkjixITMQLqDQqfkdmiVCeHcNKLSf4oQlKnk92GsmD2qEyg+BRmOYHRwUrmR4Vgal9ld/T4NT1AaTBo9exLu6RMAw0eYUIvQFEB7OlR8+ctx0vw1Ao0kgwlVcBqXUNCq/KiJRciI86VTjAp/vLbOF1VgPiCFor05ANE4GrSswpwwigbJzT5qtofjequSzdMjTM1HBUz6QCdnzIPAFK93MA6arfbvbaYHEybefuMl1RIFvR+XfVWor4TLJT2wqMJAlFYZ64XoOnd/V2i1Jn6T3EclnM1Gr9hWpmVsRDnO2WKtQ0iMQ3/L5CTcuPCmXm4Jw6LHMoQBrSwJvs1I5udM0MCK5Xuw9vhB29TODgJPUpJxB22MbrzRsp70+yKAY4XmZAu1xzbc1oBrADtzaVpBvrdJk+P+67HAAByDoeV3UwFMVAnbGWjzhehqEAshDpREeOLAMXepTY2mZIfEEztm5ipwGRcdWUYeuOg/jpNmkyfLGhw7QcuuZCi7/RY3Ewqb4vHg6BqYo8V3e7nur5CeqEmSn+dtcZFYdoMn8vcQLA3kNh1Z7CsXHqA9PJX13XaB/IlPJyZ2AesSN6KWxQw+/mvRe2YRCgnCdi1+Yhz0jeSNzHthme402pwzBW3IUAKzGMcrgEVlU2F++fGzWwHNYDMbugpaychoreZbOiNFs/pWq0Gt6eEniVsfksl2E4AEuDJs2MRCtez9mok0NB7KN6Hrxn4mc+rxPQ+hbjZRgKQW72ANnMZbfqveKGVfeL4Qe4yNxz4Ocyvbb0FIKhIeHcOtNSmQkBMmVIOvAB6O0N9BhoD/fFmPkCre3zmK70z0716X7ymFLoNjymWgPgrriKRM+GcJ/pYnOj3t0lvbjG1OeUGBeYq3zJ7gVcS0sch+j5B3vG2dyQ40jacqElA0hGLa+frjmBPwBZCAbIq3ub98dHn8MOXB3xj3lsE4cmQOPjgLTiyvM+7+4CgLbuXe6x9FgRCSw2r8Ng2wACxcS0eA1OjgKQ2Ztbcj8iq3NXsib0MJuYkaZXQC/Rv18ZZtdm1/zeyOBg9rDduIYB4HOrVO0GO5Q87R3VtO8wvqyZEZFPi8j/LCK/LCK/KCL/uf/+L4vI/ykiv+D//cnynr8kIr8iIv9CRP7dD3UldJ2peM3N4q7ZJELq9RJTzAs4cJRg2kS5rqfbrahF831AATX95CAeUlKHeivaEJEedRf05g+cD4hGrJUUYWXJkfFJTQUKDHMDMi7mZ5Fv0Ht4RpG18IKhAPem0G0ptN7De3fk4mdPzox3i0vNhUjArLJCAfud33v9fWqJFMSfz7luDAfjgv3avdXixV33ElJRmQxAkRvUyF7EPAbAegoJeAAAcWJXTzI2nkiGbR4yxeHEUC9wgJYG9lL6cDCDx7mLzS75jOv1MCzipmdBIa+1kujKYZFzWNPbbiT4eQVEf9vxYTyKHcAPqurPi8jHAfxTEfn7/re/rqp/tb5YRP4wgO8F8EcAfAuAfyAi36Gqp+OtDEW4cJPiVKTO5pSPPufCAb6BHVOo9G4pi6ZWCjJNxjJ2B+kC6yBtG5h7e1S3n9dpF5+bSxZU3YNY2CR8obj5S5He3xCbU7DPHk78Hhl/s8KwzfhLXM+UTVAovEiO8bffk3kDw572SSuCbEjDX5zAdKpWlO7PZ7HaFRKBpBqJ+n2cw7NqVC3wU3EPbCRmoRpZHb3dLDRpl5TEJ2+ghDGxbp5ZgpOYjJjLb/TsmhE5YxAWus6d3bV4BeU59I4oriuGf/aGWmSm7Jriwp942FO2r9Dinx1MBnCdvMP4soZCVT8L4LP+8xdE5JcBfOpLvOV7APykql4B/KqI/AqAPw7gH32ZL3IthWGgmT+0Wsyi9CgC9EsEP4BHpik5uX7iRqeveopwIzAFWBB51S00GbBtdk39bnIRs3M54+ZCSuolz18xDcaYNfPAv3fLd6fIrOEB0X4PyLieG6d+vhuFJKQ5N2QrnH+eyAQXAUfux0TuEqpruYpXLLStZFr42ss6GSkRyYY2cd2Y4nml0eOz5mZqCG9IlhZ6EfR4TKRXZ1e6ErHoBdYsBMOYEIoZ+ZyqollrkMXn5vExgFuoYUMROlQ9CLHTXD94TAHdu1klbWreM0aCsq1Fa8hqRKfsDNJ7iXV29tAcPLfX+P9doIe0c23TjH3k8ZEQDhH5NgB/DMA/9l/9gIj87yLyt0Tk6/13nwLwG+Vtn8EzhkVEvk9Efk5Efu423uQp3tpTV+s8MTwlowKz54brhgVEWtLBz1DFJiilI111fg+Q/9526OPV/ituMjuQR6UejZaHIeJELSEivWV38qnJD08g0nB5nfUaCEJJy+tj927eK4lhy4Jgi0bquIJgLTtU8RmEW3oCw4qB5Zyz7ibA394h93dZZatWBaoE+Kq3E59Xfj57GsOfJbkoTbx+o82pRbJs6epz47CitwCexEzUqzNDzSoqf+fNqbdtOjCUc00hIV8T2G7F6y2hTiGMzWFOKwdDCT3cqEQ4xXXEZj6VV8Lwux5GEVq0DD15qEibvd53rPX40IZCRD4G4O8A+Auq+nkAPwrgDwH4TpjH8df40mfe/iRAUtUfU9XvUtXvurT72PAWoxKdd2+hnmBSH0zP+JpkrBqrMU5nuqzSYlXju6aHl9eXuECg4gWJ9lx2nF40WI4dhNTeOd4EQgdyQsSfiyEr/duFcJQpRg+XiH1ETP1krsqC8f+Eryc+wv+AMMBKfkA1rFLYnuzOVlOHx2Gb6LYFdTgM15QVKFmc/QjVL+ITsfmLEY7NzszAkwVVwlOmu1Vt3l0HU4sBMIzqSA+NhoQbtBKaJqyhGAMOr8/gIQLyXui1nd3+wKgksIwpbKSRq2uSGTzygSTxqrh/Yljx3swaflVqPURkhRmJv62qfxcAVPW3yt//JoC/5//8DIBPl7d/K4Df/DJfEC653oZRq0mksS9z9wrmJdyMYSjrOgOalTgFzFmEdZm9BkHZ5MlQDLASiFReuPi6p0FgHUhcv6ejmNOmcYoy4lTmoiBN+9jrTCvyc3qHiGuBBrhoJ6buTuumyw5Yio4VkpXA5aK2rGTlNcX99TQUDDNM0m6kUXNQ1rIGPXgS0Qrv8LBwvczPQtzYuDBL9Prwky96W4wB/cDbVzHFWrwzqEIZ/rkrzlL+afP2BqCEHNuWnAR/3gxDaXCmdDiJZp4GjUMLyLSpn+TCtgzknbDvB/VNGTowpOD627YAbdm4OMItYArv4tlWI8wMUG+pFubZPI3PaobDEKfTW+yDd631+DBZDwHw4wB+WVV/pPz+m8vL/hSAf+4//zSA7xWROxH5gwC+HcA/+dBXNDym5mKtqSbnEcxuocflx4i/hXta3Vt+BpAb6qykFWFPc9HcUo15tTBkSjlWJFzKZ/tJFroTZ28hshY9jVtBp0OfoL5PWVVYQiWRZA7SuBEoXUu38HBFJU9+ZipuZUOtq923E5BilFDhyQYjVlJDICetMZQM7ZAaDp1i5lpZOuFNQwsAnW65cn7C+Lj7fnbbe8luuKcRQPXlEqS48HJ4bXThuY7OYS6QHgu9J4ZQda6IP9BQ7WX9RFboFI6xNymNFNcYCWj0QE736BeVc8zPrEDqW44PY2b+BIA/A+Cficgv+O9+CMCfFpHvhIUVvwbgz9t16i+KyE8B+CUYhv79XzLjYW/KmO1SdCs54SHGcbi7mMivLA1Y7iDqEufloVZh2CfdnQDo6OHCU49RHh4yxUZ8Qg29D2yA7QRIvAEQWQggvQ2So6SEL9KKYvUNOo6UXL967MuHyoyLK3OHd9P7bOTINOQG4P3RGFRws3ejZwM2L4+P6V3ce7cpnuy6GZmpAaaBW+JulmxzHo7ihZDFegI41Z+ZFcy5u353iTAn5rIu9tXb7e27GV43slPYxs1EZSvAN48XuZ0zNDTKjnGEwAubJAeR6fB08A7RltXFY8+Yf00DlRW0PN3n+eL8xHOWNvWlsTCypMQJVPM9QB6gvq7t5wIaM0SmsaR9+GKZkQ85PkzW4x/iedzhZ77Ee34YwA9/6KtQZKoSgPEDBoBsFGyTMUx0hZtvXV3S3kIDAdI6S1rYAIk4qgX210xgE1OHywKRA1CXRS/vZdqpxu/x8D1kwd2IVF4AbvV5eS1FVlwa+1DuWtxTcDc4pABUPMVq6OWSfxRHGW8ewQIkc1lLMRR/FyXrR578QR4qWEZlax5HoPfTz5Ei9rknBb0YWNKltcFOddkTBOUzWMp1nq+1UN3ntDc9RZtX1rFo8eqmrAiQquU0kK1Z2ECwux3AQZ2IHeol4GG4W7d7LY2L7LsGUJZcPLMuibV40V3MDzGQ0Jg4MBWU1WwNr10kJPFiVI8oXnzCST7ieBnMTPAEsQ0iarGfMtXZO6LDVMfkPj6pUIwU0oBerxnzAonwF6ZbEn16hgl+4k1anK0DKxAdw5bFpP25SeneX4olIMBWPITpIRZmY7izPDWxxIKs1PO4dgqV8PRz1Dtc8Pffz7BiWcJgRvPbSgAjriNl4RYyTxi+MS/UYA9SYKgt84YkqMZUdmU8AnNoSH4GT74+061tI1/CyAiJX8xswDMq5zl1MHcuOCvGnobv2UrSEQaK9S0s/a+Fe6b1IfP91M/Uo3gMEu9N6YERilcTZjVoTHhto3xOSwyqZNOi9yn5F/RqSg3I24wXYigyhorCInHXiRsFAJD4AWCutZQNk8SanJzIg4vMxBpH1oPTzzz9GwfXCmNOLivk0qA3JEhXsBAjLBWAk0ZG2qx/WDEHCsHyu5oYiMXXkCuxLhDcTRmXqX8FmZMxlZKhnGSfVTRJgJgYBb93LbJ1fv1R10CQlkVUBGUjLcqYvIQevI5yr1XMJ8DNY0A/yCxOhI1c5Iznm8nRRSMchgq1mM5VwHX3Z0Ex5WLYpiKs+jwK4U6ZhekdoUZOtmQQ0UxThCzI2JQ43XtwJWBztzqOw1CK3J5h2hLS/Xd8XjW8q9jGUOBuQbu/s98Xej2lGXiYxf54Rx7FCzEUPpj6XBbIPRLlBkrcXjyC09C6yfw9Fo6ULAh/L+IIMaBDs3pwKzEukAtNWDbOX/upQ2+Ei40bIe5JAiGH1HoCtRM4FrOBm8FLADDzLnwzxM2Op6egC/gor6umcoFkfxYwTgZSdEVLmwKfx3Dbh/dvrSQqDqZKAbCidu7N4h5MqSaNTEPJMtj7nSi0bSFTh2Uxst12y7J/6mrUjBg3cIC2STYLEPKcZQgjAxCEntZKUMhbbkR6hQfCYyX+Mj33ocDqHsnuB1PFLTg3QHoqLuocRro+3/IMY45r/ZCrdEV1Ku+RgPI7jJdhKAQZM3KT+UOR6jJGGNETC+BE1PcCuRClAXeFaEQMYozM13stf9KHyyIEMgNB5h0NArMQfKitWTrP43Ke5LK0xFJIQqru4OSCF6Pm8bi+eTTvaVkgH3ttn8sU2hiJAwBZZMUyc6brnBBVXfCoPGWIUjMwTYA3W3wvgBRJ4bWhxPweWwP2GXozPsW4XjMTU5mfS7fN5eQl/eBNpkDHknO+Hdl5XIqqOqXsh2MRBK+X7tkp73PhjX4n74IeZAGFpzL4h3uQ2cv5lFcP0ZbSRHMa2FOUZfjTcAAY6lkKpqhpPGO9eRhEQV3Arh/wEMdSuuZdGoYS0v6q9v6LhzPjgO4S9xqYzzvSt4GXYiiAE0+hWlJ3ob16cjqheTrViYh4XbL8mMIxJw6/xXdexUdwack4m6DcpMpEoI6x69nj4Uav+MYz3k9SmzVTuuXzBJLu+fUalZM2VwX5jpvxhXu9GkcjFmcxSCQb1exJE4v3J5KPG+OT5xYiu34CT1qYfpKxMEvW1a6Z2YZT+BWnYQjXFIASiFoXPm+b4wZE57cTsewJTd6EXaIZ0XFYCFDviXPNQ6o8nmC2VmA8iFTFmLO7W2iVHHmYAblZa92N1wI9SXVXcJprldcYlbQpaSARZg6oMAQhRnMirb3jeCGGosbqDmpyAR0Ze8mCtLCBIntcXfkB5O8HBdnfpxZrThwB4HlwTTXcuagbIT9D0yOJXh+RsfEQBfDXGuHIRHNP