astropy/astropy_hands_on.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hands On Astropy Tutorial \n",
    "**Tutors:** Axel Donath and Christoph Deil\n",
    "\n",
    "This hands-on tutorial gives an introduction and overview of the [Astropy](http://www.astropy.org/) Python package for Astronomy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preface\n",
    "We recommend to follow this tutorial by **executing the code cells on your local machine**, along with the tutor. Every sub-topic we will cover in this tutorial will be concluded by a few **exercises with different levels of difficulty** (*easy*, *advanced* and *hard*). We will give you **~15-20 min to solve the exercises** and present a possible solution afterwards. In case we don't have time to show all the solutions or in the likely case that you don't manage to solve all of them: we provide a **sample solution** for all exercises in the [solutions notebook](astropy_hands_on_solutions.ipynb) you can look at **after the course**.   \n",
    "\n",
    "The estimated time for this tutorial is ~3 hours. Feel free to **interrupt at any time** to ask questions or **talk to the assisting tutors** when you encounter errors or the code doesn't work as expected.\n",
    "\n",
    "We have marked some of the sections that deal with more advanced topics as \"optional\". \n",
    "\n",
    "The material presented here is partly based on: \n",
    "\n",
    "- Astropy [documentation](http://docs.astropy.org/en/stable/index.html) webpage\n",
    "- Notebooks provided in the [Astropy Tutorials](https://github.com/astropy/astropy-tutorials) repository\n",
    "- And the [Astropy Introduction for Gammapy Users](https://github.com/gammapy/gammapy-extra/blob/master/notebooks/astropy_introduction.ipynb) notebook\n",
    "\n",
    "As the content that can be covered in this ~3 hour tutorial is very limited, we recommend to also **check-out the ressources** listed above after the school.\n",
    "\n",
    "We're happy to receive any **feedback or questions** on the tutorial via mail to *axel.donath@mpi-hd.mpg.de* or using the \n",
    "repository's [issue tracker](https://github.com/Asterics2020-Obelics/School2017/issues). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is Astropy?\n",
    "\n",
    "![](astropy_banner_96.png)\n",
    "\n",
    "    \"The Astropy Project is a community effort to develop a single core package for Astronomy in Python and foster interoperability between Python astronomy packages.\"\n",
    "\n",
    "\n",
    "The concept and structure of the package is decribed in more detail in the first [Astropy paper 2013](http://adsabs.harvard.edu/abs/2013A%26A...558A..33A). The development infrastructure\n",
    "and status of the v2.0 core package is described in the second [Astropy paper 2018](http://adsabs.harvard.edu/abs/2018arXiv180102634T).\n",
    "\n",
    "The **Astropy package is structured into several submodules** and we will cover (what we consider) the most important of them in the following order:\n",
    "\n",
    "1. [astropy.units](http://docs.astropy.org/en/stable/units/index.html) and in particular [astropy.units.Quantities](http://docs.astropy.org/en/stable/api/astropy.units.Quantity.html) to do astronomical calculations with units.\n",
    "\n",
    "2. [astropy.coordinates](http://docs.astropy.org/en/stable/coordinates/) and in particular the classes [SkyCoord](http://docs.astropy.org/en/stable/api/astropy.coordinates.SkyCoord.html) and [Angle](http://docs.astropy.org/en/stable/coordinates/angles.html) to handle astronomical sky positions, coordinate systems and coordinate transformations.\n",
    "\n",
    "3. [astropy.tables](http://docs.astropy.org/en/stable/table/index.html) and the [Table](http://docs.astropy.org/en/stable/api/astropy.table.Table.html) class to handle astronomical data tables.\n",
    "\n",
    "4. [astropy.io.fits](http://docs.astropy.org/en/stable/io/fits/index.html) to open and write data files in [FITS format](https://fits.gsfc.nasa.gov/fits_documentation.html).\n",
    "\n",
    "5. (optional) Plotting of astronomical sky images with [astropy.visualization.wcsaxes](http://docs.astropy.org/en/stable/visualization/wcsaxes/)\n",
    "\n",
    "In addition to the Astropy core package there is an infrastructure of  [Astropy affiliated packages](http://www.astropy.org/affiliated/) dedicated to specific fields of Astronomy or analysis tasks, such as:\n",
    "\n",
    "- [Astroplan](https://astroplan.readthedocs.io/en/latest/): observation planning\n",
    "- [Reproject](http://reproject.readthedocs.io/en/stable/): reprojection of sky images\n",
    "- [Regions](http://astropy-regions.readthedocs.io/en/latest/): handling of sky regions \n",
    "- [Photutils](https://photutils.readthedocs.io/en/stable/): source detection and photometry\n",
    "- [Gammapy](docs.gammapy.org): gamma-ray Astronomy data analysis\n",
    "- ...and many others, or maybe your package?\n",
    "\n",
    "\n",
    "You can **get help on Astropy** beyond this course via the following channels:\n",
    "\n",
    "- [Astropy mailing list](https://mail.scipy.org/mailman/listinfo/astropy) (for general questions / help)\n",
    "- [Astropy gitter channel](https://gitter.im/astropy/astropy) (for quick questions / chat)\n",
    "- [Astropy issue tracker](https://github.com/astropy/astropy/issues) (for questions / bug reports)\n",
    "\n",
    "If you would like to contribute to Astropy, please start by reading the [contribute page](http://www.astropy.org/contribute.html)\n",
    "on the website.\n",
    "\n",
    "Let's start with the setup and check of the notebook:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Setup\n",
    "\n",
    "Check package versions. All examples should work with Astropy > 2.0 and Numpy > 1.11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline  \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy: 1.11.2\n",
      "astropy: 3.0.2\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import astropy\n",
    "print('numpy:', np.__version__)\n",
    "print('astropy:', astropy.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Units and Quantities\n",
    "\n",
    "The [astropy.units]() subpackage provides functions and classes to handle physical quantities with units. \n",
    "\n",
    "### 1.1. Basics\n",
    "The recommended way to import the `astropy.units` submodule is: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy import units as u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Quantities` are created by multiplying any number with a unit object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 lyr\n"
     ]
    }
   ],
   "source": [
    "distance = 1. * u.lightyear\n",
    "print(distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or by passing a string to the general `Quantity` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "distance = u.Quantity('1 lyr')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the availabe units with tab completion on the units module, `u.<TAB>`.\n",
    "\n",
    "Quantities can be also created using lists and arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.   3.  10.] lyr\n",
      "[  1.   3.  10.] lyr\n"
     ]
    }
   ],
   "source": [
    "distances = [1, 3, 10] * u.lightyear\n",
    "print(distances)\n",
    "\n",
    "distances = np.array([1, 3, 10]) * u.lightyear\n",
    "print(distances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.,   3.,  10.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distances.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The quantity object has a value attribute, which is a plain `numpy.ndarray`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distances.value\n",
    "type(distances.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a unit, which is represented by a `astropy.units.core.Unit` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "astropy.units.core.Unit"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance.unit\n",
    "type(distances.unit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A quantity behaves in many ways just like a `numpy.ndarray` with an attached unit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$[10,~30,~100] \\; \\mathrm{lyr}$"
      ],
      "text/plain": [
       "<Quantity [  10.,  30., 100.] lyr>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distances * 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many numpy functions will work as expected and return again a `Quantity` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$10 \\; \\mathrm{lyr}$"
      ],
      "text/plain": [
       "<Quantity 10.0 lyr>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(distances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$4.6666667 \\; \\mathrm{lyr}$"
      ],
      "text/plain": [
       "<Quantity 4.666666666666667 lyr>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(distances)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But there are exceptions, where the unit handling is not well defined, e.g. in `np.log` arguments have to be dimensionless, such as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.0986123 \\; \\mathrm{}$"
      ],
      "text/plain": [
       "<Quantity 1.0986122886681098>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#np.log(30 * u.MeV) # Will raise an UnitConversionError\n",
    "np.log(30 * u.MeV / (10 * u.MeV))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probably the most useful method on the `Quantity` object is the `.to()` method which allows to convert a quantity to different units:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$9.4607305 \\times 10^{15} \\; \\mathrm{m}$"
      ],
      "text/plain": [
       "<Quantity 9460730472580800.0 m>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance.to('meter')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.30660139 \\; \\mathrm{pc}$"
      ],
      "text/plain": [
       "<Quantity 0.3066013937879527 pc>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance.to(u.parsec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quantities can be combined with any arithmetical expression to derive other quantities, `astropy.units` will propagate\n",
    "the units correctly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299792.458 km / s\n"
     ]
    }
   ],
   "source": [
    "speed_of_light = distance / u.year\n",
    "print(speed_of_light.to('km/s'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5902068371199996e+23 Angstrom / d\n"
     ]
    }
   ],
   "source": [
    "print(speed_of_light.to('angstrom/day'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For standardized unit systems such as `'si'` or `'cgs'` there are convenience attributes on the quantity object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.9979246 \\times 10^{8} \\; \\mathrm{\\frac{m}{s}}$"
      ],
      "text/plain": [
       "<Quantity 299792458.0 m / s>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "speed_of_light.si"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$2.9979246 \\times 10^{10} \\; \\mathrm{\\frac{cm}{s}}$"
      ],
      "text/plain": [
       "<Quantity 29979245799.999992 cm / s>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "speed_of_light.cgs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 1.2. Equivalencies\n",
    "\n",
    "In Astronomy and other fields of physics quantities are often measured in more practical units, which are equivalent to the actual physical unit. In `astropy.units` this is handled with the concept of \"equivalencies\".  \n",
    "\n",
    "For example consider units to measure spectral quantities such as wavelength, frequency and energy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$1.2407003 \\; \\mathrm{MeV}$"
      ],
      "text/plain": [
       "<Quantity 1.2407002987020492 MeV>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequency = 3e20 * u.hertz\n",
    "frequency.to('MeV', equivalencies=u.spectral())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$0.99930819 \\; \\mathrm{pm}$"
      ],
      "text/plain": [
       "<Quantity 0.9993081933333333 pm>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frequency.to('picometer', equivalencies=u.spectral())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Miscellaneous\n",
    "\n",
    "Astropy provides a lot of builtin physical and astronomical constants quantitites in the [astropy.constants]() submodule:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "299792.458 km / s\n"
     ]
    }
   ],
   "source": [
    "from astropy import constants as const\n",
    "\n",
    "print(const.c.to('km / s'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a [list of available constants](http://docs.astropy.org/en/stable/constants/#module-astropy.constants).\n",
    "\n",
    "If you write a function that you would like to share with others, you can make the input is given in the right units using the [astropy.units.quantity_input](http://docs.astropy.org/en/stable/api/astropy.units.quantity_input.html#astropy.units.quantity_input) decorator: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "@u.quantity_input(frequency=u.hertz, temperature=u.K)\n",
    "def blackbody(frequency, temperature): \n",
    "    pre_factor = 2 * (const.h * frequency ** 3) / const.c ** 2\n",
    "    exponential_factor = 1. / (np.exp((const.h * frequency) / (const.k_B * temperature)) - 1)\n",
    "    return pre_factor * exponential_factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Interfacing quantities with third-party code (optional) \n",
    "\n",
    "When writing code that uses quantities we are typically bound to use it everywhere in the code. But often we'd like to interface with functions (e.g. from [SciPy](https://www.scipy.org/) or [Matplotlib](https://matplotlib.org/)) or other third-party code that doesn't know how to handle quantities.\n",
    "\n",
    "For Matplotlib, Astropy has a builtin support:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/axel/Arbeit/Software/Anaconda/anaconda3.5/lib/python3.5/site-packages/astropy/units/quantity.py:1092: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  return super().__rtruediv__(other)\n"
     ]
    },
    {
     "data": {
      "image/png": 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HgFuAR4AdwD3uvt3MbjWz+Ol+1wN3x3YwHLECqDezrcBjwBfjZxWku2atFphw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa61492bf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from astropy.visualization import quantity_support\n",
    "\n",
    "plt.figure(figsize=(8, 5))\n",
    "\n",
    "temperature = 1000 * u.K\n",
    "frequencies = np.linspace(1E-5, 0.5e15, 1000) * u.hertz\n",
    "\n",
    "radiance = blackbody(frequency=frequencies, temperature=temperature)\n",
    "\n",
    "with quantity_support():   \n",
    "    plt.plot(frequencies, radiance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But in other cases there is only the option to convert the quantity to well defined units, strip off the unit and re-attach it after the computation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.           1.29154967   1.66810054   2.15443469   2.7825594\n",
      "   3.59381366   4.64158883   5.9948425    7.74263683  10.        ] TeV\n"
     ]
    }
   ],
   "source": [
    "emin, emax = [1, 10] * u.TeV\n",
    "energies = np.logspace(np.log10(emin.value), np.log10(emax.value), 10) * emin.unit\n",
    "print(energies)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.5 Exercises\n",
    "\n",
    "- (*easy*) How long does the light travel from the sun to the earth in minutes? How long does the light travel from the Galactic center (assume a distance of 8 kpc) in years? \n",
    "- (*advanced*) Define a new unit called `\"baro-meter\"`, which is eqivalent to 25 cm and use it to measure the height of the empire state building (assume a height of 381 meters). Please read the [Astropy documentation on equivalencies](http://docs.astropy.org/en/stable/units/equivalencies.html#writing-new-equivalencies) for an example how to do this (For other ways to measure the height of a building using a barometer see [barometer question on Wikipedia](https://en.wikipedia.org/wiki/Barometer_question)...)\n",
    "- (*expert*) Find the frequency with the maximum photon rate of the black body spectrum $\\mathcal{B}(\\nu, T)$ with temperature $T=5000~\\mathrm{K}$. For this you can use a numerical optimization routine such as [scipy.optimize.minimize](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html).\n",
    "As the frequency as well as the radiance can cover many orders of magnitude, the stability of the algorithm can be much improved by minimizing the (negative) logarithm of the radiance $-\\log{\\mathcal{B}}$ as well as minimizing with respect to the logarithm of the frequency by introducing the variable $x = \\log{\\nu}$. Finally compare the result against the analytical solution from [Wien's displacement law](https://en.wikipedia.org/wiki/Wien%27s_displacement_law). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Coordinates\n",
    "\n",
    "With the submodule [astropy.coordinates](http://docs.astropy.org/en/stable/coordinates/) Astropy provides a framework to handle sky positions in various coordinate systems and transformations between them.\n",
    "\n",
    "\n",
    "### 2.1 Basics\n",
    "The basic class to handle sky coordinates is [SkyCoord](http://docs.astropy.org/en/stable/api/astropy.coordinates.SkyCoord.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.coordinates import SkyCoord"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be created by passing a position angle for longitude and latitude and a keyword specifying a coordinate frame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<SkyCoord (ICRS): (ra, dec) in deg\n",
      "    ( 83.63,  22.01)>\n"
     ]
    }
   ],
   "source": [
    "position_crab = SkyCoord(83.63 * u.deg,  22.01 * u.deg, frame='icrs')\n",
    "print(position_crab)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As for `Quantities` the instanciation with `lists`, `arrays` or even `Quantities` also works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "positions = SkyCoord([345., 234.3] * u.deg,  [-0.1, 0.2] * u.deg, frame='galactic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively the angles can be specified as string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "position_crab = SkyCoord('5h34m31.97s', '22d0m52.10s', frame='icrs')\n",
    "\n",
    "# or\n",
    "\n",
    "position_crab = SkyCoord('5:34:31.97', '22:0:52.10',\n",
    "                         unit=(u.hour, u.deg), frame='icrs')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where in the first case the unit doesn't have to specified because it is encoded in the string via `'hms'` and `'dms'`.\n",
    "\n",
    "A very convenient way to get the coordinates of an individual object is qerying the [Sesame](http://cds.u-strasbg.fr/cgi-bin/Sesame) database with `SkyCoord.from_name()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<SkyCoord (ICRS): (ra, dec) in deg\n",
       "    ( 83.633083,  22.0145)>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SkyCoord.from_name('Crab')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To transform the coordinates to a different coordinate system we can use `SkyCoord.transform_to()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pos_gal = position_crab.transform_to('galactic')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For convenience we can also directly use the `.galactic` or `.icrs` attributes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<SkyCoord (Galactic): (l, b) in deg\n",
       "    ( 184.55754381, -5.78427369)>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_crab.galactic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<SkyCoord (ICRS): (ra, dec) in deg\n",
       "    ( 83.63320833,  22.01447222)>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_crab.icrs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To access the `longitude` and `latitude` angles individually: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$5^\\mathrm{h}34^\\mathrm{m}31.97^\\mathrm{s}$"
      ],
      "text/plain": [
       "<Longitude 5.575547222222222 hourangle>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_crab.data.lon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$22^\\circ00{}^\\prime52.1{}^{\\prime\\prime}$"
      ],
      "text/plain": [
       "<Latitude 22.01447222222222 deg>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_crab.data.lat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Measuring distances between positions in the sky\n",
    "The angular distance between two [SkyCoord](http://docs.astropy.org/en/stable/api/astropy.coordinates.SkyCoord.html) objects, can be found using the [SkyCoord.separation()](http://docs.astropy.org/en/stable/api/astropy.coordinates.SkyCoord.html#astropy.coordinates.SkyCoord.separation) method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$172^\\circ38{}^\\prime26.7431{}^{\\prime\\prime}$"
      ],