0z1hMOKXInliE/1GOc2BbJjDzV2B0SYImT9uKBLMJl5Jy9CmU2W7zDlHdVlpDEpqESiboc5d99YHERqc0nOlrobfIyIWxtDzYJZoOc2bHhmWlMZEQXarmEjL/0svGxIAjiM3YJ2vWDczGF0FgKI0nc+Rz4D/ieM2PKwqh2dTZ/XKPNen71c5MiMzFc4Vo8L1R+NwHIHXRDj6jqxM4MUYCrd8hVxiYJbFmFK9DD/ZtcrscyM7eCnnE2Y4NwNXCwFePczA2eIKWQcteZ9l7Fgw5W6mHiMMVxiQOsKrUMBz7gpE1iWQaxrA2uTmoegjPD7aqfrwAMBP8NrkWMR0NJYlZBwsmRDSiwAAHbhJREFUS+RcBQe6gqZN/OM44tRHc8EglQRMve7B7qGIB9FNV01eSQ2hlsXed716f5QO+dhru46afmbo5RyF+Oz7u4zRuR6cWBdGhM8zhHAKVlMK5qb1wo3HzUV2KoHcygE50mWX3izkIMC+JRPVwrQOud6g+zZnvioPhinMh/u4Tt2ujgeVLBVxIn4OkB6LFoU2zmEJKQEkF8dpBQBiDmp6+G3HyzAU9R64gAgu0ZI6+23CIZzBp8BsGI7DgEKi1W3E54iQA+GxorToCxIpWhqs3Yk1vUNe3Vn8x7Jn+PXxJGaWhexNuv4n4C96MDCEWjpYlj0z6VpwGgjI6raH2AquN3Pt96IKNS2k4Qv8lHE5VxkyO6NHovTLkhJ8qimzx5OZ8fatxtrlxDwMNxFeS/1+wD0uD1EiXi/vZ+zdZTZEZy4MP1eQXhwPkuI5PgG5K4B8vj6yOH2OUqdTc85K2BjUcGa+GNqoGlBeQ0ZufJ/LKXSjofA0cK3biP4dWp5dGKVigPl8qxcnLnh8nA6zjzhehqGouexa3MOmKr2nu30c6W6eASRp+VCIJfDnQjWeF+UooYlCZEyLMOJy/5xpQcTlj0SbK35QekDy9bHJyGDU0z1U179SdGEZGi4QMh0tXTkiQxG1IPRWVI1P4oCbLAu0n5ow+0adUmoV/AXMoJDaHaHBkWAne6ywJoUYEge/L4BN/30lF8UGO4ISruNUUl69qcrZWBaYmEc+1+ADk+vA9bKcgFh+J933fvJwiafUTFOwg8t6PdcmDU2B22Bt6pw50iIE5LwJ9rlNfEPnzwU92n76TNfJOAYiXe33IOfQ7yOOl2EoFA7GOUhTFLMjPrxewSpEWVFAGxSQUYDF0fAC4mQ9vy0M3dObiDx2xKUHcHPT1TqkWxyttw3YbpGWi4xLjROHQl6/wkSXLcVQmbYDAEtrab0P4hIkMPGa7lyr0qnHE9MSyJPqQIZeawG63jyGlyOf+HhWGAKJdZDoQ8Cu6DTIuqS3Q/pzuNr1RB5xEgZNenca+7aFBxWl0arQTTPFx3sZZWPUuh2uiWq8jv+vvauLlS0ryl/t3T9nZIiIoJkgEZB5kAeFkUwm0fCARmFeRhON84I+kJD4k+iDDxgSxcQXTJTExIgYSIAYAVEjMTFKFMKTIODMABJkwElECIMKKHDP6d57lQ9VX1WtPufec+fMvacPY1dyc7v77O699tpr189XX9WaocNoSqJmH1QR7eAWC2AxJDbF64+ircQubE8VD3ntZJ7NOskQiGDjOBrlf70OZVz3Y8G4zLkr4Z2sOERN76blGrU0fe4vY9/xzNI8WybGjUzwSlxxdPVBm6I4a9+NC8jVUBRAxvksouECKxNolrS4+5ETRz6AjLOrNWExDRCWvNt1vCyWRPa1WBSNHL4cHeWCo4sMFLd47BVYKKnyvlhFs8rZ3Dd7gFYQMT2LaknjN2r2gw9XbeVWp7l0gKJECzn2nKi4S83qkB0LBGErQFYCkw6okgUav0VgUpm1cCXLcvuw0EPOi2MG4cmhnN89QVKru9CnaXpfO2LHO45BVVtS5srwEbDmO0DnGbFXqTbv3rWcTgO1bvSEYQMxNrJNJ5xSDkHt51w1BzxjTofwruGVyQpEHYvMs6WVuf6HEj66MXwycmUURWrwkjGg0H2jAvBFV3fy0mG0yWiONAdRashFTnef6VYvmgLgBWRDbyX58KvvI1HTirNvKMMNiZirZ3gUMa8BmLHXA0E0Ycqu9JhYLlN5MUTxwi2Ceeo1FwBOZ2+AwD7i7TAk5wIIhafkn7BkfYJ5TRHeMWyac+HX3bm6sIgPoCIUZVPoXBbqinRjfyK220hBBtg6TVGCL0ABt5d9ajg4HGNWDDt5revmVWo6AJRYf1G8BQHgoYErLVXfSKc05Ym+FDuKOhSeDEYxd6BVAGNDdpm3Bo2iviFCjFPUbyDnv83AdjavkCBthK5TAJXEQuSOVSh9Egkh0tcLXUCujKIAgGDY0ZWHW7umQJcZoSuf8aLtSSGZaaDwoSPNuKmVZq88tUngkbnws7yBcUyyDZHm2d3lUUsGAQWXbcV1Pu1ehtJjXpwg4a4VZAp1LBvxVivf/abjAnpGz4WmMW8impsWU+ERH2IYw4faPS32q4zSai5kGcJNDm9MFqe8ujp3HUtQGMoZASvuCdmutSZlmgxnKGzZ7vo4156+jWyFDS7nje9by2t1RW4VrWurWq3jHMfwNE/1SgXyoWd6epc9zGyXljA00pwtMQwg1zcb7dAw8Jzkx4hANA1HZnp2sLLK87igXA1FwZtIJaAt9tbpLp4T7C7crhg70r7TAWRxgKAShXSQdHVJNtr10Pj9FZuqtLgRXRv0RQHWxH433M55R3EB4U532wgGwj7HolcnSXUWkCQt+qvkLWCRjWmYOWKKDrBFOo4ActtBc1tHA/hqCHG9dFqQjZKroG3sFzqPc0p5PMScDwcTY48WHTJ9vFwkJb5yIcYh8YxqgSuTduPeIlvwV55LHXuMsaXy865c9CSiLWP5fjTQ4d61dc10rNMkeunxcRiWrp8I71sQBDUxuHEVWImtqbG/hlUSrk5dW00FM2QB+j6eF5CroSiq+OQx/u42mOXDP00JYElx4VjIdLS2DXmvXYsFbAh6b63l6Mhbx8/58BPFd80d5xfJzAsAqECYgpUhdyqL5i2j5b1Z+LT1G+nUam0tLYRr/SjlpmUUSTCsKjzWOZT5wii2wJkeGzKLEcfMcxKYxsFSqwVE7CjKJyf+kI6hnNkDVDdbyGppCqKVh2C97l3dADyR7jkZqNMEXDu24xa5pyg5EjLPWURVuRciiIpKMkgLHsD9PqIVnyup2BMFgEiDMkPCniGtZcaoUt8ZrqIYAYLZIgFydrvKr1fA2kq/BUfuCZWwa5rMk/FGQfRoFAi6evAqnF0qHE8pius61lc+hiRwy+5nXVXqBeRqKAoqBMZd1bX2h87qObZGt24KcGvBEeBmtFG/7xu0BFIPWIl4I56BYqFzsbNs2ZSOGnGpAn9NC1g0FqXhi1gdpKQ2F0FwJnYRewofcqBPJ/L6a2Ebf7PyFuYZUL9uJG7Dnp8yOJ2aGEnE5RxP+S3ejmEwFz94Hu7Kcj6Dxly6eC2XYBFa3WQnw7nRQsLyAIZLTTZmPEiImNse+OxpIZJLNhRqU3S9kVhs1ZAut3tcAHqm5zAbK5buPjt6cw0uFj5Xc/6vhadRsbTqsbDak+lf6fENO7eHi/RqqjKJkFJiLZgXuIkMUbeNpE1Ihu/ot0i8jn9403JFFAUsBejMOvIUrDHNImO5sHDoUorRdai6Xf43u7GsqJvDtQ5QKXLuudC6jICUBx7o93yk21keND0+yTi2uvLMGIhkmXjE2jv9N0tqVEQcwOyzByIefzMmj7jZcIoYEXEL9i+gJYzPkKEcMYszsh7RxRrwAjdml1p4ALSKqSTKfhui0BOmhl2q8mFGR0oD38HBPD6L5QHP7RAlsYl4UF1xymAGxbNTclSsqmcRbLxz4hSsJK0S6efCoyBPI0KxHQPAtUgvwOtUZBgA9hedZwT/ZmJdi5zGUnid7s3UcKg7jh6GlPQvx/WU6EchvgFuqYQMLgXTZzBLJ+tVKo2qoefcg0EWmu3cm1OvydNvCgwN2MxQ3UQWQ4Aso671Bq4kso7AXEURQYvzLZw/MQDeLLZSqO0BNUpz1+wGyKwBQxdWfVbFAcRCs07RrWxw1AOw0WgXRcnFPNNbKqnoUroeyoBly85UDeWiGmXTTFEPT1tC16tkpQIFmEWfnqVidq9IVis0rzAdACeQmcXuqNNFibOKVzdbm3d38bW1CCOy4C0zMLbtn8fptbdDFa9IZf1HhJrc1sFxBGISBsCujYJfskPVsMlyaTUb02REN2bqWGU85IbRkabmvaEiqoBsIXx1u7IzJBuXMf6oaJ5m6De/efY136RcDUUBdHsukJYt8IW22SKq6QCwtNxem9sZLjBwGnGmjKM1i1Fzm7F1SyKKYHWWQjAA6Sq7B6C8AY4fKBcnYLiE94AMclWkSQt6TwyE491uMm9OqR5CuJRDKBY7RDoQUgmCNnehpe6V4p8Tjyl0Ymx8Qx6R9AaYXvS0IIBUMJFdkAgbdXRAszIW6Q0wXKo9HLxRjiwX6ZK7hTVG7nXAasDwKRTKs/dbUGYmXElEnA4PFbzvZCivSg8fdsBBCsNcKffPBgMWmmkjCImcOxqz2VL2hp+I4Qrs46lWDJjbTZQQl+sVphylFAgG4Fu9mKIYoh1kzVI9JfpRqKJ9/Rv22oE7mWdr9sEJFN9VabvNm+DfPdVshqg9ratIhxQDZr1iu7tYXIt4r1OzNBng3aq9+a4M+VAtFhbjM8UaYUNLywxkPD5mtaeMy6hNiNLv6noyvNluy8bGC9s9iyg9EB247LKHBOB4nV0YIskx2Wq69wyhqpKg0qBSJu24Kr/mxXm++MMiuicYBVqBg9jc6GYL8Z23hjuO4rxaDYBaJ7GuOTC9vEGS+OYM2fCkhlXf/Cfo8DP0uIR7nloOuvmMaEOo1Up7MaAsR2BcJeYwiDMkHTiuRWilJFyvXYvCMPOWt52hC6yj9NfQaePXuw6PSJt5NuZpl+ronTBFCxtTTzb5PN35NOB/cGG5MooiJCzgjkdQqb3kVXilJ5YO6ASo2NKlppvr1oIAH11piQdiCoUEndOC8Nx1HFVJkQXXWu6xsd1YSjPi+NI49sh2Q+/AK1qKCj7xNVOYVGIMk/ggagOmfDDs2hSnA22kAnFyU3wWCpYxLuehQbfeaZysQn5nmnLOIq2XcbiSMAb4GIkxuQJzC2tKhCGhW8Pd3hTwkIOZACBJbovRer1zXIvemwwPYbcJ7jCap7AbulOJDpKtA1VOHxOpaV9rUaLfoGPLzElk3QrLkkrcH2QFDOOpHJGxVDA7EU1WK6926O9t5wUR7NcWpLZY409CroaiQLH0JaQAZuhmzsIasiy7/LNbKmkOYGkAlOFZ6Jz5/Oa1AUBagabRiUnYa3Eoi9UXcRRNcRGQmenWUBg6ddTtAapT3rT1ysa7e+NIyWV6s4ZRLByrSorhC61icYu7TM1uCEaXvrr2Qyo0goCWcpag0vNXstmPRLweFbGeKg4FSiiA1+NWPFr3NwVWQyQUonVfeAFmDESHwF9iTw56XwT4zsJlWjEcqj5nlYPQu+5ByKNXFbTw0luVshMedPeT95LjoVLz9Rq/s9la2pRz5JmbYKoCtl69cRE7uUVj5AgtqqJQRDrYlZQOMBzlScjVUBQlPhM22m19vT2Aor3FYkpH1BXNSp6BBP242KNPxTZ/s50UwE1skW6sbBuz3/hZDZjkuL7Ne0IsM+8dzXTFOBZx05jSdMqtzKWIa7MFhhKSTBk2RXdltvAjl4MuZjPlZPySESwK6qjRPG5Axqzz3D8wXLy7fTRkMGBoKA9jwYW0WnQqasBicz6wbc4UtrY+rGIMD2dZzjMEyxhLl5HxIsAMXZpRmXmNnnGR4EaIUdX5gE2T7x8yp0Lx42wfkTmA6Ejj7oCQGAYr9vItIOG7r8VarH1LticOpAIBOosADK24zluhtg8CGVdJX/eaFxK62FaxK1ikJ8w1M88WlpDz48AyTjbA6LuT7VDZLyJXQ1EAHUhnue9C4lmvCti1oxnprgIZH08T7GHzG0nr19T3nGwZx3ICl0uId/IOJl5pYNJZ3dKiLIQhS4yrWIoibGhrWxxOydEvFaYiCyjOCA38vUIzFGMPDTaV8dSmyCK8ryCqRfrM06Il1RddkUgTr9gEU3hUMvScYgEOJXXIcGNnv1FeC89XLam3xa+eSx6fXJiur4OnRdXZmF0pdTAS51Tm2HHRK82ZVZ2Vg0IP0X9PGroQNrNWhpUEkMqKZFe40Zhms835Z7q0W/NlrxivFQmjM47oODbk3ngRG+Y5qQRAEt343d0w/gJydRQFkOEFrc6ae2gOkCktQ+yDMM3eetBi4mRoeg47rKI3XFVF22z9wSwsueYhgfPr44bvZibG0VzFEvcGeYvjd9C0A+EG6TCGaK5SQgR7mKdYdKHw5inbtg9Z7h6uLMuSd1N0HbdCDCOINCMfkFKWvbB0ZbL+WpSG2/eziY9da3HDOV57cyqsimtklWhNd147NtCYmRv+HhmldfduemwEcGcvuS7KAKrA5LjAqvBwthPAYxejk7Vajnvw+0orTa+Df3cFHNwJXmP05mh9+IOKjww53hnA4N7Y5iR6iMjRkWWpBkG7dmxzz20hxyEVW8F49JvXnBLQMCyNvYmTTYKYgKebvQ3gk5Aroijckg32srM80wTMFUwcElSb56RlEyWvgOfJSeEbmGUUppb4fcZ+JPy0ElvXbfGqNWUcC/6pWIpSao3mad7lunNrwUwJXflqWXY9lbhOY4rSI6g9JZTFTcRWgM4CBbhIxUc6d7U0taBqMUK4t6s6gBAkKsb/mves4A+79TXVokmDcSXKNcaRNW0bYU0LDwvCfT7mArj6sXOzlcy43TexDmUTwHCzTZjjfpaNrsnurClgKWuNtGviXfQAF2OMO/CRSFG2CBeAAlCTxl6JgQwfNZvySACdUtLVQyh+nUkmVAPQj8XWvGdZale3p07oUSsna/t5aQkA1QVIQCyq5Crg525nUwM3mb4qZdmBogdHYE6yTLEypAyHGz1tEuGv/R3JZnS3n4BpOWE+WH7+rp4FSCA0YnNx5dmj5fy+YGexRYMZsyIRMlBiz4iW3yF4Chj+Mfjir6naWk9Qqhr9BmV1Lo8rQFoX05d7122ZEGGXK1IqNCrehYdAuk2viZ6Plg5k5C1sN9DJrHB4mZHlmbOHw2oVGFDgXEPxFkYAw9LqLMbiKS2So0HyVjTpjc8BYM6Sc29GE9mwEXnfnSMkquYZr1YF0HVjE2nrzOYNdxzZWnT8DZtt1u4AfRuCswzQE5BzFYWIHAH4IIC1H/8eVf1NsZ3K3wngmQA+BuBVqroRkTWAtwP4IQD/BeBnVfWxc8+zXtlCZy6YFs/j59pMt7M+QD7kzdNLVeM3umC+mIYCctIl9Lx/u3bc1R1kv8S0GDqZpYuekKcuZHBXeDZwbfZeAjaZuceFCLBaheWLBb2pm936opUGblQUD9Rma+5zU9uHwhmrenxcQg5ffAT/gO6hz56MrlxIwZ7mZDdWUlJU7w6J3zTkcVyM7i3J0RpytA7SnM6bVEr+IAy7PTU4Bxxnszb7skBiLpst9OTEmJl+n6OhzOQGYuR3p2irZz9vilhG79swz31tCoXhTW03R1B5mqKyswOd6zVw/c4eJjAc8CbCsY+Hh9B1bxbccRSUeHqfOhc+zMmUxwFAO0rlXUB6w0U8DDtrrT4BGc4/BCcAXq6qPwjgxQBeISL3AXgDgDeq6t0AvgLg1X78qwF8RVVfCOCNftw5QqsoiZ5XjvrWNpOJ3app5YRotcdw3IyFseZiRGyMK5LW2zMiFsOuem+GxVC7Hgzf14rSGuZE6jbxkxAWhu3kv+N3/NrlLP4IkO5z3ck64mjWlQzpikfarHXX3p98CNAu5rKk5frmNAQ65x3CFR/mcj/okY07HhWvY/e3q2ynbEQT9yJDP+JNxgsoXk6EQ34tVPb+L9rv8bccIBeGJpTB18uqVHUS2G2pBJWkqwjHPEtH7Oz4OLJsUdjH31wuI6MSc0IWq9b55Jqiwvbz+R6otTbJfqevVyJwb7//5LwJ4CYUhZp83d8u/Z8CeDmA9/jnbwPwk/76AX8P//uPyqlVeoZQ27aiqR2oq52OgzRUeyYUPkT3Px88v/lYr+3/GgcP+RCJ14ew8CsWBTMAVD6jo98FlMzr8DQiadkyeFPa0uGJcXvkwys+sMjwqdZx1OtSDbS7Q8OpMHw+dUplUlO34WmRmu6Yh/gilnHIv9Gq0a33BySp4WfcWgJunIu5KDixMDA256nKkr8V4SNCQXLzp/B0WJjmcxab4fA8Aw3DmFkqhnqrVX5/V4kOkilwD0/rXqmRgdkFjOmRbbfm8fgu6eIGQFarUFDxnW3WMYUBIg7Ee+/KInrHMus2DBmmMqPFNLT2gHFnkC4oN4VRiMgI4KMAXgjgDwB8FsBXNTZlwOcBPMdfPwfAvwOAqk4i8jUA3wngP3d+8zUAXgMAR8OdXoCTaZ0g5xTXtGuHxp4AnEDSaQv9OB4mgohAamV3IUWbAX1k4TmFtnIcZLX0PSeGqOfAdjKehbbc1cs3UY6U5LzNEKZiDG6RpHEz3LQu0c+CbrSPmRkUWa+MYlwVD9DhOvGeczmlImOqWb14jVgLwTMAffWol5pHIx6Gf3ccGQWe2QO6284ulKNCf2ehF+8X50KGtNyAzbEXl3Xb4Q2DNaTlGJh2rIByra71LI0ByUtEgxr2GvG5jhQwFcE09ZtHUSFXop8KZH2UrRRPTvIezXM8oMaFSG6GVo8wwpdteCXMask8W5hCZQFkKEpCoN+X4F7McxbIdWQ9x6l2084XkJtSFGrF/i8WkWcA+EsA33/WYf7/WWM65fuo6psBvBkAROTLf/vlP/oGdpTJnuVZqOPZ/8hsPF/b9zBC+vnZv1yt8Vy7QuMxm/AsAN970Z94QlkPVf2qiHwAwH0AniEiC/cqvgfAF/ywzwN4LoDPi6UMvh3Af5/zu88WkY+o6kuf6AXcLjmM58ZyGM+N5YqO53kX/f65GIWIPNs9CYjIHQB+DMCnALwfwE/7YT8P4K/89Xv9Pfzv/6CnancPcpCDfCvJzXgUdwF4m+MUA4B3q+pfi8i/AHiniPw2gH8G8BY//i0A3iEij8I8iQdvw7gPcpCDXKKcqyhU9REALznj888BuPeMz48B/MwFxvLmC3zndsphPDeWw3huLE+p8cghKjjIQQ5yntwM4eogBznI/3PZu6IQkVeIyKdF5FERee2exvCYiHxcRB4SkY/4Z88UkfeJyGf8/++4jed/q4g8LiKfKJ+deX4x+X2fr0dE5J5LHNPrReQ/fJ4eEpH7y99+3cf0aRH5iVs8lueKyPtF5FMi8kkR+RX/fC9zdIPx7GV+/PePROTDIvKwj+m3/PPni8iHfI7eJWJbJIvI2t8/6n9/3g1PQNbePv7BGPmfBfACACsADwN40R7G8RiAZ+189jsAXuuvXwvgDbfx/C8DcA+AT5x3fgD3A/gbGF/lPgAfusQxvR7Ar51x7Iv83q0BPN/v6XgLx3IXgHv89dMB/Kufcy9zdIPx7GV+/BwC4E5/vQTwIb/2dwN40D9/E4Bf8Ne/COBN/vpBAO+60e/v26O4F8Cjqvo5Vd3Aiswe2POYKJWKXinqt1xU9YM4zTW53vkfAPB2NflHGJ/lrksa0/XkAQDvVNUTVf03AI/iDKD7SYzli6r6MX/9v7D0/HOwpzm6wXiuJ7d1fnwcqrex1GLfiiLo3i6VCn6ZogD+TkQ+6tRyAPhuVf0iYAsDwHdd8piud/59z9kvuzv/1hKOXdqY3EV+Ccxi7n2OdsYD7HF+RGQUkYcAPA7gfXgCpRYAWGpxpuxbUdwU3fsS5IdV9R4ArwTwSyLysj2M4WZln3P2hwC+D1ZF/EUAv3uZYxKROwH8OYBfVdUbNZ/f13j2Oj+qOqvqi2FM6XtxC0otKPtWFKR7UyoV/NJEVb/g/z8Oq2W5F8CX6K76/49f8rCud/69zZmqfskXYwPwx0j3+baPSUSWsIfyT1T1L/zjvc3RWePZ5/xUUdWvAvgASqnFGeeNMclNlFrsW1H8E4C7HZldwUCV917mAETkaSLydL4G8OMAPoGeil4p6pcl1zv/ewH8nCP79wH4Gt3v2y07cf5PweaJY3rQkfTnA7gbwIdv4XkFxvj9lKr+XvnTXuboeuPZ1/z4uW9vqcWtRF4viNbeD0ONPwvgdXs4/wtgiPTDAD7JMcDitb8H8Bn//5m3cQx/CnNVtzBN/+rrnR/mMrLU/+MAXnqJY3qHn/MRX2h3leNf52P6NIBX3uKx/AjMLX4EwEP+7/59zdENxrOX+fHf/wFYKcUjMAX1G2V9fxgGoP4ZgLV/fuTvH/W/v+BGv39gZh7kIAc5V/YdehzkIAf5FpCDojjIQQ5yrhwUxUEOcpBz5aAoDnKQg5wrB0VxkIMc5Fw5KIqDHOQg58pBURzkIAc5Vw6K4iAHOci58n8subQhdAMw5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stackhd_im = fits.open('./data/input_data/XMM-LSS_PACS100_v0.9.fits')\n",
    "im=stackhd_im[1].data\n",
    "stackhd = fits.open('./data/output_data/100um/psf_native.fits')\n",
    "psf = stackhd[1].data\n",
    "hd = stackhd[1].header\n",
    "plt.imshow(psf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert units MJy/sr to mJy/pixel: http://coolwiki.ipac.caltech.edu/index.php/Units\n",
    "#psf=psf*2.35045e-2*(np.abs(stackhd[1].header['CDELT1'])*3600)**2\n",
    "#print(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\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resol= np.abs(stackhd[1].header['CDELT1'])/np.abs(stackhd_im[1].header['CDELT1'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33333333333393333"
      ]
     },
     "execution_count": 6,
     "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": 7,
   "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": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# build the array of coordinates\n",
    "x = np.arange(hd['NAXIS1'])\n",
    "y = np.arange(hd['NAXIS2'])\n",
    "xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy')\n",
    "xp = (xv-imax)*np.abs(hd['CDELT1'])*3600.\n",
    "yp = (yv-jmax)*np.abs(hd['CDELT2'])*3600.\n",
    "r = np.sqrt(xp**2 + yp**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.6666666828012"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hd['CDELT1']*3600."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(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": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.00929045\n",
      "[[-0.04289755 -0.01685593 -0.00042402 ... -0.03155088 -0.04470865\n",
      "  -0.03546879]\n",
      " [-0.04068028 -0.01758436 -0.00998386 ... -0.02778365 -0.03870987\n",
      "  -0.03045889]\n",
      " [-0.0222855  -0.00300549 -0.002389   ... -0.01173082 -0.01861041\n",
      "  -0.01800535]\n",
      " ...\n",
      " [-0.00373254  0.0033824   0.02259926 ... -0.03212694 -0.0209357\n",
      "  -0.0133829 ]\n",
      " [-0.00162448  0.00143449  0.00991452 ... -0.03100019 -0.02511169\n",
      "  -0.01604878]\n",
      " [-0.005374   -0.00283796 -0.00558631 ... -0.03304774 -0.02139016\n",
      "  -0.01101167]]\n"
     ]
    }
   ],
   "source": [
    "# This is clearly. \n",
    "print(np.median(psf[0:5,:]))\n",
    "\n",
    "print(psf)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Encircled flux')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(nbpix, encircled_flux)\n",
    "plt.xlabel('Number of pixels')\n",
    "plt.ylabel('Encircled flux')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1685.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbpix[200]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets do a linear fit to the outer part of the curve to determine the backgound\n",
    "p = np.polyfit(nbpix[200:], encircled_flux[200:], 1)\n",
    "bkg = p[0]/resol**2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.1371992087821656e-13\n"
     ]
    }
   ],
   "source": [
    "print(bkg)"
   ]
  },
  {
   "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 100 µm PACS, taken with 20\"/s scan speed. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f = open('./data/EEF_grn_20.txt', 'r')\n",
    "lines = f.readlines()\n",
    "f.close()\n",
    "radiuseff = np.zeros(len(lines)-3)\n",
    "valeff = np.zeros(len(lines)-3)\n",
    "i = 0\n",
    "for line in lines:\n",
    "    if line[0] != '#':\n",
    "        bits = line.split()\n",
    "        radiuseff[i] = float(bits[0])\n",
    "        valeff[i] = float(bits[1])\n",
    "        i = i+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc2aaec0cc0>"
      ]
     },
     "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 10\" where our PSF is well behaved"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc2aaeb5860>"
      ]
     },
     "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, 50])\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 0x7fc2aae15ef0>"
      ]
     },
     "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, 50])\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 2 and 10\"\n",
    "idx, = np.where((radii > 1 ) & (radii < 5))\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 0x7fc2a9e3be80>"
      ]
     },
     "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": [
    "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 = 1.282, ff = 1.000, residual = 0.004\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 0x7fc2aa5f3be0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A3g3wl8Ew9lqYfJ/TkSnVKk0WbVRZ4+GJhT/x+KfrMQauGz+Iq447iNR4H7re8LefFsKXf7Om/5APLj+/gqv8LyYRbvgOvn4UPvgdfPO41U37qfdow0kV1DRZtMHG/FKun/sdK3cUcdrIXtw6+RD6devEx03ejLEafsVnwA3fa6IINUddD9mXw1szrZ5rKwutlvZKBamAJgsRmQT8DXABTxlj7mu0vj/wLyDF3uZWY8y7gYypvXI27eXK560+qZ6+JJsJQx1+1rzi39ZgQtMeC4/xIbqiqFg480nAwPcvWm9OnTlHSxgqKLVxxBvfiYgLeBSYDAwDzhORxsOh/R6YZ4wZDcwAHgtUPB3x7ca9XPj0N3SLi2bB9cc6nyiqK6whSnuMhMNmOBuL6piICJj+T6sPrx/nwb9+ZvXaW1PldGRKNRDIksWRwHpjzE8AIvIKMA1Y6bWNAZLs6WRgewDjaZe1u4q5/LnF9EmJ5dVfHEV6QozTIcG3c6w2FRfND6/BhLoqVxRc9w18+0/4753wzKkHbqMvLyiHBaxkAfQBtnrN59rLvM0GLhSRXOBd4JcBjKfNiiuqueaFJbijXLx45djgSBSle+CzP0PWRBh0otPRKH+JiIBx11oN+SbMgmj70WJib+vzhelQmu9cfKrLC2SyaOrBa+PBM84DnjPG9AWmAC+IyAExicjVIpIjIjl5eXkBCLVpd/9nJZv2lPKP80fTKzm2087bopfPtSpDtd+n8OROhuNuht/lwuxCuHmVNbhS/lp4cJD1YoNSDghkssgF+nnN9+XAx0xXAPMAjDFfA24gvfGBjDFzjDHZxpjsjIzOGYXskzW7mZeTy7XjBzHuoLROOWerti+1KrVT+kP3oU5HozpL5jFw5C+s6WWvOBuL6rICmSwWA1kiMlBEorEqsBc02mYLMAFARIZiJYvOKzo0o6qmlrveXsmgjHhumJDldDiW6nJ463rrscSVHzsdjepsk+6zKsHnXwNVZa1vr5SfBSxZGGNqgJnAB8AqrLeeVojIXSIy1d7sZuAqEVkGvAxcaoJgnNe532xmY34pvz9tGDGRQVCBbAy8dinsWgGn/UXHeO6KIiLg5Dut6S//6mwsqksKaDsLu83Eu42WzfKaXgkcE8gY2qqi2sPjCzcw7qBujB8SBDdlY+DdW2Dt+3Di763ur1XXdMgUGHEWfPFXGHYG9Gj8JrpSgRPIx1Ah6bUluewuruSGCVmBHXfCV1/93RqjYuy1Vu+lqmubeI/VKeGrF1gjIirVSTRZeKn21PLEwg2M6Z/CUcFQqZ27BD76AwyZAqfeqy17FST1gnNfhL0/wQMDYe2HTkekughNFl7mf7+NbQXl/PKkIChVlOTBUydZFdpT/2E9s1YKIPNYq0EmwCvnw6LH9ZVaFXB6B7IZY3j6i40M7ZXkfF1FyW7488HW9Iy5EB8EpRwVXAadCL/60Xqt9v1b4ZHRsHej01GpMKbJwrZk8z5W7yzmkqMGOFeqMAa+ex7+bL+uO/GP0GeMM7Go4JfS3yphTLwH9m2ER0ZB+T6no1JhSpOF7YVFm0l0RzJ1VG9nAqipggUzYYHd48nZz8DRQdX7iQpGInD0TJh0vzU/72LthFAFhI5nAeSXVPLujzu4cNwA4qIduCQVhfDQMKgqgYyhcMnb2pZCtc24a6yu6t+6Dl6/zBpe16X/vZX/aMkCeHXxVqo9hgvGDuj8k9fWwmuXWYni5Dvh+kWaKFT7jL4AJtwBq/8DL07XV2uVX3X5ZOGpNbz0zRaOHpTGwd0TOj+A+dfChv/BlD/Dsb/q/POr8HLcTXDK3bDxM+vV2lVv65tSyi+6fLL4ZPVuthWUc9E4B0oVH/8RfngFDjoRjriy88+vwtMxN8D431nTr14I9w+AnGfAU+NsXCqkdflk8dK3W+ieGMPJwzp59LsfX4fPHrTaUcyYqw3ulH+N/y38ZgP0ORyi4uA/v4Y/9YHNXzsdmQpRXTpZbCsoZ+Ga3ZyT3Y8oVydeik1fWI+fAGZ+C9HxnXdu1XXEp8NVH8NNq+Cc5yEiEp6dDGveczoyFYK69OsS8xZvxQDnHtGv1W39JjcHXjwbUjPh8g+sN1iUCiQRGDYNug+zXq19eQYM/Rn0PwqiEyCum7UudaD2FKCa1WWTRY2nlnk5WzkuK4N+3eI656Tl+6w3n+LTrdHP4rp1znmVAkjPgqsXwif3WIMorXq74fqoeKv04U6G3qPgiCvgoPGdH6cKSl02WXy6No8dhRXc8bNO6ubZGHhmMhRtgys+1NdjlTMiY6wheU++0/ryUl0OxTthx1LIXwc1FVYnhasWWD8HnWiNoZI2yOnIlcO6bLJ4+dstpCfEMGFoJ1VsL3oc8lZZw2P2ze6ccyrVHJH9JdvkPtD38Ibry/bCpw9AztPwj2zIvhyO/w0k9uz8WFVQ6JIPKHcUlvPx6t2ck923cyq2N34OH9wGSX2t4TGVCnZx3WDyffDLJZB1qjWmyl9Hwge3Q2WJ09EpB3TJZDFvcS61BmYc0T/wJzPGem0R4PL3tQJRhZaU/nD+K9ZbVf3Hwdf/gH8eZw3xq7qULnfn8tQaXl28heOy0umf1gkV24segz3r4MirIaUT37pSyp/6HG71WXbmU7BvE8w58cAKchXWulyy+GxtHtsLKzj/yE4oVRTvgv/eCf2PhskPBP58SgXaoT+3ShkiVuvwVy+Cbd85HZXqBF2ugvslu2K7U1psL/il9Z9q6t+1hbYKH71HWw393vst/DjPemsqJhkSe0B8BiR0t3omSOptvSbeYzj0HOl01KqDWk0WIjLMGLOy0bLxxpiFAYsqQPKKK/l49W6uOu6gwFdsf/8irPsATp4N6QcH9lxKdba4bnDWk9ZruKsWWHUYZXugNA92/ghr3oeacmvbcdfBpD85G6/qMF9KFvNE5AXgAcBtf2YDRwUysEB4f/kOPLWG6aP7BPZEBVvh3f+DAcfC2GsDey6lnJTUC8b+4sDlxkBFgfUKblRs58el/M6Xr9djgX7AV8BiYDtwTCCDCpS3f9hBVvcEhvQMYBcbxsDbN4CnCqY8AFHuwJ1LqWAlArGpVmO+JIdGn1R+5UuyqAbKgVisksVGY0xtQKMKgF1FFSzetJfTDu0V2BPlPAMbPraK3T2GB/ZcSinVSXxJFouxksURwLHAeSLyekCjCoAPV+7CGDhtZACTxe7V8M5NMOgkyL4icOdRSqlO5kudxRXGmBx7eicwTUQuCmBMAbFw9W76d4sL3Gh4NZXw5tXW9LTHtPGdUiqs+JIsdotI40YJnwYimECpqPbw1YY9/Dy7LxKoV1g/vR92LIMZL1mVfkopFUZ8SRbvAAYQrDqLgcAaIGQeyC/etJfyag/jhwSop9cti+Dzh2DE2XDIaYE5h1JKOajVZGGMadCaRkTGAE28Kxe8Pl+XT7QrgqMOSvf/wasrYMENkNwPfvY3/x9fKaWCQJtbcBtjvhORIwIRTKB8v2UfI/smExvt8v/B/3sH5K+BC96AmADVhyillMN8acF9k9dsBDAGyPPl4CIyCfgb4AKeMsYc0D+3iJwDzMZ61LXMGHO+L8f2VY2nlh+3FXL+kQP8eVjLjh/g2ydh2BmQdbL/j6+UUkHCl5KFdwu2Gqw6jDda20lEXMCjwClALrBYRBZ4dx0iIlnAbcAxxph9ItK9LcH7Ys2uYiqqazmsX7J/D1xTCW9dD3FpcNpD/j22UkoFGV/qLO5s57GPBNYbY34CEJFXgGmAdz9TVwGPGmP22efa3c5zNWvZ1kIARvVL8e+B35oJO3+Ac+dCfJp/j62UUkGm2WQhIm9jPRpqkjFmaivH7gNs9ZrPxeo6xNtg+1xfYj2qmm2Meb+V47bJsq0FpMRF0b+bH8euyHnG6m0z+woYerr/jquUUkGqpZLFnzt47KYaNDROPpFAFjAe6At8LiIjjDEFDQ4kcjVwNUD//m0bh2LljiJG9E72X/uKFfPhPzfBwadoT5pKqS6jpWbGs4wxnwJTjDGfNv7x4di5WB0Q1umL1Qlh423eMsZUG2M2YrXfyGp8IGPMHGNMtjEmOyPD97YSnlrD2l3F/uk40BhrHOLXLoVeh8GZcyAypuPHVUqpENBSyaKXiJwATLXrGxp8NTfGtDY81mIgS0QGAtuAGUDjN53mA+cBz4lIOtZjqZ/aEH+LNu8ppbKmtuPJYvv38Mm9sO5DGHg8nPsiuP1cYa6UUkGspWQxC7gVq0TwFxomCwOc1NKBjTE1IjIT+ACrPuIZY8wKEbkLyDHGLLDXTRSRlYAH+I0xZk+7f5tGVu8sBmBoz6T2HSB/PXx8N6ycD5GxMP42OP43EBGA9hpKKRXEmk0WxpjXgddF5A/GmLvbc3BjzLvAu42WzfKaNsBN9o/frd5ZTIRAVo82NpYr2Aof/h5Wv2PNH30DHDXTGjZSKaW6IF9enW1XoggGa3cWk5kWjzvKh5JAwVb48TVY+z5s/cZa1m8cnPGYNYCLUkp1YW3u7iOUbNpTysD0+NY3XPwUfPgHqC6z5o+4yhoqMv2AunallOqSwjZZGGPYureMcQe10mDuq3/Ah7db42Wf8SikZnZKfEopFUpaapTXraUdjTF7/R+O/+wtraK0ytNyY7yfFlqJIvM4uPgtrbhWSqlmtFSyWML+cSz6A/vs6RRgC9a4FkFry17rkVKzyWLfJnj9CkjLgvNf1UShlFItaLZRnjFmoDHmIKzXW39mjEk3xqQBpwP/7qwA26s+WaQ1kSw8NTDvYqgut0a2i/ahXkMppbowXwaKPsJ+BRYAY8x7wAmBC8k/ttrJol9qE8niy4etIVDH3woZgzs5MqWUCj2+VHDni8jvgRexHktdCPit4VygbNlbRnpCzIEDHq16Gz6+B4ZNg2NucCY4pZQKMb6ULM4DMoA37Z8Me1lQ21ZQTt/U2IYLy/bCO7dAjxEw7TFnAlNKqRDkS6O8vcCNIpJgjCnphJj8YkdBBUN7Nerm473/g9I8OOd5HQJVKaXaoNWShYgcbffdtNKeP0xEgvpruTGGbQXl9Ep271+48i2rhfaxv4b+jYfVUEop1RJfHkM9DJyKXU9hjFkGHB/IoDpqX1k1lTW19E6xH0N5quH92yBjqNURoFJKqTbxJVlgjNnaaJEnALH4zfaCcoD9ySLnGSjaBifdDlHuFvZUSinVFF/ehtoqIkcDRkSigRuAVYENq2O21ScLN1SVwkd3wMEnwyE6BKpSSrWHLyWLa4DrscbUzgVG2fNBa4d3yWLlAqgph8MvA38NraqUUl2ML29D5QMXdEIsfrO9sILoyAjS4qLg4z9CbCoMOtHpsJRSKmS11JHg37Ea4TXJGBO0Ldq2FZTTO9mN7F4BRbkw+UHt0kMppTqgpZJFTqdF4Wc7CsqtR1B1I90NnuhsQEopFeJaGlb1X50ZiD9tL6jgmEFpVn1Fz0N1jAqllOogXxrlfSQiKV7zqSLyQWDDar/aWkN+SSWD3IWwewUcFvQ9kyilVNDz5W2oDGNMQd2MMWYf0D1wIXVMYXk1NbWGrNqfrAV9s50NSCmlwoAvycIjIv3rZkRkAC1UfDstv6QSgP6V60AioMdwhyNSSqnQ50ujvNuBL0TkU3v+eODqwIXUMXkllYChz+6FkHGIvgWllFJ+0GKyEBEBVgBjgHFYw6r+2m57EZTyS6rozR4S9q6AU+91OhyllAoLLSYLY4wRkfnGmMOB/3RSTB2SX1zJYREbrJk+Wl+hlFL+4EudxSIROSLgkfhJXkklAyN2WzNaX6GUUn7hS53FicAvRGQzUIr1KMoYYw4NaGTtlF9cyeHRRRCZoAMcKaWUn/iSLCYHPAo/yi+p5JCIrZAywOlQlFIqbLTUN1SSMaYIKO7EeDqsuLiIkTXLIStou65SSqmQ01LJ4iXgdGAJVrsK7/69DXBQAONqN09JHi5qIT3L6VCUUipstNQ31On258DOC6djjDFQuheigJgkp8NRSqmw4UvfUNNFJNlrPkVEzvDl4CIySUTWiMh6Ebm1he3OFhEjIh1617WovIax/GDN9DqsI4dSSinlxZdXZ+8wxhTWzdj9RN3R2k4i4gIexaogHwacJyLDmtguEWuo1m98Dbrm3dbsAAAXlElEQVQ5eSWVDI7IpSy2F6RqBbdSSvmLL8miqW18eYvqSGC9MeYnY0wV8AowrYnt7gYeACp8OGaL8ksqSaKUWne3jh5KKaWUF1+SRY6IPCQig0TkIBF5GKvSuzV9gK1e87n2snoiMhroZ4xpsXW4iFwtIjkikpOXl9fsdvkllURTgys6xofwlFJK+cqXZPFLoAp4FXgNqwRwvQ/7SRPL6nurFZEI4GHg5tYOZIyZY4zJNsZkZ2RkNLtdfnElGVKIy62N8ZRSyp9afZxkjCkFmq2cbkEu0M9rvi+w3Ws+ERgBLLT6K6QnsEBEphpj2jWka0FhEUNkKwyY0Z7dlVJKNaPVZCEig4FbgEzv7Y0xJ7Wy62IgS0QGAtuAGcD5XvsXAule51kI3NLeRAEge9cTIQYyhrT3EEoppZrgS0X1a8ATwFOAx9cDG2NqRGQm8AHgAp4xxqwQkbuAHGPMgvYE3JK0fUutCR0dTyml/MqXZFFjjHm8PQc3xrwLvNto2axmth3fnnN4SynbRLnEEav9QimllF/5UsH9tohcJyK9RKRb3U/AI2sHqS6jMiIOpKm6daWUUu3lS8niEvvzN17LgrJvKFdNGTUxsU6HoZRSYceXt6FCom+oGk8t0Z4yPJH62qxSSvlbs4+hROT/vKZ/3mhd0A1uXVBeTbxUUBsd73QoSikVdlqqs/BurHBbo3WTAhBLh+wrrSKBciQm0elQlFIq7LSULKSZ6abmHbe3pJI0KSLCndz6xkoppdqkpWRhmpluat5x1TtX0FP2Ud3/KKdDUUqpsNNSBfdhIlKEVYqItaex590Bj6yNJG81ANEDjnQ4EqWUCj8tjZTn6sxAOipq3wZqjZDYW7v6UEopf/OlUV5IiCjLYx+JuGP1bSillPK3sEkWrsp9lETom1BKKRUIYZMsoqsKKHUlOR2GUkqFpbBJFu6aIiojNVkopVQghE2yiPcUURWd4nQYSikVlsImWSTVFuFxpzodhlJKhaWwSBZVFeXESSXEarJQSqlACItkUbR3NwAR8WkOR6KUUuEpLJJFcYGVLKITNFkopVQghEWyKC3IByAmSZOFUkoFQlgki8qiPADiUro7HIlSSoWnsEgW7NsEQEJ6P2fjUEqpMBUWySJh73K2mTSS03s7HYpSSoWlsEgW7vKdbKMn0ZFh8esopVTQCYu7a3zlbgoitXJbKaUCJSySRVLNHkqjNVkopVSghH6yqK0l2lQh0QlOR6KUUmErDJJFNQBR0TEOB6KUUuEr9JOFx0oWMTGaLJRSKlBCPllUVFYAEBPjdjgSpZQKXyGfLIqKSwFwa7JQSqmACWiyEJFJIrJGRNaLyK1NrL9JRFaKyA8i8j8RGdDWc5TuWgdARKq23lZKqUAJWLIQERfwKDAZGAacJyLDGm32PZBtjDkUeB14oK3nqd25EoCIHsM7FK9SSqnmBbJkcSSw3hjzkzGmCngFmOa9gTHmE2NMmT27COjb1pNE5K+iyMSS0D2zo/EqpZRqRiCTRR9gq9d8rr2sOVcA77X1JFFFW9hsepASr29DKaVUoEQG8NjSxDLT5IYiFwLZwAnNrL8auBqgf//+DdZFVBZSYBIYGhfVoWCVUko1L5Ali1zAu9a5L7C98UYicjJwOzDVGFPZ1IGMMXOMMdnGmOyMjIwG66KqCilzJRLpCvkXu5RSKmgF8g67GMgSkYEiEg3MABZ4byAio4F/YiWK3e05SUxNMZVRSR0OVimlVPMCliyMMTXATOADYBUwzxizQkTuEpGp9mYPAgnAayKyVEQWNHO4Zrk9pZjoRL/FrZRS6kCBrLPAGPMu8G6jZbO8pk/u0AlqPURTBdHxHTqMUkqploX2g/4qq/V2pFt7nFVKqUAK6WRRW2kliyhNFkopFVAhnSxKigsAiI7TCm6llAqkkE4WhUWFAMTGaQW3UkoFUkgni8q8jQBEp/ZyOBKllApvIZ0sInZ8R7VxEd3nMKdDUUqpsBbQV2cDLXrvWjaY3iTFx7Fx40YqKiqcDilsud1u+vbtS1SUdquiVFcU0skipmwHa00aAwrzSE5OIjMzE5GmuqRSHWGMYc+ePeTm5jJw4ECnw1FKOSCkH0PFVewiLyKdqqpK0tLSNFEEiIiQlpamJTelurDQTRbVFcTXFFAS0wNAE0WA6fVVqmsL3WRRvAOAitgeDgey386dO5kxYwaDBg1i2LBhTJkyhbVr1za7fUKC1Zhw+/btnH322QA899xzzJw5s0Nx/PWvf6WsrKx+fsqUKRQUFHTomEqpri10k0VVCQDRcckOB2IxxjB9+nTGjx/Phg0bWLlyJffeey+7du1qdd/evXvz+uuvt+lctbW1za5vnCzeffddUlJSfD6+Uko1FrrJotp6fh4XHxwN8j755BOioqK45ppr6peNGjWK0aNHM2HCBMaMGcPIkSN56623Dth306ZNjBgxon5+69atTJo0iSFDhnDnnXfWbzN06FCuu+46xowZw9atW7n22mvJzs5m+PDh3HHHHQA88sgjbN++nRNPPJETTzwRgMzMTPLz8wF46KGHGDFiBCNGjOCvf/1rg2NfddVVDB8+nIkTJ1JeXh6YC6WUCkkh+zZUeVkxsUBCYsNkcefbK1i5vciv5xrWO4k7fja8xW2WL1/O4YcffsByt9vNm2++SVJSEvn5+YwbN46pU6e2WAfw7bffsnz5cuLi4jjiiCM47bTTSE9PZ82aNTz77LM89thjANxzzz1069YNj8fDhAkT+OGHH7jhhht46KGH+OSTT0hPT29w3CVLlvDss8/yzTffYIxh7NixnHDCCaSmprJu3TpefvllnnzySc455xzeeOMNLrzwwnZcLaVUOArZkkVhkZUQEhOCo2TRHGMMv/vd7zj00EM5+eST2bZtW6uPpk455RTS0tKIjY3lzDPP5IsvvgBgwIABjBs3rn67efPmMWbMGEaPHs2KFStYuXJli8f94osvmD59OvHx8SQkJHDmmWfy+eefAzBw4EBGjRoFwOGHH86mTZs68FsrpcJNyJYsSoqtfqGSkxvWWbRWAgiU4cOHN1nvMHfuXPLy8liyZAlRUVFkZma2+gpq41JH3Xx8/P5xOzZu3Mif//xnFi9eTGpqKpdeemmrxzWmySHQAYiJiamfdrlc+hhKKdVAyJYsKgqtUViT04KjX6iTTjqJyspKnnzyyfplixcvZvPmzXTv3p2oqCg++eQTNm/e3OqxPvroI/bu3Ut5eTnz58/nmGOOOWCboqIi4uPjSU5OZteuXbz33nv16xITEykuLj5gn+OPP5758+dTVlZGaWkpb775Jscdd1w7f2OlVFcSssmipsh6lJOWHhyvzooIb775Jh999BGDBg1i+PDhzJ49mylTppCTk0N2djZz587lkEMOafVYxx57LBdddBGjRo3irLPOIjs7+4BtDjvsMEaPHs3w4cO5/PLLGySUq6++msmTJ9dXcNcZM2YMl156KUceeSRjx47lyiuvZPTo0R3/5ZVSYU9aejQRjLKzs01OTg6bHjqZisJdDJn9A6tXr2bo0KFOhxb2Vq1apddZqRAlIkuMMQd+8/RRaJYsqsvpU7yMpZGHactipZTqBKGZLPLXEmWq2BI/0ulIlFKqSwjNZFFpVd66k7o5HIhSSnUNIZksaiusrj6SklMdjkQppbqGkEwWxUX7AEhN0ZKFUkp1hpBMFgWFVrJI65bmcCRKKdU1hGSyKNtnNcjrnpHhcCT75ebmMm3aNLKyshg0aBA33ngjVVVVHTrmpZdeWt8Nx5gxY/j6668BWLRoEWPHjmXUqFEMHTqU2bNnA1b35hkZGYwaNYpRo0Zx8cUXd/TXUkopIESTReyuJWyo7UWv7sGRLIwxnHnmmZxxxhmsW7eOtWvXUlJSwu23396m43g8ngOWPfjggyxdupT77ruPX/ziFwBccsklzJkzh6VLl7J8+XLOOeec+u3PPfdcli5dytKlS3n++ec79osppZQtJJPFgNJldBs2nkR3lNOhAPDxxx/jdru57LLLAKtvpYcffphnnnmGsrKyAwY0Ov3001m4cCFgDYA0a9Ysxo4dW19yaMrxxx/P+vXrAdi9eze9evWqP9ewYcMC9JsppZQl9DoSrKlEKgpJHXxgf0kAvHcr7PzRv+fsORIm39fs6hUrVhzQPXlSUhL9+/evv8E3p7S0lBEjRnDXXXe1uN3bb7/NyJFWu5Jf//rXDBkyhPHjxzNp0iQuueQS3G43AK+++mp9L7U33nhjfQJTSqmOCL2SRY3ds2qP4Pk2bYxpsiV5c8u9uVwuzjrrrGbX/+Y3v2HUqFHMmTOHp59+GoBZs2aRk5PDxIkTeemll5g0aVL99t6PoTRRKKX8JfRKFtV219npQ5pe30IJIFCGDx/OG2+80WBZUVERW7duZdCgQSxbtqzBMKjeXYm73W5cLlezx37wwQfrx+f2NmjQIK699lquuuoqMjIy2LNnjx9+E6WUalpASxYiMklE1ojIehG5tYn1MSLyqr3+GxHJbPWgFYXQYwTEJAQg4vaZMGECZWVl9RXKHo+Hm2++mUsvvZS4uDgyMzNZunQptbW1bN26lW+//bZD53vnnXfqx6ZYt24dLpdLx9hWSgVUwJKFiLiAR4HJwDDgPBFp/OzoCmCfMeZg4GHg/lYPXF0Goy/yc7QdU9c9+WuvvUZWVhaDBw/G7XZz7733AnDMMccwcOBARo4cyS233MKYMWM6dL4XXniBIUOGMGrUKC666CLmzp3bYulEKaU6KmBdlIvIUcBsY8yp9vxtAMaYP3lt84G9zdciEgnsBDJMC0Fl94kyOet2Qdz+1tvadXbn0OusVOgK5i7K+wBbveZz7WVNbmOMqQEKgZabZcenN0gUSimlAi+QyaKp14Aalxh82QYRuVpEckQkJ68y2i/BKaWU8l0gk0Uu0M9rvi+wvblt7MdQycDexgcyxswxxmQbY7IzgqiLD6WU6ioCmSwWA1kiMlBEooEZwIJG2ywALrGnzwY+bqm+oiWhNjxsqNHrq1TXFrBkYddBzAQ+AFYB84wxK0TkLhGZam/2NJAmIuuBm4ADXq/1hdvtZs+ePXpDCxBjDHv27KlvJa6U6noC9jZUoGRnZ5ucnJwGy6qrq8nNzW3Q2E35l9vtpm/fvkRFBUd/XEqptuno21Ch14K7CVFRUQwcONDpMJRSKmyFXt9QSimlOp0mC6WUUq3SZKGUUqpVIVfBLSLFwBqn4/BBOpDvdBA+0Dj9JxRiBI3T30IlziHGmMT27hyKFdxrOlKj31lEJEfj9J9QiDMUYgSN099CKc6O7K+PoZRSSrVKk4VSSqlWhWKymON0AD7SOP0rFOIMhRhB4/S3LhFnyFVwK6WU6nyhWLJQSinVyUIqWbQ2prcTRKSfiHwiIqtEZIWI3Ggvny0i20Rkqf0zJQhi3SQiP9rx5NjLuonIRyKyzv5MdTjGIV7XbKmIFInIr4LheorIMyKyW0SWey1r8vqJ5RH7b/UHEenYWLodj/NBEVltx/KmiKTYyzNFpNzruj7hcJzN/juLyG329VwjIqc6HOerXjFuEpGl9nJHrmcL9yH//X0aY0LiB3ABG4CDgGhgGTAsCOLqBYyxpxOBtVhjjs8GbnE6vkaxbgLSGy17ALjVnr4VuN/pOBv9m+8EBgTD9QSOB8YAy1u7fsAU4D2sAb7GAd84HOdEINKevt8rzkzv7YLgejb572z/n1oGxAAD7XuBy6k4G63/CzDLyevZwn3Ib3+foVSyOBJYb4z5yRhTBbwCTHM4JowxO4wx39nTxVjdsTcePjaYTQP+ZU//CzjDwVgamwBsMMZsdjoQAGPMZxw4OFdz128a8LyxLAJSRKSXU3EaYz401rABAIuwBiNzVDPXsznTgFeMMZXGmI3Aeqx7QsC1FKeICHAO8HJnxNKcFu5Dfvv7DKVk4cuY3o4SkUxgNPCNvWimXcR7xunHOzYDfCgiS0TkantZD2PMDrD+4IDujkV3oBk0/E8YbNcTmr9+wfz3ejnWt8o6A0XkexH5VESOcyooL039Owfr9TwO2GWMWee1zNHr2eg+5Le/z1BKFj6N1+0UEUkA3gB+ZYwpAh4HBgGjgB1YRVWnHWOMGQNMBq4XkeOdDqg5Yo2uOBV4zV4UjNezJUH59yoitwM1wFx70Q6gvzFmNNYAZC+JSJJT8dH8v3NQXk/gPBp+oXH0ejZxH2p20yaWtXg9QylZ+DKmtyNEJArrH2iuMebfAMaYXcYYjzGmFniSTioyt8QYs93+3A28iRXTrrrip/2527kIG5gMfGeM2QXBeT1tzV2/oPt7FZFLgNOBC4z94Np+rLPHnl6CVRcw2KkYW/h3DsbrGQmcCbxat8zJ69nUfQg//n2GUrLwZUzvTmc/s3waWGWMechruffzv+nA8sb7diYRiReRxLpprArP5TQcB/0S4C1nIjxAg29swXY9vTR3/RYAF9tvnYwDCuseBzhBRCYBvwWmGmPKvJZniIjLnj4IyAJ+cibKFv+dFwAzRCRGRAZixfltZ8fXyMnAamNMbt0Cp65nc/ch/Pn32dm19h2s8Z+CVcu/Abjd6XjsmI7FKr79ACy1f6YALwA/2ssXAL0cjvMgrLdJlgEr6q4fkAb8D1hnf3YLgmsaB+wBkr2WOX49sZLXDqAa65vZFc1dP6xi/qP23+qPQLbDca7HekZd9zf6hL3tWfbfwzLgO+BnDsfZ7L8zcLt9PdcAk52M017+HHBNo20duZ4t3If89vepLbiVUkq1KpQeQymllHKIJgullFKt0mShlFKqVZoslFJKtUqThVJKqVZpslBKKdUqTRYqJImIx+4CermIvC12l9tt2H+2iNxiT98lIid3MJ76rqk7chx/EpFz7S6o/+N0LCr0abJQoarcGDPKGDMCq0fQ69t7IGPMLGPMf/0Q0wZjzKi27FDX2jcQjDGvAlcG6viqa9FkocLB19g9ZopIgoj8T0S+E2ugp/pu7EXkdrEGzvkvMMRr+XMicrY9vUlE0u3pbBFZaE+fIPsHtPm+ruuUlojIfLuH3xVevfwiIiV2aeYb4CgROUJEvhKRZSLyrYgkishwe3qp3QNrlr3vhV7L/+nVtcQk+3deJiL/6/glVaqhSKcDUKoj7JvlBKx+cQAqgOnGmCL7pr9IRBZgDV4zA6vr5kisrhiWtOFUtwDXG2O+tHv2rPBhn8uNMXtFJBZYLCJvGKuTuXisAXJm2f2crQbONcYstnsoLQeuAf5mjJlrb+MSkaHAuVi9B1eLyGPABSLyHlane8cbYzaKSLc2/F5K+USThQpVsXb9QCbWTf8je7kA99rdr9dilTh6YI078KaxO9GzE0hbfAk8JCJzgX8br87jWnCDiEy3p/thdSq3B/Bg9Q4KVglnhzFmMYCxu5UWka+B20Wkr32+dSIyATgcK/EAxGL1IjoO+MxYgwJhjPF1QCGlfKaPoVSoKrfrBwZgDbNbV2dxAZABHG6v3wW47XW+dIRWw/7/F3X7YYy5D+v5fyxWaeWQlg4iIuOxeiU9yhhzGPC91/EqjDGeuk2bissY8xLWeB7lwAcicpK97b/suppRxpghxpjZzR1DKX/SZKFCmjGmELgBuMXuzz8Z2G0/pjkRK5kAfAZMF5FYu77hZ80cchPWt3ewehAFQEQGGWN+NMbcD+QALSYLO459xpgyO7GMa2a71UBvETnCPk+iiETa3Vv/ZIx5BKv31UOxeg09W0S629t2E5EBWHU2J9hdd6OPoVQg6GMoFfKMMd+LyDKsOom5wNsikoPVTfNqe5vvRORVe9lm4PNmDncn8LSI/I79w+MC/MpOPh5gJQ2HJW3K+8A1IvIDVpfai5qJvUpEzgX+btdtlGOVSM4FLhSRamAncJdd//F7rKFxI7C6zL7eGLPIrkD/t718N3BKK/Ep1SbaRblSfiDWuMf/sV/lDRr247BbjDGnOx2LCm36GEop//AAycHWKA94DNjndCwq9GnJQimlVKu0ZKGUUqpVmiyUUkq1SpOFUkqpVmmyUEop1SpNFkoppVr1/1Q7+pQgbZ+LAAAAAElFTkSuQmCC\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, 200])\n",
    "plt.xlabel('Radius [arcsec]')\n",
    "plt.ylabel('Encircled flux')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "37819220000.0"
      ]
     },
     "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": "markdown",
   "metadata": {},
   "source": [
    "### Validation\n",
    "To check PSF is reasonable, lets look at a 100 micron source, e.g. `XMM-PACSxID24-1-69605`. We can see from `XMM-LSS_PACS100_v0.9.fits` that it has a flux of 27 mJy. Maximum value in our normalised PSF gives a peak below. Since PSF is three times resolution of map, it could also be off centre. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "PACScat=Table.read('./data/XMM-LSS_PACSxID24_v1.fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Column name=&apos;HELP_ID&apos; dtype=&apos;bytes21&apos; length=69614&gt;\n",
       "<table>\n",