      "text/plain": [
       "<Angle 172.64076196501316 deg>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_saga = SkyCoord.from_name('Sag A*')\n",
    "position_saga = SkyCoord(0 * u.deg, 0 * u.deg, frame='galactic')\n",
    "\n",
    "position_crab.separation(position_saga)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<SkyCoord (ICRS): (ra, dec) in deg\n",
       "    ( 83.63320833,  22.01447222)>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_crab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 ALT - AZ coordinates (optional)\n",
    "\n",
    "In various cirumstances, e.g. for planning observations, it can be usefull to transform a sky coordinate into a position in the horizontal coordinate system given a location on earth and a time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.coordinates import EarthLocation, AltAz\n",
    "from astropy.time import Time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a location using [EarthLocation](http://docs.astropy.org/en/stable/api/astropy.coordinates.EarthLocation.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GeodeticLocation(lon=<Longitude 2.3508 deg>, lat=<Latitude 48.8567 deg>, height=<Quantity 7.260544597042039e-10 m>)\n"
     ]
    }
   ],
   "source": [
    "paris = EarthLocation(lat=48.8567 * u.deg, lon=2.3508 * u.deg)\n",
    "print(paris.geodetic)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a time using the [Time](http://docs.astropy.org/en/stable/api/astropy.time.Time.html) object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2018-06-04 14:36:49.897673\n"
     ]
    }
   ],
   "source": [
    "now = Time.now()\n",
    "print(now)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can define a horizontal coordinate system using the [AltAz]([docs.astropy.org/en/stable/api/astropy.coordinates.AltAz.html) class and use it to convert from the sky coordinate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<SkyCoord (AltAz: obstime=2018-06-04 14:36:49.897673, location=(4200910.643257838, 172456.78503911156, 4780088.658775934) m, pressure=0.0 hPa, temperature=0.0 deg_C, relative_humidity=0, obswl=1.0 micron): (az, alt) in deg\n",
      "    ( 233.16725174,  53.81802477)>\n"
     ]
    }
   ],
   "source": [
    "altaz = AltAz(obstime=now, location=paris)\n",
    "crab_altaz = position_crab.transform_to(altaz)\n",
    "print(crab_altaz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Exercises\n",
    "\n",
    "- (*easy*) Define the sky coordinate for your favorite astronomical object and find the angular distance to the Crab Nebula as well as the Galactic center.\n",
    "- (*expert*) Make a plot of the height above horizon vs.time for the crab position at the location of Annecy. Mark the time range where it is visible. Would the Crab Nebula be visible tonight?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Tables\n",
    "\n",
    "Astropy provides the [Table](http://docs.astropy.org/en/stable/api/astropy.io.votable.tree.Table.html) class in order to handle data tables.\n",
    "\n",
    "### 3.1 Basics\n",
    "\n",
    "Table objects can be created as shown in the following"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.table import Table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table = Table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We add columns to the table like we would add entries to a dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table['Source_Name'] = ['Crab', 'Sag A*', 'Cas A']\n",
    "table['GLON'] = [184.55754381, 0, 111.74169477] * u.deg\n",
    "table['GLAT'] = [-5.78427369, 0, -2.13544151] * u.deg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By executing the following cell, we get a nicely formatted version of the table printed in the notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=3</i>\n",
       "<table id=\"table140351195047584\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>Source_Name</th><th>GLON</th><th>GLAT</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th><th>deg</th></tr></thead>\n",
       "<thead><tr><th>str6</th><th>float64</th><th>float64</th></tr></thead>\n",
       "<tr><td>Crab</td><td>184.55754381</td><td>-5.78427369</td></tr>\n",
       "<tr><td>Sag A*</td><td>0.0</td><td>0.0</td></tr>\n",
       "<tr><td>Cas A</td><td>111.74169477</td><td>-2.13544151</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=3>\n",
       "Source_Name     GLON         GLAT   \n",
       "                deg          deg    \n",
       "    str6      float64      float64  \n",
       "----------- ------------ -----------\n",
       "       Crab 184.55754381 -5.78427369\n",
       "     Sag A*          0.0         0.0\n",
       "      Cas A 111.74169477 -2.13544151"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Accessing rows and columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have access to the defined columns. To check which ones are availbe you can use `Table.colnames`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Source_Name', 'GLON', 'GLAT']"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table.colnames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And access individual columns just by their name:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "&lt;Column name=&apos;GLON&apos; dtype=&apos;float64&apos; unit=&apos;deg&apos; length=3&gt;\n",
       "<table>\n",
       "<tr><td>184.55754381</td></tr>\n",
       "<tr><td>0.0</td></tr>\n",
       "<tr><td>111.74169477</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Column name='GLON' dtype='float64' unit='deg' length=3>\n",
       "184.55754381\n",
       "         0.0\n",
       "111.74169477"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table['GLON']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And also a subset of columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=3</i>\n",
       "<table id=\"table140351195047976\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>Source_Name</th><th>GLON</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th></tr></thead>\n",
       "<thead><tr><th>str6</th><th>float64</th></tr></thead>\n",
       "<tr><td>Crab</td><td>184.55754381</td></tr>\n",
       "<tr><td>Sag A*</td><td>0.0</td></tr>\n",
       "<tr><td>Cas A</td><td>111.74169477</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=3>\n",
       "Source_Name     GLON    \n",
       "                deg     \n",
       "    str6      float64   \n",
       "----------- ------------\n",
       "       Crab 184.55754381\n",
       "     Sag A*          0.0\n",
       "      Cas A 111.74169477"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table[['Source_Name', 'GLON']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Often, it is handy to get the column data as [astropy.units.Quantity](http://docs.astropy.org/en/stable/api/astropy.units.Quantity.html#astropy.units.Quantity) using the `.quantity` property:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$[184.55754,~0,~111.74169] \\; \\mathrm{{}^{\\circ}}$"
      ],
      "text/plain": [
       "<Quantity [ 184.55754381,   0.        , 111.74169477] deg>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table['GLON'].quantity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rows can be accessed using numpy indexing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=2</i>\n",
       "<table id=\"table140351195047920\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>Source_Name</th><th>GLON</th><th>GLAT</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th><th>deg</th></tr></thead>\n",
       "<thead><tr><th>str6</th><th>float64</th><th>float64</th></tr></thead>\n",
       "<tr><td>Crab</td><td>184.55754381</td><td>-5.78427369</td></tr>\n",
       "<tr><td>Sag A*</td><td>0.0</td><td>0.0</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=2>\n",
       "Source_Name     GLON         GLAT   \n",
       "                deg          deg    \n",
       "    str6      float64      float64  \n",
       "----------- ------------ -----------\n",
       "       Crab 184.55754381 -5.78427369\n",
       "     Sag A*          0.0         0.0"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table[0:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or by using a boolean numpy array for indexing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=1</i>\n",
       "<table id=\"table140351124214728\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>Source_Name</th><th>GLON</th><th>GLAT</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th><th>deg</th></tr></thead>\n",
       "<thead><tr><th>str6</th><th>float64</th><th>float64</th></tr></thead>\n",
       "<tr><td>Crab</td><td>184.55754381</td><td>-5.78427369</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=1>\n",
       "Source_Name     GLON         GLAT   \n",
       "                deg          deg    \n",
       "    str6      float64      float64  \n",
       "----------- ------------ -----------\n",
       "       Crab 184.55754381 -5.78427369"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selection = table['Source_Name'] == 'Crab'\n",
    "table[selection]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is also a more sophisticated indexing scheme, which is explained [here](http://docs.astropy.org/en/stable/table/indexing.html), but not covered in this tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Reading / Writing tables to disk\n",
    "Astropy tables can be serialized into many formats. For an overview see [here](http://docs.astropy.org/en/latest/io/unified.html#built-in-table-readers-writers). To write the table in FITS format we can use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table.write('data/example.fits', overwrite=True, format='fits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table.write('data/example.ecsv', overwrite=True, format='ascii.ecsv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=3</i>\n",
       "<table id=\"table140351124352752\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>Source_Name</th><th>GLON</th><th>GLAT</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th><th>deg</th></tr></thead>\n",
       "<thead><tr><th>bytes6</th><th>float64</th><th>float64</th></tr></thead>\n",
       "<tr><td>Crab</td><td>184.55754381</td><td>-5.78427369</td></tr>\n",
       "<tr><td>Sag A*</td><td>0.0</td><td>0.0</td></tr>\n",
       "<tr><td>Cas A</td><td>111.74169477</td><td>-2.13544151</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=3>\n",
       "Source_Name     GLON         GLAT   \n",
       "                deg          deg    \n",
       "   bytes6     float64      float64  \n",
       "----------- ------------ -----------\n",
       "       Crab 184.55754381 -5.78427369\n",
       "     Sag A*          0.0         0.0\n",
       "      Cas A 111.74169477 -2.13544151"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Table.read('data/example.fits')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4. Miscellaneous\n",
    "\n",
    "These are a few other useful operations when working with Astropy tables.\n",
    "\n",
    "Sort by key:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table.sort('GLON')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=3</i>\n",
       "<table id=\"table140351195047584\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>Source_Name</th><th>GLON</th><th>GLAT</th></tr></thead>\n",
       "<thead><tr><th></th><th>deg</th><th>deg</th></tr></thead>\n",
       "<thead><tr><th>str6</th><th>float64</th><th>float64</th></tr></thead>\n",
       "<tr><td>Sag A*</td><td>0.0</td><td>0.0</td></tr>\n",
       "<tr><td>Cas A</td><td>111.74169477</td><td>-2.13544151</td></tr>\n",
       "<tr><td>Crab</td><td>184.55754381</td><td>-5.78427369</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=3>\n",
       "Source_Name     GLON         GLAT   \n",
       "                deg          deg    \n",
       "    str6      float64      float64  \n",
       "----------- ------------ -----------\n",
       "     Sag A*          0.0         0.0\n",
       "      Cas A 111.74169477 -2.13544151\n",
       "       Crab 184.55754381 -5.78427369"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that `.sort()` is an in place operation on the table, i.e. changes the actual table.\n",
    "\n",
    "To remove a specific row by index:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table.remove_row(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Astropy tables also support row-wise iteration in Python loops:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cas A\n",
      "Crab\n"
     ]
    }
   ],
   "source": [
    "for row in table:\n",
    "    print(row['Source_Name'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another useful feature for quickly inspecting the data contained in the table is the `.show_in_browser()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table.show_in_browser(jsviewer=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Exercises\n",
    "\n",
    "- (*easy*) Add columns with the `RA` and `DEC` coordinates of the objects to the example table.\n",
    "- (*advanced *) Load the Fermi 2FHL catalog table (`'data/fermi_2fhl_catalog.fits'`) and find the brighest source (the brightness value is stored in the `'Flux50'` column). What is the common name of the source (column `'ASSOC'`)?\n",
    "Find all sources within 10 deg from the position of this source.\n",
    "- (*expert*) Make an allsky plot (using an 'Aitoff' projection) of all the sources in the Fermi 2FHL catalog grouped by source class (i.e. choose a different marker color for every source class). The class of the sources is stored in the `'CLASS'` column. There are a few possible ways to identify the groups of source class. One of them is to use [Table.group_by()](http://docs.astropy.org/en/stable/api/astropy.table.Table.html#astropy.table.Table.group_by) followed by a loop over the groups (check Astropy documentation!) another way is to use a regular Python `set` to idenfity the unique entries in the `'CLASS'` column and loop over those. You can use `plt.subplot(projection='aitoff')` to instanciate a matplotlib axes with `'Aitoff'` projection. Note that the `'Aitoff'` projection requires angular positions measured in radians."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. FITS Images and WCS\n",
    "\n",
    "The [flexible image transport system](https://fits.gsfc.nasa.gov/fits_documentation.html) format (FITS) is widely used data format for astronomical images and tables. As example we will use image data of the supernova remnant [Cassiopeia A](https://en.wikipedia.org/wiki/Cassiopeia_A), taken by the [Chandra X-ray observatory](http://chandra.harvard.edu/).\n",
    "\n",
    "### 4.1 Basics\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.io import fits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To open the fits file we use `fits.open()` and just specify the filename as an argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "hdulist = fits.open('data/casa_0.5-1.5keV.fits.gz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can retrieve some basic information on the  header data unit (HDU) by calling `.info()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Filename: data/casa_0.5-1.5keV.fits.gz\n",
      "No.    Name      Ver    Type      Cards   Dimensions   Format\n",
      "  0  PRIMARY       1 PrimaryHDU      26   (1024, 1024)   float32   \n"
     ]
    }
   ],
   "source": [
    "hdulist.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It contains only one `PrimaryHDU` with data dimensions `(1024, 1024)` of format `float32`. To access the hdu we use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "image_hdu = hdulist['PRIMARY'] \n",
    "\n",
    "#or\n",
    "\n",
    "image_hdu = hdulist[0] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can access the data with the `.data` attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       ..., \n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  1.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.]], dtype=float32)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image_hdu.data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is a plain 2d numpy array. We use `plt.imshow()` to visualize it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fa60f2118d0>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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m5BmtfG2ot08hsbdnkLSVJwHfWsna6pQhx7zc12kHhq66/QGrU8ZO6EusvPNE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\naAC9gQYa6LKiAfQGGmigy4r+PwQXtNuIOA41AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa60ae46748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(image_hdu.data, origin='lower', cmap='afmhot')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Additional meta information is stored in the `.header` attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SIMPLE  =                    T / Fits standard                                  \n",
       "BITPIX  =                  -32 / Bits per pixel                                 \n",
       "NAXIS   =                    2 / Number of axes                                 \n",
       "NAXIS1  =                 1024 / Axis Length                                    \n",
       "NAXIS2  =                 1024 / Axis Length                                    \n",
       "OBJECT  = 'Cassiopeia A'                                                        \n",
       "DATE-OBS= '2007-12-05T22:01:59'                                                 \n",
       "DATE-END= '2007-12-08T20:07:24'                                                 \n",
       "LTM1_1  =                    1                                                  \n",
       "LTM1_2  =                    0                                                  \n",
       "LTM2_1  =                    0                                                  \n",
       "LTM2_2  =                    1                                                  \n",
       "LTV1    =                -3651                                                  \n",
       "LTV2    =                -3807                                                  \n",
       "CTYPE1  = 'RA---TAN'                                                            \n",
       "CTYPE2  = 'DEC--TAN'                                                            \n",
       "CUNIT1  = 'deg'                                                                 \n",
       "CUNIT2  = 'deg'                                                                 \n",
       "CRPIX1  =                445.5                                                  \n",
       "CRPIX2  =                289.5                                                  \n",
       "CRVAL1  =          350.8841248                                                  \n",
       "CRVAL2  =          58.78133011                                                  \n",
       "CDELT1  =     -0.0001366666693                                                  \n",
       "CDELT2  =      0.0001366666693                                                  \n",
       "EQUINOX =                 2000                                                  \n",
       "RADESYS = 'ICRS'                                                                "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "image_hdu.header"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now use the header information to create a world coordinate to pixel coordinate transformation, using the [astropy.wcs.WCS](http://docs.astropy.org/en/stable/api/astropy.wcs.WCS.html#astropy.wcs.WCS) class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from astropy.wcs import WCS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WCS Keywords\n",
      "\n",
      "Number of WCS axes: 2\n",
      "CTYPE : 'RA---TAN'  'DEC--TAN'  \n",
      "CRVAL : 350.8841248  58.781330109999999  \n",
      "CRPIX : 445.5  289.5  \n",
      "PC1_1 PC1_2  : 1.0  0.0  \n",
      "PC2_1 PC2_2  : 0.0  1.0  \n",
      "CDELT : -0.00013666666929999999  0.00013666666929999999  \n",
      "NAXIS : 1024  1024\n"
     ]
    }
   ],
   "source": [
    "wcs = WCS(image_hdu.header)\n",
    "print(wcs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the helper methods [SkyCoord.to_pixel()](http://docs.astropy.org/en/stable/api/astropy.coordinates.SkyCoord.html#astropy.coordinates.SkyCoord.to_pixel) and [SkyCood.from_pixel()](http://docs.astropy.org/en/stable/api/astropy.coordinates.SkyCoord.html#astropy.coordinates.SkyCoord.from_pixel) we can now convert every position in the image to the corresponding sky coordinate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<SkyCoord (ICRS): (ra, dec) in deg\n",
       "    ( 351.00119731,  58.74184873)>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "SkyCoord.from_pixel(0, 0, wcs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array(511.598868063533), array(511.2967000331248))"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_casa = SkyCoord.from_name('Cas A')\n",
    "\n",
    "# or\n",