       "<tr><td>XMM-PACSxID24-1-00001</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00002</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00003</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00004</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00005</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00006</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00007</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00008</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00009</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00010</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00011</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-00012</td></tr>\n",
       "<tr><td>...</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69603</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69604</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69605</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69606</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69607</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69608</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69609</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69610</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69611</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69612</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69613</td></tr>\n",
       "<tr><td>XMM-PACSxID24-1-69614</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Column name='HELP_ID' dtype='bytes21' length=69614>\n",
       "XMM-PACSxID24-1-00001\n",
       "XMM-PACSxID24-1-00002\n",
       "XMM-PACSxID24-1-00003\n",
       "XMM-PACSxID24-1-00004\n",
       "XMM-PACSxID24-1-00005\n",
       "XMM-PACSxID24-1-00006\n",
       "XMM-PACSxID24-1-00007\n",
       "XMM-PACSxID24-1-00008\n",
       "XMM-PACSxID24-1-00009\n",
       "XMM-PACSxID24-1-00010\n",
       "XMM-PACSxID24-1-00011\n",
       "XMM-PACSxID24-1-00012\n",
       "                  ...\n",
       "XMM-PACSxID24-1-69603\n",
       "XMM-PACSxID24-1-69604\n",
       "XMM-PACSxID24-1-69605\n",
       "XMM-PACSxID24-1-69606\n",
       "XMM-PACSxID24-1-69607\n",
       "XMM-PACSxID24-1-69608\n",
       "XMM-PACSxID24-1-69609\n",
       "XMM-PACSxID24-1-69610\n",
       "XMM-PACSxID24-1-69611\n",
       "XMM-PACSxID24-1-69612\n",
       "XMM-PACSxID24-1-69613\n",
       "XMM-PACSxID24-1-69614"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat['HELP_ID']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=1</i>\n",
       "<table id=\"table140194132615464\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>XID</th><th>RA</th><th>Dec</th><th>F_PACS_100__A4</th><th>F_PACS_100__A5</th><th>F_PACS_100__A6</th><th>F_PACS_100__A7</th><th>F_PACS_100__A8</th><th>F_PACS_100__A10</th><th>F_PACS_100</th><th>Ferr_PACS_100__A4</th><th>Ferr_PACS_100__A5</th><th>Ferr_PACS_100__A6</th><th>Ferr_PACS_100__A7</th><th>Ferr_PACS_100__A8</th><th>Ferr_PACS_100__A10</th><th>Ferr_PACS_100</th><th>F_PACS_100__SKY</th><th>F_PACS_160__A4</th><th>F_PACS_160__A5</th><th>F_PACS_160__A6</th><th>F_PACS_160__A7</th><th>F_PACS_160__A8</th><th>F_PACS_160__A10</th><th>F_PACS_160</th><th>Ferr_PACS_160__A4</th><th>Ferr_PACS_160__A5</th><th>Ferr_PACS_160__A6</th><th>Ferr_PACS_160__A7</th><th>Ferr_PACS_160__A8</th><th>Ferr_PACS_160__A10</th><th>Ferr_PACS_160</th><th>F_PACS_160__SKY</th><th>HELP_ID</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th><th>deg</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy</th><th>mJy / pix</th><th></th></tr></thead>\n",
       "<thead><tr><th>int32</th><th>float64</th><th>float64</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>float32</th><th>bytes21</th></tr></thead>\n",
       "<tr><td>35346</td><td>37.189607</td><td>-5.359364</td><td>24.75368</td><td>33.91122</td><td>39.201374</td><td>42.93285</td><td>50.577137</td><td>53.45504</td><td>27.005695</td><td>25.116787</td><td>22.750774</td><td>22.183317</td><td>22.005985</td><td>22.450182</td><td>24.190016</td><td>15.973581</td><td>0.0</td><td>8.490818</td><td>19.619059</td><td>26.27224</td><td>31.353258</td><td>32.08416</td><td>37.23328</td><td>18.46733</td><td>33.844845</td><td>28.466045</td><td>26.428268</td><td>24.746319</td><td>23.908075</td><td>24.301949</td><td>17.06235</td><td>0.0</td><td>XMM-PACSxID24-1-69605</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=1>\n",
       " XID      RA       Dec    ... F_PACS_160__SKY        HELP_ID       \n",
       "         deg       deg    ...    mJy / pix                         \n",
       "int32  float64   float64  ...     float32            bytes21       \n",
       "----- --------- --------- ... --------------- ---------------------\n",
       "35346 37.189607 -5.359364 ...             0.0 XMM-PACSxID24-1-69605"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max PSF = 9.5294 Jy/sr, off pixel Max PSF = 9.0621 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]*0.027,psfok[cpix-2,cpix-2]*0.027))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mc741/anaconda3/lib/python3.6/site-packages/mpl_toolkits/axes_grid/__init__.py:12: MatplotlibDeprecationWarning: \n",
      "The mpl_toolkits.axes_grid module was deprecated in Matplotlib 2.1 and will be removed two minor releases later. Use mpl_toolkits.axes_grid1 and mpl_toolkits.axisartist provies the same functionality instead.\n",
      "  obj_type='module')\n",
      "WARNING: hdu=0 does not contain any data, using hdu=1 instead [aplpy.core]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n",
      "WARNING: Cannot determine equinox. Assuming J2000. [aplpy.wcs_util]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x648 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import aplpy\n",
    "import seaborn as sns\n",
    "sns.set_style(\"white\")\n",
    "cmap=sns.cubehelix_palette(8, start=.5, rot=-.75,as_cmap=True)\n",
    "fig=aplpy.FITSFigure('./data/input_data/XMM-LSS_PACS100_v0.9.fits')\n",
    "fig.recenter(PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']['RA'],PACScat[PACScat['HELP_ID']=='XMM-PACSxID24-1-69605']['Dec'], radius=0.004)\n",
    "fig.show_colorscale(vmin=-0.001,vmax=0.003,cmap=cmap)\n",
    "fig.add_colorbar()\n",
    "fig.colorbar.set_location('top')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, the PSF is within 10% of this source, and given noise and shape of source will add additional uncertianty, as well as non-zero background, this seems reasonable.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create PSF fits file¶\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "stackhd[1].data=psfok\n",
    "stackhd.writeto('dmu18_PACS_100_PSF_XMM-LSS_20190125_sr.fits',output_verify='fix+warn', overwrite=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "352.94086"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(psfok)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.max(psfok)*2.35045e-5*(np.abs(stackhd[1].header['CDELT1'])*3600)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.hist(psfok.flatten(),bins=np.arange(-0.01,0.05,0.0005));\n",
    "#plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAADWhJREFUeJzt3W+IZfddx/H3x6xJ/RNSG6OE3cQkzCZkH2grQ5qqD0qpsiluU2rQLAWrLFkiRioIskERfNgntgRi60pDnpTEGIvdxpVQ0oYghDabttYNy9ptUDKkuFvTRvCBMfXrgzmb3kzmz525c+fOfu/7BcPM+d1zzv3Nb3c/nP2e37m/VBWSpL5+ZNYdkCRNl0EvSc0Z9JLUnEEvSc0Z9JLUnEEvSc0Z9JLUnEEvSc0Z9JLU3J5ZvnmSQ8ChK6+88p6bb755ll2RpEvO888//92qumaj/bIbPgJhcXGxTp06NetuSNIlJcnzVbW40X6WbiSpOYNekpoz6CWpOYNekpqbadAnOZTk+KuvvjrLbkhSazMN+qr6QlUdveqqq2bZDUlqzdKNJDVn0EtSc62D/oZj/zDrLkjSzLUN+oshb9hLmndtg16StKzl9Eqv4iXph+ZieqXBL2meWbqRpOYMeklqbm6C3vKNpHnVLugNdEl6s3ZBL0l6M4Nekpoz6CWpOYNekppr9WTsRjdivVEraR7NxZOxkjTPLN1IUnMGvSQ1Z9BLUnMGvSQ11ybox51R48wbSfOmTdBLklZn0EtScwa9JDVn0EtScwa9JDVn0EtSc9se9EluTfLpJI8n+b3tPv92cIqlpHkyVtAneSjJ+SSnV7QfTHI2ybkkxwCq6kxV3Qv8JrC4/V1+K4NbktY27hX9w8DB0YYklwEPAncAB4DDSQ4Mr30Q+CfgqW3rqSRpS8YK+qp6BnhlRfNtwLmqerGqXgMeBe4c9j9RVb8EfGQ7OytJ2rw9Exy7F3hpZHsJeHeS9wIfBq4ATq51cJKjwFGA66+/foJuSJLWM0nQZ5W2qqqngac3OriqjgPHARYXF2uCfkiS1jHJrJsl4LqR7X3Ay5s5wXYvJShJeqtJgv45YH+SG5NcDtwNnNjMCVxKUJKmb9zplY8AzwK3JFlKcqSqXgfuA54EzgCPVdUL0+uqJGkrxqrRV9XhNdpPss4N140kOQQcWlhY2OopJEkbmOlHIMyydONDVpLmhZ91I0nNzTTonXUjSdN3yZduLMFI0vos3UhScwa9JDVnjV6Smrvka/SSpPVZupGk5gx6SWrOoJek5rwZK0nNzfXNWB+2kjQPLN1IUnMGvSQ1Z9BLUnPejJWk5ub6ZqwkzQNLN5LUnEEvSc0Z9JLU3NwHvQ9NSepu7oNekrpzeqUkNef0SklqztKNJDVn0EtScwa9JDVn0EtScwa9JDVn0EtScwa9JDVn0EtScz4ZK0nN+WSsJDVn6UaSmjPo8aOKJfVm0EtScwa9JDVn0EtScwa9JDVn0EtScwa9JDVn0EtScwa9JDVn0EtSc1MJ+iQfSvLXST6f5Nem8R6SpPGMHfRJHkpyPsnpFe0Hk5xNci7JMYCq+vuqugf4HeC3trXHkqRN2cwV/cPAwdGGJJcBDwJ3AAeAw0kOjOzyp8PrkqQZGTvoq+oZ4JUVzbcB56rqxap6DXgUuDPLPg78Y1V9bfu6K0narElr9HuBl0a2l4a2PwDeD9yV5N7VDkxyNMmpJKcuXLgwYTckSWvZM+HxWaWtquoB4IH1Dqyq48BxgMXFxZqwH5KkNUx6Rb8EXDeyvQ94edyDd9NSgn4mvaSuJg3654D9SW5McjlwN3Bi3INdSlCSpm8z0ysfAZ4FbkmylORIVb0O3Ac8CZwBHquqF6bTVUnSVoxdo6+qw2u0nwRObuXNkxwCDi0sLGzlcEnSGGb6EQiWbiRp+vysG0lqbqZBv5tm3UhSV5ZuJKk5SzeS1JxBL0nNWaOXpOas0UtSc5ZuJKk5g16SmjPoJak5b8ZKUnPejB3hZ9JL6sjSjSQ1Z9BLUnMGvSQ1581YSWrOm7GS1JylG0lqzqCXpOYMeklqzqCXpOYMeklqzumVktSc0yslqTlLNyv4wWaSujHoJak5g16SmjPoJak5g16SmjPoJak5g16SmjPoJak5n4yVpOZ8MnYNPjglqQtLN5LUnEEvSc0Z9JLUnEG/Cuvzkjox6CWpOYNekpoz6CWpOYNekpoz6CWpOYNekpoz6NfhNEtJHWx70Ce5Kclnkjy+3eeWJG3eWEGf5KEk55OcXtF+MMnZJOeSHAOoqher6sg0OitJ2rxxr+gfBg6ONiS5DHgQuAM4ABxOcmBbeydJmthYQV9VzwCvrGi+DTg3XMG/BjwK3LnN/ZMkTWiSGv1e4KWR7SVgb5Krk3waeFeS+9c6OMnRJKeSnLpw4cIE3ZAkrWfPBMdmlbaqqv8E7t3o4Ko6DhwHWFxcrAn6IUlaxyRX9EvAdSPb+4CXN3MClxKUpOmbJOifA/YnuTHJ5cDdwInNnGA3LyUoSV2MO73yEeBZ4JYkS0mOVNXrwH3Ak8AZ4LGqemF6XZUkbcVYNfqqOrxG+0ng5FbfPMkh4NDCwsJWTyFJ2sBMPwLB0o0kTZ+fdSNJzRn0ktTcTIPe6ZWSNH3W6CWpOUs3ktScpZtNWLkQiQuTSLoUWLqRpOYs3UhScwa9JDVn0EtSc96MlaTmvBkrSc1ZupGk5gx6SWrOoJek5rwZO4Zxn4D1SVlJu5E3YyWpOUs3ktScQS9JzRn0ktScQS9JzRn0ktSc0ys3sNFiI5uZerlT0y93wzTP3dAHXXr8ezMdTq+UpOYs3UhScwa9JDVn0EtScwa9JDVn0EtScwa9JDVn0EtScwa9JDXnk7FjWu+JvdGnXsd9cvbiMasdtx1PB673vuMes16fpvEEo09Fbt1O/PmsdX7/3HY/n4yVpOYs3UhScwa9JDVn0EtScwa9JDVn0EtScwa9JDVn0EtScwa9JDVn0EtScwa9JDVn0EtSc3u2+4RJfgL4S+A14Omq+ux2v4ckaXxjXdEneSjJ+SSnV7QfTHI2ybkkx4bmDwOPV9U9wAe3ub+SpE0at3TzMHBwtCHJZcCDwB3AAeBwkgPAPuClYbcfbE83JUlbNVbQV9UzwCsrmm8DzlXVi1X1GvAocCewxHLYj31+SdL0TBLEe/nhlTssB/xe4HPAbyT5FPCFtQ5OcjTJqSSnLly4MEE3dt5GCy2MLiiy2eNHFyJZubjDam0rz7eZBUfGXVhkZZ82u8jKyt9hvf6v9t4r9xvnd1xtvNb6vcbp+1r7bffiLGv9ua/1Xmvtu9F7TPL6Vo7bykI4q+271b5v9Henu0luxmaVtqqq/wZ+d6ODq+o4cBxgcXGxJuiHJGkdk1zRLwHXjWzvA17ezAkupaUEJelSNUnQPwfsT3JjksuBu4ETmzmBSwlK0vSNO73yEeBZ4JYkS0mOVNXrwH3Ak8AZ4LGqemF6XZUkbcVYNfqqOrxG+0ng5FbfPMkh4NDCwsJWTyFJ2sBMpz9aupGk6XOeuyQ1Z9BLUnMzDXqnV0rS9KVq9s8qJbkA/PuUTv/TwHendO5OHKfxOE7jc6zGM8k4/VxVXbPRTrsi6KcpyamqWpx1P3Y7x2k8jtP4HKvx7MQ4WaOXpOYMeklqbh6C/visO3CJcJzG4ziNz7Eaz9THqX2NXpLm3Txc0UvSXGsb9GusZzu3Vlv3N8k7knwxybeG7z81tCfJA8PYfTPJL86u5zsryXVJvpzkTJIXknxsaHesRiR5W5KvJvnnYZz+fGi/MclXhnH6m+GTbUlyxbB9bnj9hln2f6cluSzJ15M8MWzv6Di1DPp11rOdZw+zYt1f4BjwVFXtB54atmF53PYPX0eBT+1QH3eD14E/qqpbgduB3x/+7jhWb/Y/wPuq6heAdwIHk9wOfBz4xDBO3wOODPsfAb5XVQvAJ4b95snHWP6U34t2dpyqqt0X8B7gyZHt+4H7Z92vWX8BNwCnR7bPAtcOP18LnB1+/ivg8Gr7zdsX8HngVx2rdcfox4GvAe9m+cGfPUP7G/8OWf448/cMP+8Z9sus+75D47OP5YuD9wFPsLw6346OU8sretZez1Zv9rNV9R2A4fvPDO2OHzD8t/ldwFdwrN5iKEd8AzgPfBH4NvD9Wl6rAt48Fm+M0/D6q8DVO9vjmfkk8MfA/w3bV7PD49Q16Fddz3bHe3HpmvvxS/KTwN8Bf1hV/7Xerqu0zcVYVdUPquqdLF+x3gbcutpuw/e5HKckvw6cr6rnR5tX2XWq49Q16Cdez3ZO/EeSawGG7+eH9rkevyQ/ynLIf7aqPjc0O1ZrqKrvA0+zfE/j7UkuLmg0OhZvjNPw+lXAKzvb05n4ZeCDSf4NeJTl8s0n2eFx6hr0E69nOydOAB8dfv4oy/Xoi+2/PcwouR149WLZorskAT4DnKmqvxh5ybEakeSaJG8ffv4x4P0s32z8MnDXsNvKcbo4fncBX6qhEN1ZVd1fVfuq6gaWc+hLVfURdnqcZn2jYoo3QD4A/CvLdcM/mXV/Zv0FPAJ8B/hflq8ajrBc+3sK+Nbw/R3DvmF51tK3gX8BFmfd/x0cp19h+b/K3wS+MXx9wLF6yzj9PPD1YZxOA382tN8EfBU4B/wtcMXQ/rZh+9zw+k2z/h1mMGbvBZ6YxTj5ZKwkNde1dCNJGhj0ktScQS9JzRn0ktScQS9JzRn0ktScQS9JzRn0ktTc/wNF6gnD0eXNzAAAAABJRU5ErkJggg==\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(-10,400,0.5));\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90601"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(psfok.flatten())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (herschelhelp_internal)",
   "language": "python",
   "name": "helpint"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}