    "\n",
    "position_casa = SkyCoord('23h23m27.94s', '+58d48m42.4s', frame='icrs')\n",
    "\n",
    "position_casa.to_pixel(wcs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Exercises\n",
    "\n",
    "- (*easy*) Read in the data from the other energy bands (`'data/casa_1.5-3.0keV.fits.gz'` and `'data/casa_4.0-6.0keV.fits.gz'`) as well, sum up all the data from the three energy bands. Plot the summed data using [plt.imshow()](https://matplotlib.org/devdocs/api/_as_gen/matplotlib.axes.Axes.imshow.html) again.\n",
    "\n",
    "- (*advanced*) Cutout the central region of the image using [astropy.nddata.Cutout2D](http://docs.astropy.org/en/stable/api/astropy.nddata.Cutout2D.html) (size of 0.05 deg x 0.05 deg around the position of `'Cas A'`). Find the sky position of the brightest pixel in the cutout data. For this [np.argmax()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html) and [np.unravel_index()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.unravel_index.html) might be helpful. Make sure you use the updated `.data` and `.wcs` attributes of the `Cutout2D` object to achieve the latter.\n",
    "   \n",
    "- (*expert, very hard*) Calculate a radial profile of the image data to estimate the size of the shell of the supernova remnant. For this sum up all the data that is contained in the rings (specified  by `radii_min` and `radii_max`) around the center position of *Cas A*. Choose a total minimum radius of `0 arcmin` and total maximum radius of `5 arcmin` divided in 50 steps. You can use [np.indices()](https://docs.scipy.org/doc/numpy/reference/generated/numpy.indices.html) to get arrays of x and y pixel positions, that can be transformed to sky positions. Make sure you use clever numpy masking and broadcasting to avoid a Python loop over the `radii_min` and `radii_max` arrays (**hint**: [ndarray.reshape(-1, ...)](https://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html#numpy.reshape) might be useful to expand the data and radius arrays to the third dimension). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Plotting of sky images (optional)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "The [Matplotlib](https://matplotlib.org/) package is a very popular plotting package for Python. Astropy provides a helper module [astropy.visualization.wcsaxes](http://docs.astropy.org/en/stable/visualization/wcsaxes/) to simplify plotting of sky images with Matplotlib.\n",
    "\n",
    "To use it we just pass `projection=wcs` to the `plt.subplot()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GP+M84+pWBpQ8qGAyq8n1E3urAY/Oq11qjEZSY1iTota9PV2lrKm9ffn1Mcos3kY11pSP\n+/qZH+e+VJvwdsKGdgEoSU2/rqkifR1b4osjJ6lNkknbKng5NXtCrseAAhTq6H373mTqXovVyW3i\nqpFTdx+wecmFMx8HvNqzbjEOdMrPDdC6txZj43WtqRaeZo76uxjZtySrmHnS8PM1EMz2jhrY53fr\nZfoz1d5LFtUlR0/ne2oTyCRg7vvdNxFNkl0ASjJJz9Zx7sy1GanWmfqk78XVOlg2MOreWv41QPF6\n5vM5uNBnf7eBueS1UbkM/e4Dub6Z35dXePlet1od/DdsfwcOgGIgmeUN0m8H65q9w+upcnId9Axe\ndo1Z5HtrAYs1MHXJzyw7XM3gm99dBmOva1+7uuyE/UzKZ1eS9M0QNcak67WXNmS8I9dmuBr7UUfM\na63y7FabQfMAVj612T1/lE8eiP5sNfaW88/t54A2tN9KO+yOnfnMp+fJLEd11IDzZ1B+2PW8W2BW\nDfO7c9CogeOg8sHS+XN7O9JzrgaMkq1KukmTUW4zvb9a9HQfy5mkWvadmya7ADSD9L3UmmSduE+1\nGlWu1zqCD3bv1OqUm4wPvlq9+zxtXk6fUTeXl5dDDO1DSuu/a8ywNut7HdYsjwERVCLg8Lo7kDug\n5Tw30zk9s08CAjm/5mXp29mMJAOYA1Yfs6iBVS4v55ufrRbuUJuUcj/u6zdZ+ia4yyG7AGTSpwb1\nDdw+FSuDRs6nxnDybJbzdRDJs1lNnREo+Iyd880qgANBVhVqW3vmz4Dx7Vgl2VPiYOiGT9l6Mtvx\nzx7GDchedgY5HWeWKDZU8+C4ZyyHEGDXdG8GIrWhhyZ4Xf042+W8ffr6mfKsGYwd7Prele7P79el\nj63mel4O8NgFIJM+Wpk7kl+bNItNYzewHXwm1aF2PqtJzgY8T2cHXtdahK7yy3Yfr4cDnETG48wa\ncj6uhgpMvXy5+hWuvm7lDlIeC116bfK1l+KB9HrXwL/2Ln1wzzPejt4GDiaqvzMzVxtd3B6Tn9vv\n7RNvzz5w1PutsUrdnx0HuYxafi6TtIKdgMrTOg5o0uCf1sC1tLWB7GmYcr3GHHInU4fx2BF3Uyuv\ngaXrkwwAUBhITX2ozX7ZdpTd0jV2pzKz8dbTK81eAoBc/cogC9vbKYPmkFDpMhvMNhmvrzOZPIi9\nDp7ejyf1i1r9czyR1wu2t3+t7/bF8vSlq9Wz756aTLq+Gwc0RfpmQx3XUL8vbf6uzSp9oNSngtVA\nZcT22JFsSBwxPrtOmg2zQdbv8xl9wc7V2J7XJTMcVzUyaNbUC6lai3b9UHcs1cwBxkFprqvrgl3b\n7D5igDpWmSrX2YU/k37X3pEDXPbA1SaErJJ5HhkER5W0NTZa+632qNWnBnR9Mo3l1Pr6TuRpDUCS\nTDUz3a+l83N5hswzex60khqjyGny/5B7p85qoXdy78R5YGVDrTMSL8fBaN3Oe96eRs+twe0zse+D\nvGDXnMntoQywDcrWpZvA2e6ePZQgRQGPQGcOWGZc1VQ5c919bjh39cjtIvn9uuiZHTCcdbjxOren\nv4fMOBwcvOwcGuCMdhIDdBtVlhrby/eqbSYBRM0sUevnk+RprYJJptHMnCbP/pOAJUvNgDiN4pLS\n1mbgPjVJMyFWbp5hPe00FWpg13O+OT8BhdgTFDVoHlhlfAP5vMxj2B0vdvctUEBKwLTelX+gSzPX\n3SO7kZiQgxnd9x7qQY/+DDWW6mzJQcfbJr+TrPblPtPnEq+929pvV/9q6lWtrNpz5glmUv+c1nd3\nVbAJkgdxPpcZyTSqOUnFcqkZEGtGx9rsojxrgJcpfJ5da2CT1QLvxINKOuXlAOAd2YEmD8hL3Ud5\nZGN1juPR8aLV7WB3fhM4T2wwdX1XrtQvlb9JAJrvu6L6iAUJpBYpDEyzv7eNg96i5af2yoCka1ge\nuu62rz6G6pLVtJyvxMvO6lX+7ovbck9rZlQ1hj5t0p5FdhkQ/Sxj1gausZpMl3O+fWwlsytS2gwK\ntTr6rJw7kNsqcqfN7ZDZkg82z8uZ0zDlAYXZKLBwzdKKDY0snxEBDgKCNcYH/iJF3ZIN6xDwcHf+\nAkVl3GP1WKEwrQwI/u31WCSAUyECUIDO2Zqer2ZD6jNOZzuYewtrfYfKucxmJt2TJTsvppXHDHm6\nzMKAdgGoR3ZKPWsg5tIXuwFFbZiUrqYG1bxkNWDLKpevf8oLPvMzZbDKLCnXS2nca7VFMJF1S+uD\nfpPYU3eOUMuWKKqb15nu/EXCO+axPHsJVqR0lyhMSqrWGgUM9zK+Xm+VcZf0oj2DQEv2qr74nxrI\neN1r76oGHjVPltsV+9hSzcBdk2l9tW9ynEU87a4KNkFqD57pZY1Oe9o+VcjFjaFKo2/9zuCTgcU7\nYVatssF7kD4+MBy8pMp4uTBedlbDxGC8Pq766Lx7nJSPG389BmWPnYfxPYTciHqJAB66e9YJgFrp\n2u88AVxDu6YtNjcp9iGBiMBIDGxoabcoQKg2kK3JVUM9R363uscN367i5GDNrFbVbERb9u3XaoZu\nta3qIKmpTxloapKfq09qYRXT5GnNgCapMNDPQPJgrsXh9DGSWlmzqnxZtavFs/Spgfk5fEb38vOM\n62VrMHk+YjdblXMQA32JYv/xeoiZYPXc290j47PycpVkw9IJcPZSGN1WV+aK3SObkDMX1W0Pxcum\nwUtKO08xoI8YnygEKgLeGpOUTDLw18Bglr5RU+/9fe6U5fT1+VlF6XdVsB6ZpII5sPi5/LI0uGfV\njWudZBJg1VQ1Se3+mhekZnPwWbK2cVhtlvRZWQNMnql5CuPY6I7djuMszevtf1WkMjVbr1IG836K\nrUWAI5ARyCm/FQpgyDCt62JpYkxiPQLBZQIkL1DYYTZguwdv2KV3didQz7tQus3JpTbBZaldzwx5\nFs/qJFDJ76EPCGt1q5Uv2VXBHofU6GZNJakZeZ2R9P3/9zB9e75ZderrEG570DnfvmIzpfVny0bH\nWrxK3zUNNjETqSaLjNtH1imgsdzlqSUTYkvucRGoXKCoWQuMs5hLFG+VRItVNygq04Eu3UXGDcd0\n5xyUxJ4EmKrzHkundl4gwHCxu76PEvCYjdp5SYYA08Hf84Z6rJi/f8/TgSyz0pq5QNeUT3YkjFIa\n0rVJ4OP12QlLkuwyoE5qjCMzgJze09Rk0oyUXe/ZBpPv8x0C+2h2npEy+8iMJ+9vnWczsRwsfY2d\nefyOg7NYwZqlF3uQl0vGY/egOTC4fUm2Mt+2QwDo67bcAyYw9MhogYTHIekZ1QYyQl8iQFSsSWzr\ngtVDz+hM0BlPnsz8veicM+8+tjxNZevLt8akp+Xv+WaNoFZ+bYzsMqAdiHcCGG8Yb+i5ynW/xz85\n7yxbPdezsdnrkFmSp1e6GvjAdnuQBqKXLzVLM3ceMP6RmuSD059Bx1JlxCwERAsEKxFbdNlj5XrE\ns9pfbad8Nrpzl+yei933ke77T/4jhgJKW+l8Zmb7KWrlpn0vUEBHZfpKfbWl2sLr7ECT311tYGdx\nwMh9oY9h5es1wOorJ5sjct6wHXxmlV0GVJFJKtCktPnF+8yRWUbuCDWAysDgjMfF7VE+y/flRfqd\nDdikPHId8wAYUkBI6qBsQ7Xn0PECRbXSIM7tIDCc79IogHHOzi1Z3rITyT41TzAYBR2KEQnMpB65\nLesi40BziQJ0A4rLXm2numzYs69ZGtVZ/SFPJvmd5raS1PpkHyty5lIDQM/Dy53EiKZdzyxolwHN\nKOocfbOJMxoNiDxYRnY+68ZZXN2Cou5klcrz9vPZZlNjNq52OVDkWc/d3yPG65RZUZ6xs4tZA1wq\nlO5T4KDKGzHOcEYEiIhFSU3TgNegpjt3iMI0fCsOd1VLVJd1wp4kANokgETLNuSlE3DoWd0Lp3sV\n3OjhDJoE5PL3thmm3wLQbF/zfpgnKBh3IuQJLefjzKU2aXl6LF3uIzX7YJ+69nhY0NOeAdVQXjKJ\nyvbp1LqWB8FW+j1I52usRuf7Imyl/mi2zgbWAWX2HVbSTGJjGXx8k3sF/skrJLDZQwxqD6x0mwjE\nwMzqlbvLVef99swO+uco9iHVXexFkdFiMFKTHNwUDa0YIffUuSFf59xg7kCndK7KSXRdbTaw33rG\n3P4w3re8HIFwH9sh3VdjVH3sfFqe08SBMEdw7zKgCZL1bj+fX2BG/pwmp/VgsbxVRJ6Vap3FmQwU\n+0YGOSgDJwf+eT1cNavZdfweB0V5sKRKSW1RXI/v0wPFLS3Qk9fKZ3fZabB8BUpHuzRHKUzD2cjF\nLs+9lAGuz76uXguMg5zqMCLAcZESlS0AVR1Ud3el65pAtfafaApS1G+1o2xf+Y8sa30LSh/xCUzv\nUe+qr9/W8usTz9/7kY5rdifSea+HysxMfBZ52jOgmvSxoppqJMn6by04MecxSc/2e7y8oX3W03mB\nzSbFi6Nj79i1evugWaAwGQ1iHbttIwOcG4x92YU/ryKUVynMQfaVOQJczlHAZp/Vd0QEDApsL3XX\ntVJeXjvfS1q2mRGhusl+45HTi12ZAnqxI6lXrmZ6+4sVaa0YFHUt28AyiPi7qLEIT+sTQ60Pen4u\nNc+US82WU2NBOZ9aH82TF+wyoImSH9ztJPl8Zjs1gPDOCdsXE9biPJRfFl875OqR6rLJOL0fUGwO\n6sTrds7BcMB4gJ3v+7K3+61ZXItG5XJ2Q7HKkZ1GKo5YgJ5j3q4prUBMg00AsgpcCdxJrHwX+Bzs\nvi8QcT5q20OU2B7VSeCx3H0gVszvp7AeMZq1rsxTjNuccvR2Bmi1aQ2IswvebWcOHr41a1bNssre\nx7R1D2wHGlexJD5J5bSeb05Tc2jUjjM7n0WetgCU9W01fGYI/kLyi1Jnwe71l+4dJwejedkOfj6T\neYfJ9crPUfvHUre9aCBoZnawEBjIbqN1Ux5y4OqMRNcXLN06ZfsKqUkCnw0KqMk7pVXtGtzXAMcW\n4Xj3+7UE8Mjwu9qdeyEBEocpQCeVarH7bHRpVIcDBKjJu6X6e2DlopUjNS6vgduyPOUh0/k8YXif\n0LHSuz3Q+4QPeL0TsaK8UVifCu8qdrb7TWLlue/WwKpmmIZxljer7KpgFZlGXV28Yw3Tt3csnXND\nnV6ujKWZomcW5R1YdhYHq8yC3E6ijuOxLG6nERCpLs4GNFi11EF1lgF2le0dE8p6Lv32IMQ5yjar\nyn++OzcEThLxO0eW4H2roTJdJNjQAkVNE7gJBJ2Jrnf5PWrlP9Y90zXAhyjryra653DDr6+YV9Ci\nr5KXAwBrP1dpdL+e19eSubEbtk+EPnllUMjl5D7WByJZzfI+UTMt1M75+Vx+ll0VbAeSG7tmcINx\nyuzppeb0dR7low7uofViHM6q+v4n3sHDr4nZuGvYmY6eZ5juX2Pc5qClEAIlGWx1Xs93iXEw9Yhi\ngaIv0RCgOksRSOzr0l8AHgLuIxjQwQXY2Ciq33VdOc/s6rVMqFYC2pWubKlu+4CrumsvB14GvOmV\nwYQ+S2FQstssU7b52A/caO0kFuTbjOxh+06NamNFWgukBPYDxt+90ruNJxuIB3ZfVuWwNN7/nFVn\ntu7g5d41BzLsXB/AZBXP6zKr9Bm8v+4lqyv5uDbD5HRZdYN6R6h5MDIbygsY3WPm7mAHHi/DV2Jn\nBpXd9PreRzALqS8aiGIUFylLHQQC6siueorljBiP5RFDEpBJtTnQHV8LvAQ4vAc2N+GejQAhGYUP\ndCP12o1gLqvACyjsb5NgSRtdXVXeme77ZuCLxL1iIf/ve8PLdpQwaIvZ3Gfv55uA53b3CUgEkuvA\n7cBdFECQ219MUxOAQMpjj2B8Vb47CrK9x/dQ8v7l/bHGYLIaJ+mzIeW+7n2LlC7fW7M97UQFe9oz\noKwz61z+1u+afcbT5llG7l3fekLSN9N5h/AV33m22KIwCd+8SzYNN5LOMQ5gPnv7anOvi2wgDkpS\nlzRYfOsM3ecqoi8Y3STAR8bgawjAOXUJnnswBvk+goV8Hri4ClcMg8UcJga+8nxWl9c54BGCHWnN\n1iJwS1fO57o6H1mCw4eiLmvAoX3wqiNwx2KAkexGt3b1WgA+0bWBjNhrBDjdRwEHsRqpku4NGzEe\n4ySjuNvaauxEE5Db8PJEJkZU2zlR93ufzBOnJKt80O9tyzLruUmyawMycR3aGz8bEWv3wPiiTLf5\nQGE9bmh2YIDS6VzNyy80233ZDwdBAAAgAElEQVTEWrSr4DrjG3r5thlbjAOVBwuK4cD4YFKsj2ba\nPXa/3M1yiasNBhRj9JalXbLvPRTwO0QM8hEBJld35w/Mw2AAb3gD3H8/fMNeeOFReN/74PRpeHgN\nPtXlf0V37zcChzs0HA6DWW1swCtfCWfORB6fPgtra7B3L2xtwcWLAYCfOQcfXodnd/U7eADuORdb\nvapNThGgOU9R+ZYoNrwaaGh1vt67g4j6RHa9++Tk/TGraLks75/ZuJwnTwcvFy8r9/tpoOR1msUG\n9LRWwWCy2lWjnRKPL1HHkb4/YJyOeyNnupw9HnJb++zoapnbCqAE/+m3q2ECHdlnFFezSnFfy0gq\n1qRn1SJRD16UZ8nbC8b3yZHqpmd1tUJMarlL/wxCBXw5cHhfAMaePfDoFvz2SXjFEbjxRvjUWVhd\njc873h2q0acIoHoewYLmCZZyBrh6DRaG8Jf+Irz3vbCwAO+8G37wdVGP37k3wO3wYfid90Y9Huse\n/irgNbfD0lKA1C+ei/peYc9xiAKy6gPORtx7qLbJIO/vNqvHiuPy/uXbnTjQOMBku6H35dyfc1yP\nJNsvswliGsPZKQN6WqtgfTQz68A1O05eYKh0itHx/H1WdDrs39i3B/t5vImrdXltlXvHtD2F3MUC\nkGVi1pbXSlHNMG6zuERhJ6qXVA5nUouWt+ojO4w8QFIjVU+5xS8RhuAjXX2OH4fXvS4A57EteO1x\n+P6/PM+lSwE67zkFHztVwPMRikp3AxE/BKGqnQYe2QrgOncO7n8AlhfhHe+As2fhpkOF/QDMz8OJ\n08G2btkPDzwAoxFcuBCq3CHKtq/zXX3PM+5BzOzCPY66vkzxpMkmVgMGMWFNJDXjdN/k6Gp3Lb3n\nJ6mB1BzbwcTHSo25PB4wedoyIEmtkV3l8pej9M5CfLbR4HRXt3sZsmpVAxbZODwKeSvlJ1Dy/YEU\nrawAOg0OMbK9FJXB12epfh7BLE8QFFVK5XgAJIyrlWJaq923G60Vf6Po4yEBFnuBn/iRGPz33AOv\nehUsLoaK9R9/dYMTD0UeXyDc6auW36EBfGwEXwbuWArQON/pgueB//LuMEJfBSyOYG4uWM2lS2Fb\n2r8fXnYj/IVf+0vw7/4t/+TnQl27cCmA63MrncF8AR5aD+ATQCuuS+qXD2y1q7xh7vUSS852lsxq\nttJ9PgnCOFjo2NX+HJPk76MGfFkjcKaeTQ/ZDODMeafytGZANfEXmgEG6i/N9WT3gM2ldFDYgFiK\nzokpeMc8SHGT+xok30Rd/yahmVXsxQMMZaMRgCh4zim7Zlx33buRes7y8w24ZMsRMGqWF5s6TFHN\nlgi16bau3Me6su69Fx56CJoBPGNpnrW1YCe//VDYX8526dUGBwkw/f1RGJnnCEA5eBBecwe8eADH\n5uG1r4SX7IHj+wJYrpwL1eq1r4Xn7IcTJyLfP37zv433sACnVuHY4QCqr2zEM35sPbx1t1GYzPGu\nTnpmtdmcfYuV6h36xvg+OYipZlVuZGnFgBw8+vpl7rvOfGrsOzOqLJPUtzwWdipPewaUDXc65w2r\nF5rVMNlQst1IqtggfUTHHYRWKOqMbASq0wrFHqDOKBXG3bMKElSdvAM7O7nAOKtyVUELOGVMVpCf\nQEiGV7r0eylsZNPSjhj/twkB3l4CjG4YwDffDEfOwQPnSpvfdx8cOAD/8uc3WO0o1Be6PA4SQKRn\n2aAwm2cQsUPrK/Bq4PvfEGD0ih+/mc++4wRXzsErXgHf9ma4aQW+6UZ4/o1X8/ybr+Bj96xy7Bg0\nwwGfOTviO74DDj0Mb3t/tPM1wyjveQSj2k+AoRjQ4a7d57v3cp5x1Xhg18UuBxTXvAAneyy9D2Hv\nyVWnScxdx+qPckQ4k6nZdbJJYBq41MBvp7LrBUvije+qUz6HnXOvQgYpD513A66DluctoFJagZwb\nlOU5kvF1ze4bUIzRDjYqU6pDDWSdWQk0nMoLBLUGzO1dexhfALtCWcO1RTCG24DXvw5eciP8y1+C\nh89FxPMIeOONwVBeejP83C8FqMhQ/mLCLX/bHnjWvlDPProVz7/VlXOQovotE+Bx9SJcuwz/+WTU\n9/ru+jrwV98QrGg0CrazshKesvV1+Ie/Gnkf7vJaWoJ7VuMZBgP4xCja6g8IYD7Y5amtZcVmfaJQ\n20Fx3avtnKW6wTlPbDV1ykFHUmM4Polm9anmzoftfZR0PquEWXa9YBMko7zOecM6dc3incHtIDCu\nSmmpgoyOmaHUvqU+SaWT6qPrCxS1RIZhRT6rDLEQrWnSNdmAHMzcqDxHMbZqlbcPGAGqPF1Qts0Q\nm1unxPuIKdw5D2c34IuX4Nd/jT9hOdcTHrC77ocXLcOHT4SH6wJh5znc1ekKYHm5eKvOEsbmvwhc\nPYQvbUVdXzSE9a04fun1YVN63vvg7rvDtnTjjQEog0EYpD9yfwDVCzr3/gfvjzifa4EHCAP3xdVg\nPye7l3SeAKgbCYB61SL8t7V4P9p9UYGRYr15YbBsQ2LBAn8HjazqZA8alhbGvZ9ue3TJ4OP9kco9\n3s9z2dnGJMmANkme1gwo23Pyy8pGu76ZQL+90wzT+T2UTuE2mRprUj5iJXnJw3pPerEd31ZCjAXG\nY5TErJxhicGoDD2fByuKnaneW5RtLtYJQJEdai+hOi13aY50999wGO47HXXaPw/v34AHgZsofzZ4\nNeHp+u4Dke7ixWAs1y7DR1cCoC5Qlmc8D1hcCEYzNwcfvwR/7sbwdv3q3QFkawRwLXd5f4I43wAv\n3x/u/0+vBLNpgecQYHhLV+9TBBN7tHu2LwEvJQDpBAVEtJXIaYrq6xOUxJ0WctPnSQrG+1XOw/ug\nM5IcK5S/lb7PLpTzrKlp09Su3f8F65HajojZC5F1akmNMflx9gpkHd9drA5SGujrKQ8YZyq+oFP7\n6uR/6ZTeP6IYNweUQEUoLEX7LC9T/srGQW+uS7PH8penbtDVWZuByUt3kBIro/p/lACLOw7DQ6fD\nhvMFYl0XxMLQ4105x7qlGVctwrmVMFYfPxzgcuUc/KuTUec7gMP7A3CunIM/Phl5naSshFeE9gpw\n5yG47wzc39VZsU4/eiv8wgciuvoTBGjuI4DH/xXkDCX4cw14BcHM/jMBgI909b9AsQeJmapdtSQE\na193PGSGMkq/fRLwfpqBAurA4tcmgU+NbcHOxsMuAPXIpL/lyeegjv596fJ117MFHBIZo91A6JHR\nTq+Vvzq/VCyVpz1sZJeRyifwEJAMCaah36e6vDVY9F9cYkMeae20XQN8CHwv8IddnV4C/N2fhB/6\n2Sj/JsK79J51+DixjcZLCBsPXd1OUNzyxwkG8lJiQL9kHzw2giuHcPf5YCvzwIvm4ZMb8DHg+QRT\neRZhlD5HYVIC9b96KFS4t56ItjoFvKa7/igBGI8S4KTAzEWKfUfttdb9vp6wTV0zD7+9AV+x+y5Q\nHAhSwdRmHokuMJOqnINXRymtTzBukHcmLKkx90n2oNz/a4CGpc2AVQOi3dXwM0o22Hn8RZ/alRu/\nz0OhF6xtMTyPLYrhNM9mOh5S9suRHSgbKqUuKS8xn3UCJMTEDlHWU8mTc4QY9LJJ+JKOEeVfSuVu\nV101cG7p8rvrpwe84x/OcewQfM/PBgsRu3nHegzuAfDHBBvS3sxSFaXKnSVA6sAeeM0tcMMN8PkV\nOHYsnunZwDctwVs3AqieSYDPlUQZr70RvndfMKyru2e7GvjgGfhPJ8qarhuBTxNA+DGCwWwR4CG3\n+kVCjdIC2ce6us4T6tnngHs3Ig5J/UCgLaDw+Cq9V7fVXCQAE7s+tGNnRs6ANFnlAbxl10YpP12X\nqF+46kalvCw+4faphrPKU4YBNU1zmlC7HwO22ra9pWmavcB/pATAvqFt2y80TfNG4HDbtm/uyWum\nh84zSr6WKeuWfed7HVRyMJ+DXwY22Y9kH5BLV50MxiOOYbvBWaByhPF/hrje0im+5RTRmOcogHaE\nABR5uhaAVw2CUdxyCxw9Gobdt7wF7j4dz/qKw3DnnfDTvxJlPUAMfLGKVWIR6L3E4IcAiquI2J3R\nKLxSJ06EKvbps8F4fupH4W1vg/suRJ5e92uBF1Fc5WcIdvTyJTi/Gs8g1rdEANY1hLqlNjlFYZfn\numfXEpYPUIz1LyDUr/soA/k24L0U29o65a+exYRGdl22H5+8FtL1mprUp1apn43ScXaieL+TwVrP\n4MbrSepWzq927evRC/Ztbdv6AuM3Af+tbdufaZrmTd3x/zlrZjXUHqXffY3bZ4zL53xt1ojtkdG5\ns6gTaBBsMO5md7bljErGZ+Uju5HbG0515/Z0n1MEGMitfjudp4eiEl3flX8UOL4QYHP6NPzoj0a6\nZyzNw/Hj/O4/PsH7TsMNi/DGN8IHPgD/6FdisJ6wui8TALFFWeQJsYh0FbhhKYDn1Cl4yzvi2d5P\n+cvlH/4F+M59JWL7SPdM93T1/V0CGFa6sq4jvFh7F2CwHixLS1JGxIz2PoJZXUlRWTVoL3T5iwnK\no/lSwiBNV4chAYiyiakdFZku1VltK4BxZpRVdGcvA7tX7199xZmVRNdr6pz31007zuDTB3RY2Uy4\nZxZ5qqtgfx74N93vf0OYIyBY8Vr1jh2IA4Q6jaSP7Ui0qNRdneoUdPcoyFDH6kCa1Ws6trxUUKKS\nxXC8o6ylc3spW3fsJQaZtkSVu/xtFJf7tYQ95RDwHftD1Xl4PYBhbS0A5hk3fyMceQG84lu4dCkY\nx0NrwVre8oEYuM8kWMaQAJF54BsoG4G9sqvnI8B1w2Aqb3k7/OoDAQwnKC7/hwmV6Z9dCGC4GXjN\nbfBjr4/8TgHHKMGT5whV7LZbg60poPIPCQB6mGBcc10dtTna2a6NBACnKfE+N3RpPkrYi453+Shi\n+waKR3Kzq4MmEldjBRo6zkxIk4n3mWzfc0dGVoW8PzkDn7Pfuub35TycmTuLz2DHhONJ8lRSwT5B\nOE5a4P9p2/aXmqZZbdt2ydJ8oW3bb5ghr+pD55fgjZwRH8ZtMZJsNMxpRHvldoXCVvTbX7jOe+eU\nvcbZkIDGKbUvllyieGJkd1mjeKvOEgAh29FxiqH51kUYDuH0atz77CF8dgv+xl+OgX32LLz97XDX\nRuQz390vRrBBDPCXduUIuA92bfATb4C3/Cf4R/e8iv/59ncxT6g7WgCqtWnHCAASuF8E/sHN8Fsn\nAiS+kWAeXyGA51DXBscW4QNr5R81ZCAWKGsF/4gAjBd39+uvh2RM3t+lfYwAzCXCyH5P916eR9iF\nFNZwiaiX3r2XI+aj8z5bOvDUWM1mOufvvGYagLoaltlKn1mhT91zcMpANuLrzAvWNM2Btm3PNU2z\nD/gd4MeAtz9RAOqjjXmGcKkFWul+p8U5nkPp3BbkKpozLAGIQEgql8LqFVyI5eMdxF2+i5bGl3Vs\nULw8G5SdCrUD4DFi5fiFC7Fw89RpWNoTCz5PdNdffUsso/jQVgDOEYKNnCdUJ9V/b5f+DLHp1wFi\ng7DfOwMfoewHPSIGsRaeijnQHQtUHiEA4fZleHAl0r36WCwg/eRKGJifRYnB+TxhAF/qnk3gdrhL\n9xFCDdvoyj7L+MJe2YnUNmcJA/x5yo6MN3X13E/smKjlNecorvPD3b1yzXu/y14p7LdAUJOO+lbN\nW+We16wmudTAp3ZNeWb7U87Lz3fff6JRtm17FRV5ygCQS9M0bybG4V8D7mjb9jNN0zwHuLtt2xf1\n3POIHS5A/8v3a7V4CO8c3hH8Xu8cPuiVl9NnL0d0W2qYWI0MmAI5zbACOh07fZbBGorBE8pgEvPS\nH/1p+cUBQk0SA3rZoWA58/PwW+sxuBeIwfQVwmu1ToDCKnD7ED65FSrdFmXAC0w2KXE25wlGIgYw\nRwng09YXUIBDIQKv6NI9SLFdfdcQnjEHZ9bh4Dyc3ChhBcuEmnSGsGedp9hg9hAgoXimKwgdfj/F\noH+6S79i7f88Aqz8/8k0QTwf+Ex3zwWKK39/905OV94jjIdi9BmdM8t2sPF7+1zsOje0e2C8X9aY\nz6QJOt8DX0du+KZprmqa5mr9Bl5FTLhvB/5Kl+yvAP+1L4+2ba/SR+e8QWuxN3qJ3gm8U4zsPrfb\neF77ut+aCkSVZcfxb7cP7SE6K4yvGVJAoAaOOqH2EPI6itlo7ZgWsl6ggKHy0WcfMYg+2F1/DNja\ngrOjAJ+W2C/5EvECNojB+2nCoLtBrNN6p9V9RNnwXc8xTxh9BWSyz5ykAOOGpV0nwEN1fidla9ST\nXf4f2YKT6wES798I1eit3TPd29VvCfimYdRfe16fpngMzxFu+QvEfkUKUbiJMGi7HecRikr7GGXL\nVYHJnYN4Fx7ndbYrQ6EVAjjs3my78WU4esea0GTX8TgtnyhrLvYB4+VssX2NYL6vpgl4vftUtWny\nlAAggh2/r2majxDmgd9s2/adwM8Af65pmo8Df647nlnyw2cK2UMr/yStx2v4t4teprbfUJ5OjfP+\nzIp6VvyJ6/lO3ZWHv/ysii1SonNXGafxF4kBeSXdAk5i8F6gRFmvAu86F4P36u6eTxPgqAF3imAN\nDxC2k7sJhgGh4g0oLGAfMfhXgAPDuPZFiovcAfqwtaGeSaxupav7avf7FOPBhGJKh4B3dfce7urw\nm1uR3/MY3xZFMTkCi0cpwKTAyYOU9yi2IUfCWQKw9nZ127OnPL8Y5wHKRKBnVb9xj5QYbF7ATDrW\nxOeTj9rM0wnIdFyzI+UJt1am3+MOmGw+mFWekirYE5U+G5BegDrXRrreR0EnvXgN5AVKh9Ws5zq6\nrmkFuiKXVa5UpfNs90bUDOZucFYgISnNIoVlHaR4mxTRKwB6DcESzlMMs88nPEj3UsDiwS7fAwRb\nESD62rAzlL+xgaKeLRMAJoA90F3T4LqNCE58y6Vid5GhXHarEcU2di1hSzrX5fUthK3nc4SrHsYZ\nq2Jv9nTPebSru/by2duV81wCiO+n2INWuntvJOxehymq8fvtXWiN2L6uDDEjKAw2q+b+jp2J+/Xs\nmneVTGnUn128/7khG8b7Pel8Njz3ydeVEfpyyiQj9JD6i88DHvqNdDrOoo6YF6CKSmt3PS1x8IA2\nzXSqs89WKk8dTR1bebgtCIrNR+dkXzlDAQPleYGwtxwi1LIvd+cOdekvEK5nsRKBgAbDKWsrzbKK\nFl6mxOSsURia2um45Tno7jlNYSUCMa3aH1GATirbEcrMf7j7XCCWdPxBl79ADOCbu2c8zfjfOYuR\n3NKdu6Jrt48S4PhpQnVbAL5zAPePAqj+gMJcBUJyuWe13UHCB3kO48ieV9I9ktrEqUkp92O3CdXy\nnZRnn3zd2IC+mpJ1VjfC6bq+HaAy89lK57J9SffW4jZEj70TnmfcbrRgeTgQOpMSU9LglAFcdgut\neF8lBq12RtwgBpwWZwpMLhGeq3WCOcwTA/QQRSXx9WdLxOC/k3GAPEjZI3pA8e4NCbVFthiBl+oq\n97TsSKcYt5VJxC4HjO8EsMfqukF47u4hwOePCIBb6NLQtcuHKIZvqYzHKaEJn+1+X0ex+9xPLGKd\n757z90fRFs+2trlIiYpeY3wygvHB7+CkCcrVNO93rv4PGO9/Psno/Ialz6pWnuDc3pQn1+x0ebzy\ntAagDBYOJv6SScf5/JDtDZlnCr1wqV9KL7DQGiOpaDIwyxArEJIXRbO9AMO9aMpDq+QVzbto+ajc\ni5QV9QoUlLt7mQChs8QM/xjw7wm1RkZQuvy/kWLHeunRUgcZds9TbCVO989055YoNp9bgDcfifop\nCllbwGqTMih/dSMvoAIv54klGTd190i9VBu/ZE/8v9eNg1Alj1oerqZc6sq9usv7DGGvglA9H+7u\nu6JrAwjD9BeB2w/BVcMA8DnKynzvK/L0aUBr0hjaxycdPw/jDo+RHfu5QUrv/XXAdjDxvGD7OIDx\nJSKk6zXmP0l2mv7rSvqs/PrtdDerZEo3iYpuVdL6zLVFCUZUZ5OnS0xGM6bkLIVFiNZ7JxFb8GfR\n1hPqmEPGjd4HunLlndnbpd9LMCOpPu6ypctXz/Gprk4PA3//ZKmbDOAaXGIosm9p1fnQyjkF/Nap\nUG/Eir4beAsBFrKlzBPs5mCXRnanBeDFC/CF9Ti3SVli8RCwfCnCDB4eBbP7w658BWvKRX894W69\nj4i6/jTBgLQ8BspWuAMKaz1Kt7/0VrTHpn28/Q92x/PEe5XhXHtHS2osyNmJs7+aeSDHBNVAyn97\nn62lwdJlW1HWIKbJ09YG1BdY5fQ1A04OQMzqlO4npclbWeS0cjM70EkVOUf5WxgF1XlovlgOjO+O\n6PVasPTu7dDCSkXlCvAOUQLotGOf6gmFyWiR7C0UlewcZUtY1U2qnSK4BX4Din1lDwGEZykD5iAB\nRoqClgrmhnstrj1MYUl32n06p6BGqbIC2iHhgdMOAK8kAGeFiG+6llC9zhEGZRm7BaRSc9U+YhWH\nKMZyebyw73mCza7aOeU5T4k30lIZ93S5u9xtiK6KZ6My1IGhzyTgJgVSPtkm5Of9eNcI3SNN07S1\nhpXkhvSXXWNKeQbx69moLcq7le7VwIBiN9hH8cDILrFm6bUgU+xGjMbr5jEiGvSblh4K2Em9ka3o\nDEUV3N99nyMGx3cQ7EELPxcIteRAVy/ZrwSYUvcE+rruy1JUHzEyqV+yp3y+e/799twPdvnJS6XB\nrPVuMkYvUNp9pStXXjaJ7pf6Oge8bgFOrAczE7vUJm5SMY9QAO5A10ZDIkDyA5TtWQUMyxQ73CFK\nvJby8/2YsjgrESB5SIfbknLfrvU7zzebFpwxT2L7fUbpJ2yEbprmYNM0P9k0zX9tmuaDTdO8t2ma\nX2ia5ruapnlK249yg9fEaaV/65rrwG6HUf7YOc1QHvSVZw/NZGJAmsFWGY8vEZD4Doey77hNQQxE\ndVDaAWWG1EzswCXGc5CydawilqUSnejuEyDJJZ2N5GozqUJya/siXAGfBuCZLl8ZpvcRsUorFNal\nQT2ggMteQlXaIpiU3PNibnqWA5S/DxoS7nkIles5XXnXEOCzsh5qlMIPLlFUNL2zFcIoDeXfQxQ7\ndJAS6kBXnravFegLmPcyrl5BAWWPVlb+rkq5ypYdFnrOSeDj3zBuB+1j7nqeDD47AYZeBtQ0zb8m\nwh5+g5jc1LbXA99GrC18U9u2791BeU8KmbYjYtZroeja7tFS2r71NgICDRTX2ZXOO4Wv39JLl4dn\nk+jMegliSerQysNpeF7MuEkMPtkYNDjlbvYYJS3XkN3nGGWnvzki5uVLBAsaUCKKtYr8AuMbm/mz\n53ZzZqhnxuoyoiypGBLq1tHu+JnETotS+44S4OO2lHMUprKfAIYDjAdn/lkC5H7s9fBHnT75pgeK\nijWkMB+BpVRAZ5JaViGb14uIgMd3U1ROKKB43n7nRanyUqrdXKXKfdUBR9ddVfMJsdZn/TtPvA4y\nNZUrf0uekArWNM0Nbds+0Htj08wBh9q2PTmtkCeb5DggGH/JNTCqSZ5VBunYX2jNUJd17OxedpuT\n1AMxHQ1KgYaASHYDdV4ZJzVzurcsP5vUpKMUr45UsDnKTH0HoVq4bUjsZq5Lf5GiRnk9ZNMQ0Lg9\nxV3KYnka3NcRrm5568526fYRACOVVSAum5na2NfjrREMaIuYSf+oS/vdXf0+SsT07Gd8ycbQ8t/b\n5SevpII45ygAuEHEUEmtEoNUeuW12uWjviBbH4wvPHYDb81wrMnOWahPltn+4xNWTuPmg5pMMl5L\ndm1APZIZ0CR7kM8gOQispsblF+czz1ZKr/tFp31mdQO52JFmeSguXBksfUZTfppZVR8xMbcTyNag\ndVorlP/z0rIJLSIdEEDwni7d/u68DMHrlI3uNWDVZj6bauCpfD3nJbu+RQkd8DR6LtlMVO8NguFc\nT9iFFCqgPJe6+p6iGPePUoCR7n6B2znC7vTxrjwxT9VP7an2k9EdAlDOWpvJHnVHd/29BFuU00Aq\nlfZiOkeZTHx5Tlbz1V9gHITEfhwUanbMmurkE6+zq1knZZfLAkBN03yUWIPo8kVCLfsHbdt+fvtd\nT25xI3TthbiqRSVdPq696NwRsvhLla1GICTXtYOJllNoRbU6Xl5XpPrrGTT7LthvDXB1cMUGKVJX\nM+6AsD1dJDYn+yPG2dSIYkBe7+oiF7kASDOyIp6x+zcoW3RoKYLASXk705Mre9nKlIqq3wcsL8UP\nQXHbi/3cTiz9kMH3GHDTPDywEe72R7p8Re+lgg27Mp5HYU4LBFif7q5pQpBqusfSyP6jNjlnaSSL\nlocYZF4WNMlAnIGDdC0z8MzafbL0ydRtezWjdFbFLhcA/d9EDNpbu1M/0H1fAl7Rtu33TCvkySYC\noGyv6XuRtW/Y/gIk2cbjLnjNLFJHYHwbBYGCU2Hll1UYBd75LOkeJQ2YRcryBA8jcDuQYnbo0ss2\nsUR4ak7YOT3LnOUp1WuL4qFaY7zzOqDquaWeKW1WU6UqXaB4pvRMsn3p2cRE9jH+3/V7CFandXSv\nJGbPI4SB+W/eCr/0gbjnSmI7kce2oj3lej9F2d/nBgJsfJ2fAFtpHDCloh6iRHbvp2w9IsB0dUhg\nlbdYEVtz+54Ybc043KeC6by73HM+mb3n3/n4stqA/iRB0/z3tm3/bO1c0zQfbdv2JdMKebJJTQWr\nAUvWgTNgyZhXY0BK77YhV618zZOAQ7O4OoJm+2xr8dXY6vhSE8SStMjTY4H222+tcYKyX45Wj8tT\ntUFhXEuU+BgxEzeY76UMJIHSfgoQ7O3KOGntJnDRpl/udtbsq2dbobjn9exSDXWvbDWL9r3SlXHA\n6qYo8GdS1m+pTVX2iACo85aXhymc6tIdpqhnWxQ17CSFzelb7vdlSmS1s1aBmfehzHxysKHSOmt3\nhomld7Dxfllj8zVzA/KNdzQAACAASURBVClNnyq2EwY0nJYAWGya5uVt2/4BQNM0t1LaedaAxyet\n9LGbSXQXxtUr15ezq97tLbVoVldVZHjVzK5OrwGnwejG3flKOjEZbbkqA60zomu7j1iOoooHxJak\nH6MYQC8Crx7CA93DaVApPkkeH7WLIrkv2rPLTS8Q1WBYowx+2awERB4NLk+UDOHuhVwlGM7ZLu0q\nRWUaEANeAY9L3bcYmtZoLVAYpUDfPYJa6wZFLVMg4RJlU7Oz6Vl88Cu6fI1iQxMgirUuWJ4C4A3K\ncpLsHlcZmb07c9YEsZrSZPOAA4oDU2ZWUAceZriWZRYG9DLgVyig8yXgh4kI9u9q2/Y/7aC8J4WI\nAdVsPZKajjxJHLhq3gpdy51lLqVbsOvqfLK3KD6I7rcGzPOBDxOz/Hmis8ldLre1XNFiNoqDcZe+\n6nSIAKPnEkCU7QBSxZSfntejbwUsAhOBq4OuA7ue1WdngbfK2t+VvZ9iI1myfARY5xlXb+VVE4jJ\n3iYjtdic7ERiDqr7sqU9QgmQlErpzzOigKSHArjqKnV6ibKYd2j5OqOUN23L8vL+4xPfMJUB433b\no8h1zT2t2Qucv2teYskgnb9sNqA/Sdg013TpV6cmfpKLG6Fh/GVOOnYZpG/PyymwD6SBpXeAU8fR\nBltiBN4x3UV/lACblw/hWcvwu+fDRa01T5cYX3QqABsSs/3e7iMP1wuILSieSdhAFN+jtVOyFbiK\npEEqkFEMyyJlL2XZQdwTJjahvMSWXO1Um0jF3AN8O7EdiPYUkg3sMOOLVdcoKuQBCjNcJ7bNuESo\nTzLQC6Tp7pEaq2OxmS2ChWwQwNwyzqLc2J3VeR/0io2SoV+q6oDiINCko3CCEcUzeYYCQt6uDugO\n4n19NzP1DB61e2u2pEn2ocuyHUfTNM9umuZfAf+hbdvVpmmON03zP02778kuWaedq5zrs/S7eDRq\nNgqSzgsE5GJ2UZyNmITiXzQA1CkOEwPuAvDIFrzjfFlPdCNleYE8a1o4qfxlsD5JiUv5VJfnFcAv\n/2hEBvusqvZRG8lgLVVQg0pMY9PKFisQC1ixtHo+takbs3X9UJfHYxTVCYrKc4ayK6LbtTTAFWez\nRGzDobYQs7hAiW6WrU3bZWgSoDs+3eX1McIedpoCfHoOAYZA1vvQiKKyenyX6r1JsWNpkbIvyZGH\nUXVTWWKXUtPd2eG/vU97etUN6uAztHMZuPKxf88is6hgvwX8a+Bvt237TU3TDIEPPxWNzxKpYGrU\nTF1r9JMJv2tSm4HcaOh2jH3dtzrUEUqIvmb65S6/MwQI6V8mBpR/4zzc3f8o8Q8QUMDiaiKu5ZPd\nRwZPbYJ2uCvvNgKQINzRYlTeWTVTyxYkdUvPI4DxwadO7Mwmz9oCXbc/zHXPqr+80aB2u5NCFhRG\nINuV3qmO91MYhEBS6qrUKeyaQFNBnc6aFJUt9idA0LP4xAGF5YndKJ1UMLUbjLMytbmHYoiZ+V7T\nyi/3Xfeu1ZjS0PLI9h6lkdSAqTZJSy6XF+yDbdu+rGmaD7dt+83dufvatr1pWuZPVumLhPZzDjST\n7ECe1g10tRflM5EGmTrbIWJPnW+ah5/bKB6cG4iZ/tXEX8dsEcF2Whf2KSJmxW1GA0Kd+gRly9Bn\nECCkzn+RsrocApxeQDAjV6/ECjTwznXHK3avu5zFsDwGSDOnAu0EQG7zEXvyQap6KBZJAHGGwsS8\nfX0ycduLD1SpY2KpbvgdUVbIr1gZUhMFGOetffS8UJiTzjm7g/GdAOQMUF2dBUIxlm9Q1GXZ17xv\nCVj2UEIZfEL1PLPZYZL6RDrfZ57QuUH6PasNaBYv2CNN01xLF4zYNM1tlH2ZnrKS6ah34sxa8j3+\n29WtbAB0+4+v73JVRuWfBf7eDfDOB+BvL8O/Xwkm9AGC/fxXylapL+riVE4TgHE1oT49i/BsHRjC\nVQvwg9fD6mr8b/vv3VvWZ52zuh0h1JuPE4yqoayEXyXUOro0h7s6nKcAggazAEQRvN6+ag9f56Q2\nUD18gOu3lp6coXjqFimMRwNunhKcKM+XVEYtCfFwBS36FKDJqClv1DyxmdnDXb4HiUWqv2f5jSj/\nLKv89YwCIC9XwCe19RDFoO9xUQqjEIBuUUIJpBK6dwuK2r5h5wUczlxhvD/nuCDl5WBeA5f8O+c7\nSTPIMgsDuhn4p8Rk/ADRz1/ftu39OyjnSSW1PaFrx/m3e2U22d7QDkpZfcsvz2eWAcXwqQ6qznOY\nEmQ4T9mWQsF++7r7Vwlm9Dzguv3w3IPwkhvguuvn+P/etsk9JyJPAYsGr2ZWDU4xr3licBzp6vAQ\nsYkXxKZcGqhnKbO1bBywPeTAAccD3/T87rWSuqM4KQ3klxFq4TGiI65amktWhgbkiHHDuXvqBAYy\n0iu+yY3oR6x9runKFssR0xlR3PFiTT4wxYRkgFfbykOGXXfVT31tRAnAlMduy+5x26UDuu51FSuz\neTcDTFKlMugMUvrc73X+snnBOrvPi+i2023b9tGpNz2JZdJfM2fbTw2cMsBkvVtp1UH8fldLoNg5\nMlXXVg3LlL+TkS1jnrLnjNS0IaF2vXoJbr8d7r0XfuRHYGUF3vve+P69C8FkznblXE/sZ6w6yebk\napSWWDyLYFobFIOt7DEwvq/NiDJr63myC1cqmasQar9N+4bxaObriX8dvZlgKOdSO48oy0lGFCbi\nbe5LODxiXPcMKVHT7kzwtG6j8nLERATAAhpFbvvSGvd2Kp3KkKgM2bTEqLzt51JaBYS6uCqK1Z/K\nc06alPNxzRa6ExVs0mr41026sW3bX5uW+ZNVJtmAaoY2v97X2PqdZ5saNXUg03kf9KLQcr0eITqc\nXOhQ1hAJIBQRfCPFlf8LPw6XLsXfKj/4ILzp7ePbY+wnvDkCUVF+rWtSpxcz+AbC5nSAslr+XHff\nQaKDn6MsUXC7lKsEAh0FlmlQqS00IKUmqU2lvmoRqLb+2EdZQCpjstJLJVRdPC5pSFnx7kxBTEZg\nrPVjAtjMbLHnlB1JjFV1gwJIUl8V/SwHg4N2jomCAtRin87uPD5IKq3OO2Pq66N9fVXP5uenjRnJ\nE7UBaY3XPmLt3l3d8bcBdwNPWQBy8Zfs9FTiLytfczUqx/rkF6sZzjsJljYbGDVjbxDqxlHgh+fh\nNzZKPeQK10DT1hGKK/nnvwB/5+/Axx6EtbWwD/kWoGcYX1zqS0H2d+kUcKe6LxFeNj3TUYKVnKD8\n46rbNNx9r/bWeY8b0lqvTcoe1j7rQ/GIQQm0XCPYilRRgY/WXO2zdpW6pvbdILZvvYsSZSxglX1I\nEcor6bzbqcRgtfp9jfAmaguOY5R+citwyxE4eQr+HePqq4A7Bwc6G5T656Cd1So3GnvUOZZG9+la\nre95H67d79IHQtNkFhvQbwB/rW3bz3THzwH+edu2ExnSk1mapmlrUdB9RrVMV7PnIOvFQ/pfkq6p\nY7g3xo3VevGyZewlBvqjRBzKIcq/Xai+GsAjiqv+1gFsjQq4fJDwiN3b3ad4GUURLxIz9qGufEVQ\nX0d4HrRMQfsGnaawJsXK6DnWKQxDZUiF1H44HicktQTLQ+2igbVFMMJTjLuY77BnkjFcbatV+spL\nzEb1c+BUHTyeaLN7VrWF1FW1u961r7dbY3ssj9jcOcriWKlFinxWaMBFCjNzcFGfwOqrSUh1Vr9S\nP8v9s9bPPY2rZDVg6RsDpLSX63/BDgt8OvksMRae0qIGdiZSU7MyRcw01W0aPlvkGcTPqzwYD1xz\nQ+SWnYcY9PcS618GBEho+YAG1RqFsewjBsPZDnyuGcL3vz42Wl8nZmWpAZqFoWyGdZ4AE3neFOdz\nqTt3gNLxDlBUFbWX6i8vj8rRtS3GwVPPnlfXy9a0audl+NYyjAOEbUsDT4tDfTvZAcVoLVvMQveM\nI0pMk9pchuJLXTmvoPzvmUBGzy/gvoECfnIc6N1rzdkKBYTV5m43UnuIlSpoUmn1Ppwxq/3UZt6P\nHIygzm6yuUCglcXVVB1PY0bTZBYG9M+IfvvvCVf8DwAn27b9scdR3pNCZAPKVvtJktfRQHmBHuui\nfB1wau5M7NhpcDZma2W3KL5HFCsPzeS+UlqqitjBFcDtR+HL63DyXAwIMQaV7QFxWxTAkHFU+9rs\nB25dgPesw/94BO46VdaXva+7V/FCcovLYyQVRQND5UsFVHtp8Gigutqh2JxlYlD7gtahHY8oTEvv\nwG05znhkm8HqKeOv6qpzilpWOUfsmc5RQgV8mxRFM2s9mtRK2fC0QFWsT+qY3q/shFpUqsnAwcKZ\niKv2me3X2L9Ljc1APVbIGVBOf1kYUNu2/yvwi8R/ud0E/NJTGXwkTknz+VraTDOzcVCdU8ee71Y6\n74CVy5c6orw9ytjD+6UyQVEn5CmTcVMdfhU4vgwPnoQXH4erh8EKrqcE0+l5vOx5IjhxH+OG5RXg\n5Dr84FE4dQruOFzKvkAxTENxIWuwi/XITiOgqamx83a8aelknzpFYQoa6BcsH7HLfZT/DjvHeGCi\nL/TVu1i0tpVtTR/ZlhR7JK+gbFEH2b5L4T7GDcYCME0mAnb3zHla7JzURRiPKfPJC3smty/COChl\nqalqeZIUyPs5lfd4ZJIXrGmn0KNZ0jwZpc8N75KNyM6WMkhlI50vRM2dojYbwXgH8RnYVbx5xjuI\nu3oFQoqalQfmOuBle+DCJfje74SX/1YLv3snj737PfyLX4SPr0Sn/iKxROM6Yk9k2XoUnyQmIA+P\n9gn6vqMBbB8kjNqLlL1wpBY4u4ACkm5Y9eA+xeRAUTNHlFgf2WGGlkb5imkJwKCsZtcqeS2jyHFD\nCqqUvUy7DUiVg/K+9lPYlsBfHkN3dwukPAJdg1hxQSPLS+2r/iZD/XzXvr4OD8re2K6KYeXX+m4G\nehjvv5nN1NhNjc1fbgb0nqZpfqxpmkN+smmauaZp7mya5t8Af2VaAU920azq4jQ2zywwDiiw/eVt\nVNJ67IiO3UXqnUf5yB6itFDUEKkOB7p7ZSzVINPgegwYDOA1d0ZE9G//mYafuuM9XLoE1+yBq7p7\nn0cwoudSOqevJh8QK+XPE+rcfsLQ/ZGTERgpW4+WKbhnRbO4FllKnXVwh3HjtNpQ0cbOEDQIBbyy\nYQmYBoxPAquUbTwGlpcAR0wJCqOSGnnJ8lL6SwRwnKXYWtRPlikLXdVui4zvHS07zhnGGaGeZw/F\nCSAPnJidylL5Eg9ZyHYfSQ1YvO6Z4WPHWbL2kM0Ks8okBjQP/FXgh4gtZ1aJWLcB8C7CE3bfDst7\nUkhtMSqMN2oN0aFORV21yvqwOqPnXyvXX5x+OwNSZ9yk2D6URq7neUqskFzWdwB7F2B9Hfbtg83N\nWJ6xDtx5W5xbW4O77uqWCOyD914I9QZKxx5RbE2PEvr4A93znSZA5hixIbzuk2EXCkPQwPTFrAJe\nj2iWN8ijlj1CWO18mBIjJbuO3OHygIkZioU5aGSvmy8+PUT56x61sSKnXc2DAn4C0b0UdiLA8zVk\n2q7EwXMvMSF8mpgIHu3uEbgLuMTiNBlJjdVSDuUP4wZq1XWQ7tO30ue+rPOzMCOXyxkJfSXx/F/+\netkPCPqNbflapqne8A4m/kJ1zV927V7l6/YOXXNPieQQ0VEfJjrgQWKQ3ESJ3pVt5UCXx+v3wyfP\nw4Fl+MoGLCzA5y/Cl7bgwBKcWw1WszCM/YU+cr781bL+cUCu9g3K3/YsAF8hWJbUJhmfxQT3UIyr\nAiGpomIT3nb6rR0BZYjN4Q6q04LlI9BSWleFoLBGnxBUV4HPuqU7SFm24nYfqXpaRb+HAnCHKDsm\nXk/5i+gB4//9rnIF7noOAYZsZxcZ3597jmBOrsb7fc7ofXlL9sD6PbOOgyzZiZMB6XK54Wnb9tG2\nbT/z9QA+NdFg92NvWLmN/Vq+P6tPWZziuzrm7tNRSqeOr9lHnUhxNd9MqE4/uRAAcpyy/4/A53aC\n8SwMYwHrmbVYkvHZrbDb3LMKRw9EhPMfb8HbzocN6NXzEbgo79oByobsD3b1+ArhHr2N8AS9sEun\n9lS77aPM3lpZ7u5wNyzDuG1FbEhgrGOpQwOKS16Bi/utzWSIV7v7EgbVbYmyMl0u9U3KHtQy1KuP\nbFCWreg9aYfGB7v8jhJAJOCVHUcsUKCjdw3j234MCABUxPcyxZXvk6JPYtkWpL4gAMz9zvuas/Ca\nU6CvT/u1SWyoT57W/wvW54bP+m+23ei8X8vMRjO5B9LV9OR8j4yzUlV8hz1F1B7s7vkSoYJcS6zp\nOkkxbO4jZuMvEgspNfNKl76CYFHyDOm+FxIz7k3ELokfIBYBbhBMR51X6tO1hNrwGBHg+BHgC5RY\nmHXKxu2K8hXTcFvN0K7JjiURmxIIiNmMKHspKX7pAEU9EaBpzx+VpcEvVrOQzukdi9UJxORp8/Qw\nHiMltU8Bnfu79tI1D65UG8pLttxdk2orW5mrly55UtNvtc2c3eM2oRzykY3UNXWLyrXslv+qMaCv\nV3F9t+9ats3U3I7ZpgPlJbv7NV+rGf80QDys/wBhiJPqMN99PkeAy9/68WLP2EesGr+BoOrPpgye\ni0Qgo1z0z6XMsM+k07GJfYm+YQFesAzfSgDdY13ZG939q92zfbk7fwUBPlcSqocG1zzlT/r2U9Z/\nifmofUYU0Dpk7SsbioDCt5u9lQDKUVd3eZzEjvYCtzAeISxAdwBRLI7CDQQmdN/O2vTRO9uwa+v2\nLZuYZL5rlxspE5ICDVW/U4wvCD5HAW0Ytzs6W5lL50aM7yU9tN8q2+/PgOR9vuaudyCrnd+J9AJQ\n0zRHm6b5s5Xz39I0zQseR1lPOnH0h3HamYHB0/ngGNi9TnH9RXoMi+wcHnujTr1JGVxiQPLyfKg7\n1sB4AfAdRKf90Z8PwHk98DfuCDC4ghhQi4RR81SX91kCuB6gRDrvJ1a7S1U4sAduuAGeMRcAs0Ww\nmH3E0o7lrvzndXV50TLceWOA4Rrjyzxg/I8FNWDlFfLz+i3Vy5mSopCXiMWIsqm8ixIpfDNlYEtd\nerBrQ9luXJ11u8smMeBlZ9H9svW43crXpg0JYFE7LnbPfYRiRJet6OGu3QVgHi+0RgDvkOLh04RU\ns5P58hTl4WxH7ZYnVweemv0mM/maPdPHxhOVSV6w3wD+Vt73p2maW4C//1T8Q0KJxwFlo3FtJqhR\n05ohGjv2+7Ih2t3vvhWDOpdUAw2SZcY9GxCd9RmEijUCXgsc2A93n4+B8ICllyoh17MATgNXtpAv\nEUB0DLhyCC88Cu9/KGw9n+/Sak3TeWJvlkcptpzTVveHGB/oWnMmm8gmMUAVtKhBpcGjSG6pX/uB\nnzgQq/vftxar+BUisEwx3J6hDHzdJ7YGJa5mYL8PddcFNB7YeJQSZKg6qh1l1xoRSzUeJABekdUe\nQrHOOHBIjTtAWfIht7quSdXUe8wBhbIfbqZjtZmeQyEZztyyndPF+2u272TzQS2OSPJEVbDDtU3H\n2ra9l5gQn/LirkZnMJL8subSsfJwoMnbIrjxWLLBeIdxr8gm22cnRc76HjynCFvLPHAHMfBOnY8t\nM+6lzJbnKAziAmVgKCZHrtsFut0Uu7yeOQ/3PRRlfo4YHPd3932RGLQv2xcD9BiFrQ0p3h4xMDfi\nr1M2Vxcj0fNqPx6xozXLcw745XNw91oM9A1Lq3w18LYo/0km0IPiJZOdZ54SuKl3tGX5yN0tBiJm\npGe9SLFD3UuJYVJM1gLFGaBtNPZRwFVGc7nOtZZPoQgen+RMpmabGVAYZ54M1f7ev13tmre0+f5Z\nbKQ1cJpVJt0zP+HaMx9HWU86yUzGZ5gMAj571YzU7kLWbxiPC/L88oyRDYK6T3ElcntrtlfQ4Qqx\nncQ68G5iwd4liq1mrbv/4S6/05SBqMC8CxQ7yBLwmuPw5Y0SN3OJiJA+SjFGv/AofKoLRlqeL0s1\nvA0FRB4g6ExMz6d2ERMTGB0iVMuDXV5ngHsIlUesSurN4e73UQqwfD/wM8fgr8/Hc/kSB7GK8137\niIkJBGVzkkp0pPt9iAAV5Scg0vsS4Op5LnR107YeYn5Hu+PDwCuWiuqndWG+DYg7JaS+e4wYFMbk\nfUcTnD7YPa5GeeCsJKeB7cGNmUU9HhtQzf4q+WDTNH+tbdt/6Se7v+T50OMo60kn3sg14BHowDhg\nZMTPunjO339nA6DXoaYOqsN+I8E0fr87f5GyKFERu7KRyC3sC0FF67UsQuWNunxlI1kHvrIJL7sF\nnvkAbG3BQxsx8Bbm4YGNUNUeWYttQY4BJzYKy5ILXarQEYoHao7y18x6zkXKwtpNwrC8Shizn03M\ndKfs+gIBQgrI1LIEqVtbXXssE7avn3+o7Be9zjjbWGZ8/yJNHlCWVOj9nGV8ISvd86n+Cg4VI6M7\nPkRhQmcpm46JiR4GHlgNIFyiqIu+8FntJZuYq0YCGbWPq06yIXmfzE4U74N+PMketFW59njABybb\ngJ4N/DrxXAKcW4jn/Qtt256v3vgUkNpaMFe3PKYCxhs3G61r8UG+zmnO0nm+faCnziQbDZTBJvVL\nnT3Tas2wUl185bSM3vL0PErxYA2JgXD9AG66KaKmFxbgi5fgS5fgzIWw6chW8gjBiM4TG5GJKe0l\nDMH3dM9xA3DHfvi18yVw8nD3bGfteX3t00HCuP15yuLXdfvIKO/M5xIxwG/tnv10V689lH2ztZRB\n6s0wlat3pf2gNdh1XvE0sh+pLjCuBkrdOklRQ59D+SukG7q08rYp5OA8RT11+w9st8U4IIlxDu0c\nbGfrPplC3W7ZZ+PU/dmlPw10npANqG3bz7ZtezvwU8Q7PQ38VNu2f+apDD6S/OAONjWViZ7rUF6I\nwMBftOvarma57cnL30p5icEoKHFIMVYq2EzAJLCR0VozqYPkWve5gjKAlwnGcfgw3HUi0n7PG/fy\n2BY8fAGuGkZ+L1yOe1YJQDpNGXRaLf4w8NKujGcCd50Pm43sLHLRHyQGu9ayQQHQb50vS0kuUf48\nUANPIOLLXOaA4wfi2rMogY0DymZkWpMl4Ja6paUrUg21g4CrMosUlqi2V8T53u4j4/N5ipF0Bfgj\nSliAQOtK4PggwghcdRIDymw5sxjZqVwW0znf2QDq6k7uf33q1CSD8+Ox/UyqEwBN09zZtu1dbdu+\np2ma023bfsKuve6pvCc09NNHBwi/nm002HV9O6hIxXEAUP6izfllKy/NbFA2opdoMKguno8bSNeJ\n2Xee8md8iwSFvf0w/PLpcJs/QImzef4R2NgIz9fnfvoiS0tx37mtuP57KyU2Rfn7+iIxrc9139d0\nv5eAHyRA69OMD6yH7HmlGr21U/lOMQ7EHpOynxjcqxR15tfPwYcZZyQHKAZ8Df49FIYhG5vaU+zS\nPWtaSgJFbdPaMBmRFR2uup2i2JBWuzTXEk4C2dreN4rJRLY62Q5HFE+l+oG+1c5Q+qm8qh5ECeP9\nThObq2swPjnWvF5Ujmtj5vHKJPD6Wfv9X9K1v/MEynzc0jTNFU3TfLgLEaBpmm9vmuZE0zT3NU3z\nvqZpjnbn39w0zRtnyVMd20EjN7Y3ePZo6ZyLOsFmOu9AlkFJ1B7KDK9BIruD4oSk20NRE9yro46k\ndTPKV/aSPzgdx49RjKsXib2jRyM4vASPbsZnvksnV/tyd49cx1rdfZywB4mp3ExsnSnv0L8jGNNn\nKXvoqH1ko1K9pS6eobjxZaxeZFyd1NKPAXD7MIy72rfnJoqxWSqc2IZE718udbElRTfLfa53p5X1\nilQeUWJ7VK+LhKqllfGHCTXsasJz+UmijT9A8XrR5aEtQNYY32TNP7n/uJ1yZN81NqM+lJmV5+cg\n52n029nQE2E/0+5ven7Xjv+05H8jbJ+SfwH8UPcvrW9lB8DoDe9LJTIbyYFYmRa7/UDnaqwHtr80\nz9vXKKkT5pnJvThSGQYU1eKVjK/FEk2fIxjFWeIvmz9HqAALhC3oSJfmwXPhyh+NYO9eeGQdbryh\nxP2sdM/wAAVABsSsvpcAqjkCaO4noq5lHIbCmmSTWbFn3U9xe5/p8hd7GVFsKxpgqsvfOh4xOLcA\nf7RVVKcR42ELYgnL3fE+a0NnRIohklcMijtfbanlK77iXHFbF7o0Z7uP8vgMZeB+HvjV1VBHxXZU\njgC8ZqOCOuN2RuQG5GyvxM7X1H+PF8r9N9ejT1XbqUzygrU9v2vHX3VpmuYg8F3A/wX8DauHNJRr\nKIux1yg21pnEGx/6Y3iwNP5yndIqjkXXXPLLHPWkEYjIXpGptgIY5dU6QPH+XEeAjIy4HnX8ScK7\n1FJUlJu09yphfH7Vq2AwCGP0pUvwAwdh7p3h/frvVh/N+p/r6volgvksDyKf31yLAfUg8Ge6sh9i\nfHGrAuakglxPMfgKLGRnUvCfjPIbwI03wrFj8JZfC8PviPK3QSuM/9/Y0MpT2/rg26Ks39IkonrJ\nle1R2pt2zvuOnkv94ljXBqe7tIe6d3WKcWcFlP4hcNckJ8aZZZJ31g3Q2XOVDc1eZu16331PVCYB\n0JGmad5OsB39pjt+/mUqfyfyc8DfJJis5IeBdzRN82Xi/dwG0Lbtz26/vS7yWOUXXtN5/Vvg5CJg\nUQCZ22ewe7P3ys8rQE8GWdkY1Mll3/BZT+rIWYI5aBbdS2FXmsEHxH/GH6Wssv7274DrDsV/h62u\nwjveAcvL8X9i774rYn4O74MPXCjGcA/uu76r15cJ5vPtg9hn6GNrZS/kj1Bmig3K4leFB2gR51li\nwMrWtESod6e6uq8ALyY8cZvAB++Ft54MZneOYkCGEiekBaQSeQp9awftGyQvmOxKssXI2C+gEqCL\naeqdii3tpyyCPUEs6P1yV0c5EaRSKdA0e199YpKNzPuOB606yOR+6TbHPttNzbDs4JSB53KB0CQA\n+vP2Ow/omQf4D8jDlAAAIABJREFU5ZCmab4buNC27YeaprnDLv3vwGvatv2Dpmn+D+AfE6BUy+OR\n2nk37uUXn0EHSgfMhmrYPls4U5KtYZNxRpNVOmc6A/stYMtGxk1iRj1DMU7rW9HASxTWJEPxOaLj\nv+pQeL/+y9uCtaytwYULcOut8LGHYn+gT5yCC6MoZ39Xlhth3fN2vBvp7zpVvEMXuzoI5GV3ksv9\nWdYG30PEOv3IPPzaRgzmxyhu6xcQm6Ht2wOrl+A3T5YYETEc1Q3G98JRNLhUwKFdW6XYdGR/k11O\nE8AextmfxO1EYldiaALaj1Lsc5qg9I4VLuF9UPFcOta7ExPs62tuSNZ176veBzMgKX3u897f+4zU\nNfEx17btVdU0M25I9qwuk8/NUO5ll6Zp/hHwlyiTzh7gPcCxtm1f0KU5BLyzbdvjM+TX9jVkraGH\n9ns0Ja2/PAHMJttnDJ9VMqAJdHydj894y4z/86iC/NSZ5apXvAwUA7SeZ5FgEkvANx+Au84Fk3nh\nUfjcBTjUAdNoFMxoNIK7zoQqsUWoE0MCDJ5FeHie0eWnbTIfpiyAFfBpJveBLpvMwe76apfvowT7\nWZiHkxsxcO8C/iLwNor96Iw9vy/chHFPlWREWeWudyLA0eDW+5FNSN/Z4Ov3uodScVsLwJuOwK+c\nCrXhQ5TN+zesDvrMUVQtvXP1L7ExFwcY719i0tmO6Aypj8n3GYbzWJnGgp7oXzM3wN8DfoxQu1TX\nf9q27U9Py/irJR0D+kngewmN4/a2bR/uIrRf07bt982QR5tBo/YiJJPYET3XYHw/Fl13YHHJdiEo\ndgYBhuJOoKgUMqzmjqqlEW7TUp2WKbPuCwmj6M3A8eNw8WKoYcNhfK4YwidX4Mg+eOhCqFgq6zRh\nb9GSjud0eX6eSKfBpRXdAkqpNgq80zYiUsluJDxESwQoCUwHwBvmYX0j1JrT3XMdIrxty5Q/TfQF\noFJdBDCy3YiJKEZHYJjPuyFcTAlL6+8Cim1ug7LHz1r3jCfZbtR2tV/Bkyoz9yGBuMqr2WkGE84r\nT7c91bQAP86Mqpa2Jk90MepPEA6Gl/3/7X1/jGZXed5zxsNmWTZrZ2Mva7MYdwHHsSzXGEOtQGhx\nnMg4Vtq0aXHSFOiP0OaHQkiTtEj5g1ZCQVUiokhRVCVKASX8agspdYgbFIRoCtQYY0gwjnEXy9ma\nZXHcZW3sZRi+0z/ufXKe+8x77ndn5pudGc95pNF837nn9z3nOe/7nvecL+f8nTnn7wDwtwC8LKX0\nxnkZbzVyzqsAfgLAf00pfRadhPSLU9PX9GF33oo6OiIf/UzdXlcaLU/1eBVzlQz3SxzaHPxcD1dD\n33WjmM6JyAl4BEUq+jq6yfUX6Gwu11wDPPpoIZ+lJeA7LwYuWAJuvhFYWemMyxejk3SoyvD4xhl0\nOz0XoZNc9qMjBq3DEsr5J0qIR1GOK1zct/mBvh2nMPwN+pMA/sc54IN9eQ/15T0obaa0o1dy0MbC\nic0+o0f0MsovX9BIzT5m/c+ibNFTjSLBeBpep0FbEwC85mAhI93pWkJRrfmuV+Q7MByPJEnd9FAp\nXccTLEzVOdhnL0v/OwktEmMS0GcAfH/O+VELvwTAH+ecX7RFddpyUAIaY3BVuxyRKKoko6pTZMhz\nY6Pr6Wrn4YqnA0137OgxrGlvQLfbdAblDNKV/fMn0U1m+sscRydlPNg/vwHA93wP8JGPA3//VuCd\nH+om1/EjHTHd8Uj5zXMakJf6/P4KnTrGGxe/hnLs4lhfLqUStoFGaqB4adNudBjdZD6N4Y8j3ohi\nsH4Iw7NTVPGoyhEka31HlDioKq1geGm+HodZlXTLWCsJcSt/BR2pXoRyPetRDO/noWGcEpCSId+x\nen7TuM2FhFCpXdV/YDjeEMRhnvOgBBT9h31WTJGAxozQz3Dy6TP9an9J/a5GjXzYmSre6ktT/wx9\n+ZpfZPPxrXv9rwMN8p1qgufJFZeiP7e1uQ3/cB/O4w/LfZiutvcD+KklYP9+4EtPlsOrFwG47+Pd\n1vrqh8rth8843V1q/yPHgY+dKL5A9EV6BjqpCugknL/o63LLka6Mjz/c1f1ydBLX2/t0esbqEZRJ\nQTWGxmKeqzqMjujuRTl9TwPxErodiHehkI/aTJbkjy4EJEQe5j2H8lvyeicRSWqG4hZwAIWIuHM2\nQ9mJpIPlib5PrkbxylaSU6mFZKRjjsQX3fEDDMkkcvGIxqHG17HuvkQuvft//7xejBHQGEFOIc9d\nhZpRmuG+++GrASwciFeLyNisBkLtWB2catTeL+kpIVBKOItuknNXhVvZajuixHLnDHjiyXISewWd\nbYWT4H4U0s0AvutKYHUVuOREkQwobXwTZTfuFDqnrCMA7jldJtvNAN7Th78A5QKwmdT3MqnnAQCv\nAvCH6CYvr2y9r/98eZ/2IMql+HeikNHDKKoZjeCusvBSNPrZkJzUdwood01zAeK70ovWqGLyig5g\neIXs3Si2LHo678PaLX0atWmLUlU9mvj63204DKfhXyW5lSCPyGzg43wzhOMYU8G+hbKoDR4B2J9z\n3rVS0JRfRiUio7N+V/VJX9TSSBiwdqWJVh+3S6mzGNUUoNg9SBx07CNpqd1oBd1kooMdf0qGtorH\nUPxYLkJ3J/SB5e4nfB5Hp1rRnrKKsuPFqySOoZOGvtl/PoFylQUn4xEUCY9SzzKKDw6PMLB9Z1BO\n0c9QTraTHA+jU8UowXDC84wX+4VkT5JQ8V6Nu/SQZh/pCXzuntF/h5eKqX2ITqJP9OmAcoTlIpQj\nGKpaU8XS6zZUlSfxuVFav7tbCD+7yk/o2PUxPIYpcYDNn4a/IOd8KPj79t1MPg5dXTigFb7iRAY5\nlYoiElG1juXoS/Q81UC9z/IBCsFwNaPHMOuvJ7bPoay2Z9BN/odQfm+K11c8KfEOoRyZeMm13Xb8\nj9zaSTVMS5XjKMrF8Ef79BdKPai60G50Dp1k8jCKcX0F3VUal/dxr0Y5b0XHx5MoBmlKH/Q4vg/l\n8ntO2FMovwfPe4poQ6HUwrwobbA/SQi0AT0meS9jKBnNJA9KkZRm1GfsH/Vt1vNf7HOSxFnJj9Ia\n66hSjL5rlZjVmxoYjiPd5IA8X5XnjLuMEWLAcE5s1ji92fS7Groq6Evid2JmaZxwliyNi6/+FxGZ\nplUVbYYitnNg0iZBRzmu9BxEHJwckBej/EbVQyirKbeQ2T4agUkqRwBcdhnwvS8vv5x6FMMfK5yh\nuzP6apQDoA/0ZZ1AuZFxJmVxop1CRwb0WL6nj//Rvn0nUAiKtpf7pK775T/bz5P6tJWRwDQupRRg\n6CHtNjgayK/t63hx/y4u7uNc07db39lBFNXwQN9fxwD8AcrVIno+DSgSGg3RwPAkPPN3Z0JVmyLp\nZ2Zp3J7jdkfIc5dwaraazapje/p3wSJRkh0d+QS5ylV77p/1JUcGaicixlPX+xV0O1QPouy20P5y\nUD4fQBmgXKlXUX5V4gSGOz6cLIf7/8fQeSd/sw873Buc3nWubCE/r38OdHaiW/uyHujzvhTdcQ/0\n8U9heKm+nqni5KJN6BEUqYVnv7h7pkZgdWykpELJBSgqqV5tQkMz+2apby8vt6JjIB0kD6CcK6P7\nwLn+/7UHgP/yZPHnOSv5si700SLRqipIgtSFiJKTH8ugusp4Sj5EZI/UfCM1X+Oour+KteN8I3ag\n9rtgc+AEAaz1KCVcuiH2W3hkM+IgWpUwtetEq5ZKZ7qTRfKJyOwsuklMx0DuJNEewl2rmYV/N8qK\ne0LKvADA8ePAnee63xDjdvJfoiPDqwB8PzoyUoPs51F+L542Hdpb1CbButOLmDaVGYpRmkTBuHoc\nhTtNByUe41ASogR1EYY+OC9AMSzTqHwExfZzOYoERMmT59Oei+7eJGDo60PfI1WLHuvLIrEBQw9w\nkibfO3fY+J3jaFW+K3lQOub3iCA4zg5iCFXR2Kesi9uM1FywWalHsacJiFBiAGJdWXVv2HN9ga52\nKcFEBmbfync1jc/o1+KDjavUGQm7D2V7+4DE550+6up/G7pDknrk47PodhoygPfd1xHP4yhHK65G\ndxaLJ++/0D87hW7CPYbiif0kihc068sJT9I7g2ITWkLZ/qZ/Eyc4+4MT9DCGV7WyHE40TvRVlB23\nF2DtEZej6KSaY3384xjeB3Ss/341gJ85CrzwcuCVNw2lhSUUkiWRqOpHkiTBkNSAIsnxffE4ib5j\nXcT47oDibqCSu9sfVXJi3zGPmvrmC/E8u9BGMbYNv2dQU534XdUtPfIAlBV5xdIAa4lNHcmciPzl\nRo6KuiMCDLeOva4caNxJ0oOU+1Bu6dOrRznRT6Pc/3MNyh0nHIRfBXD/2fKTP0sodh2g/MaWXnlB\nyYuTWsmEJ81Zfz2PxXxdAqA0wYl8Tv5T+uOOF+u+Hx3RLfdt1IOdh1AO2dI+dQXKod1D6Ijqrad6\ng/PDnTrMftT3z3zZnrMoF+a/Ap2USVuY+veoR7uOCxq/NXxmYTpGXfJmf9H2xbGldY4km3l2oUVg\nz0pALq5GxmQ+g4W7GOwvxv2FSDbn7BnJwFctHThevuan5KNxOIn1dr9zEl+PZ9yL4QDmys3dmftQ\nVB0eZfgGOjWMhKjb2Ut93kelbTSmq+rB9tNRkJNJr404ifJuaPg9KHF5IJf96u/nGMpvx59B+TUQ\nJcrLUQjjODqp6rl9nIfRkctVffvvR1FzH0SR1ijJHZK6kHS53X6q75ND6NRTtoN1IXEuY636o1Lx\nssTzNqta6xJ6NMb0OaRftbwxLII89iwB6UQGhiJn9IL8hQJ1dSyKN7PvKhZ7Oq0Dd0bUMMj6AsUG\n5YOWxlmqQDTccrJQgjiDzquZhBXZXGhcpepyCt3Vqg+iSAG0oaiPDsuhnUUvXKekobs/bPNBlB9L\nBMrdynoa3PthWZ6RxM719eHOFe0blCquQDnuARQp8IvojnscQpEAefSE3tMkJbojME+gGJdpHKfU\n9yjKIV1VK3VsuIevPtOFSQ3Lrrarb4+WUYMuer4zrHMiSrdZ7OldMCKyu+jLHVPPXIWKnmu8mijt\nqxklFTVe+2Dz6xm4ixKJ48yPk4M7NSQK3THaL3GekHicVED5sUBOXh289Dmi8VmlKxLPSv+cUpra\nrNy+ARQ7CaUKtofOgnqs4RCKnYv10yMeTH+8/3y0r8dVKL45p9D5Jj2AQuAkcaBcZs/PqjLqgsP/\nXHS4MHCXjyAB6OVzLt2oFOP2mjGp3U0EDPc6ajkaBxgS01TiabtgE6Eri790IhKLnZj8xdR0al2d\n+N3z4CTVAacT3H1BYGG+sqofiHrsziyNEgCPHqiUpr5H51AcDJ9E8WQ+06fTs1osQyWwx1AGvBKn\n3rpIFZLb3I9huOVOr2pd/Zk/VSL228UYqsC0wZxEtyNGgrwFne/P3Shn4S6X/tFtep2w7LsVK2cf\nusPAtL8wPaTeq5KWefl4pMQIScN07gALDEkPEo95QOLPLI4vtpFJYBHY8wTkdh/tYO1wX2UIXe0i\n9ctXJg5KJ49IJ4/qABQ7DctnGtZDnes4aNW3hPF1NdZ4yygTjLs2PIfFVZuksR9l14o+SSQ392fh\nlrneQaN+TDMM7TTsB6oyPJBKKQ0oEpSG0TbDg6IksqN9HleieHGTeB5BZ+86je46Wfbzd/dx7u/7\n6RQK+blk8aiEE2zrSUnHOupC4cSi/cPwSOLmuFvFcAyO2XCisecGbd/18rG/KOLYsypY9ILGXpqL\n0267iQikJgFF6h4wXMU4KF3s9lWO6Vx/9zqzPlwBefKdk4I+PiQlHYicVLqrpWoc4XdQL6EYsLlL\nRUKjlMKBz2s4SFqUtGYoBvEjGBrXecnXiuTPe5jZL3oYlQ6O9EZekjaRkJ9A55rwYy8Ffu6uEpdS\nI/tuSb4rIQHDyRwtQK5yQz7TsE91ObqlEYjHqecXSeRjpoJaOqKmntWwqRsRn87QGxGB+GW4xyiC\nOPNegtttfPA5Aam+7UZE/mc6lSJ0ojE/tedwAtOQO8Pw4nqqRW6v0Cs9aSxWm9AB+a4qwxKGtibd\ndme9D0gZ2lesr6pP9EZmm/iMKhCJbx864/EdUsY+dLtZ9Kpmf9EWpFvf3Ok7jqJeKhlzu5zSH+1W\nuu1OWxRQCAoYum+oxKK2Hfarugdo3wDDsaLjJFqAgLVj2xcxzbu2YG5U7WoEVIEexQDGpR7+dyMx\nw2srR0ROTj6an4d5OZ6vi836Kw5nMJwYURkqZjNMJR3aYEgSVHM0H0pTqiLOUE6OH5Q06rejdg5K\nQpRS2CaWT4/tm9CpSXejI6Rz6Jwg+RMp9Mc5h26bGyg3LJ5GpwLdjHKwlYZobu8/gqFUSAO42spo\nj9JbCNh+JQBvt99J5I5/utgpMbn/j4br+9dNB+Y7TyL3BbaWBnPijJFTI6AKorNgNYlnyothepds\nGA6sHSRj+Ud5cHB6eUxDA7ASCCe3qouqOuh2PPPn9RKcNJRU6N/CnTGth243sw6wMmhXcvVT7SUz\ndCrVWZSDo7Th8CjDDwH4WB//eSj+NZ9Hd6/1XX0ZR1Eu/jrZl3M5OjKiqnVA/u9HMaazn6h20QUh\neodKKMvBcxIHJUhV31yaUe9sf9eaRt+7jgMnCl0o1Eak8XThcWLUPDeCtgs2gkh6cSJwnwhYPN1N\niMjHBxLBAcX//KzQcnRHxQctoXffnJO40eRgee4nopdjUU2hUyL74qzkR/LhIObkYj2oAnISsy2c\n3Grj0vqSCFkmd8x41/OFfZxT6M6oPQ7gn13UnaanXep+dJLQg309SC4n0ZEQ60oVi8ZvGsRJfJTE\nSOzah7DvSjQ6+Q+jU+tIMLRvRYZfJQItR3cqddzUttcVSkaq7vE9uUqo6aK2LhJNAurDxsTJyE9n\nHnwgsQxNH+WnO1FKHk6QKvrrSWk1WqsNgmloV1lGWe2JSHLjrhaJhrYPYGjvIFHoShtNDiV19XOi\nDYm/CqGG/v3oJKNT6BwDH5C2HkaRukigSnYkUU5atpn9wnaxDVTLeGxDby0k4bJ/XK3dJ/mpXYw2\nqkekn0h87BeiZuRdsvB5ZoDovfo4mqeGedmzkTgRmgpWQeSIWLPXOCI7zpgNqSYF1dI7KbmUQIlC\nCdHVKoarv49Ofrc/8b+3mbtXnHj7grTR4OVuFyRP/h+77mFJnull8fxO4lOCJgmxPN1t0/7hpHdS\np0GZafdJfKqjpzH0qVHpRqUa3bVSSY+/nKGXrGk9xha3MZLQMQT77G2M1LVo7K6HYOahEVAFUwjI\nw6dKS3xORJPdB0yk88PCXH/X/Nw+odIQn+mVo3ymOzBKLlpn+ulEkgKfA0PDq259sz4kMp2gnMS0\nxShJKqEyDU+RK7mo8yXrrpNcVQruopFI1AgOa6NKcNq/JCy1yankQ+LU0/QqfRHahxFB67N5Cxnz\n43f2a2RW4LvWHdRoUfLFqLYgj6HZgCZiCuOr2AqUQYHKd335Y2JxtGpxZY9sRJ4n81UyY9l63IID\nmLYZ9+FZqeQHDLeifbVmmbrbRoJgWSQlGqnZHl6bQSPvDJ0xXf2DdBJTFaJaqGqf9g+vHYnqqdvu\nBFVM9hsJhg6MbvQlaTJPXmSmvkJLGEo6KsHqd2DtDqHaaPguosVIyZJQ9XtM1YfF8/EQ9ZGmWxT2\nrATkKtA8cTRSlZw8PJ9o5YoGQ20Vi+B5jklLHNA6STVf2nB85VXJKGqnEp2qQ5rWfVN0suqJd3pt\nk1yYJ+NQ5aR6Q0lJJTrmy/KVhH0Hke1QFwXYM0IJTp0oVQpTSZAEOkPxEaJjpNdR+1zL47utqfoq\n4biEos+njNuxMRbNBa/nvIW7SUAjcAkk0r0jiSVKH0k7sPBamA8YLT/6DKy1H+hgc58SHcgqKXAi\ncZJD0rg6dlCeKynoBGAchulRhWUJOyR56GQ8K2n1GetNHx/+5I6eL2Ma9UrWSepSB/NcwtBIr5OY\n3xmf5Mj//CEAtpn1Zb2YB32G1A7H+HrMwuvnYb4IROqRE49L5Z5PLU6EqD6LwJ6VgDxsHqNPXUmm\nGq+juLU6LI08QxDuer2u5JwEvhOjUgpVEG6j+1GAmuRI2wINxhzYbsdQYlFjLQ3InJj8qR/1IVKp\nge1S9VF9j9Ruo2Wy7Xq0BBhKOzxLpq4FOlHdnkTpBxi6LWjbEdTNodKwE5KPIVU7va99THp+xKwS\nZxFoRugKnIB8p0kxTz2qqWm62jG9G/+AoZQSlRfBVR7fmRlLG5FlTW3RrXAtRwlR43CC0yCtB0Q5\nGd2juqZuqA/QiqR9Up4vyzNKMiQ1Gs7HVC1Vg/R9KAmyPpTktB8oXTENMFTNauoV+5PlaftVOmNd\n/b1oPqrOAmtJpjZua9B3EEnnU8Yn0VSwifDTwQ5dYWrk489UFZiqnrmqxTL0s0tNuoujA1OJQo9L\nLMsfMFTF1DlQDb26khN85l7W9BPyOrIP1W9IJ7Kv0JzY6kmtZKk2I5ahbVNpikZj5j3DsA9oPGYb\nuUvH+lG90zAlH9qomDf7RN+F+mqp9Me+gDyP1OhIWiYxKgEronGrY4VlLQXxWHZEaIuUkpoEJIik\nGyBWtaamAea/MF/5avEj0dlVG1eRgNjfRlfVaOX13a6xbXqtm0oLvtpruVS79PItlsPy9c5rqjwz\nDI3RrkK6OkhyoTRE9ZP5KnFpH0WLhdbZJRS6EvBIjPZZJEV4fX28eJxIRVJj9grWvhuFS2S62E0l\nlajeY2gqWAUppbwRvwaiNrnnxR0jNB80/oL95StpuO+IluFGT5eonIhUtNefwPFJqAcsgdjO4Gqt\nTpiaBKjp1YCtKz4wVJOU6NQvKFKH1SDuEgnzpaSjqujM0uv7YzuVPLU92vcRuRDRxHZScfUIFh4t\nEjXSiOyS/swxlXyARkBV1E7Dr6dzp2Bs9arFXY+OremiMvnd1SQgVtW0XE5KGpSp1uwL4ng6nSSQ\n574KE1pXXvnBz36cA1hrR1L49R/si2jLuqYaq3SgEobuqvmultqsqMZF7dayI9KujcWadLvehYx5\nOfHMy3Mj86LZgOYgevneIevpoFpcrpBLWDvhozppXvuCuFFa2nJUMmL79ksaXcmX5DtXfcj3JQx/\nu9zL1TBKH67iMZ7+9zYtY63NR3eK1LYzQ+zzQ5xFuQeaV23oVjxtQa76qLTDutbGg0pPy5ZeDwPz\nuf7X/FRCjDYP1E6l9XHC1PyBYf+7BMm8atIWLP6iF2XHniWgaIXW/5EkwpephjzPw3Vr2PfIJuBx\na2qM5u0G63NB/Jl91zr7TouGa1olJl3N/bO3ywlmGcM+1fqvYK1dhTYbr5OqQyRS9VxeRicFXY3y\nQ4XaBv3ZHDdqsw8OoLPluOoVtXVF4uyX8rRt2ne6k6iI1DsnEebD8ef2uwi+Exd9ZplR2dH7XCT2\ntApGTFF/5qlGY/p7DZFq5gZFxvMB5pPZVSpgqBrUBqo67yGI5/cJ+Yl6d6bz+unKHtmploNwTauT\nXiUNTkSqRiSOx1AIyaU+Ta+qFeE2JA3XK040X/eU1jor0av0Ehm8XdqI3n2k3o6Ni+i7QqUrL2sR\naDagCsYOo/pg8f+MQ0Ri8Tzi8dWGA5UTKTqXVcsjKleN0lq/iCR0kiiheBlu69CdKC1r3uSKiH7J\n/vvWs9Zdt77dSOx5+DN1PdDfkl/C0PlyhmJnItkeRvkdMN6mGBFkRCKRGufSRfQ5SuMEGOU3ZnP0\n/MdIx9/betFsQCOI1C9+jjrFX7y+FBeTPX+F7iqpKgAM/Uz05astAKgPCq2P/rkNStUhFf2VBHXi\nqo8Jw9SLmuGuIno52n/eP6p+8PO5IK5KY7TneD9SFVPpTz2kD6H7za8D8szz5l3XVwN4eZ/3GRSD\nPN8VyySBOfn4Zw+rLX78rjdW6k6lqtZOID42fMFz1Ma79ulWoUlAPcakmJp6xf81/xHPy0XeKD+i\nlk8k1ehEY/7zVpaaiK/PamqgktM8ydHz1bpS4lKiiyaT5ql3DakaRsO1qkr8zwnL7wfR/bDiw33Y\nOXRXuB5Gd2OiXtVxBN1FYtydowsC+5gOkVF7WfaY5OmIpGt+5vPa+3GpyvOJ8vN8ovpsRPoBmgS0\nLox1cm0Fq60QOgD1BfpEqA0SVxlUIlGDrKs8q8Fzrf88glmyz9puTriaijEm8alqqOqKSnc6IbUu\nsM/uvxOdrXLPZa0LUK5m1XSn0f1U8wF0pMPfQXsC5YZE/U0zvgs9+AoJ1/8KfwfaVpewx9RW3zXT\nsjRdVP6YFOSS/EbJZyqaBCQYk3QQPKulHROra/lMWZlqUoVO5lWLX8tLP6vNKLLfqKTheboUw3Dm\npXVziQ0YlqlpmW9EmgqGq4cyy/FrSJbkuxMJy70Wncp1V5/fwyi2n4vR3Wro/eD1j3bPYHG8r/l/\nbNHwvvdyXfKMbEEeVpNmYek2gmaErqBGQIrIWYuohdUm+VSHs7EXH01EneScsNHB2mj1dJsMRp5N\nFdEj4gGG91drGXqntKZ3cop2ympqm5a1hKHBWSfpEobnt5Ysr5eiU7342/bHUH7dVA3cwJDkIM+U\n9CKCYBu9TdEzfb7esUlMVbfXq6bV0AiogrFt+Ehy8RcPxC9kTAKp6d8R5k3+2mD2tF4Hhrv47qrf\nmETlEp0+j/JVAvHdOWBt/V3S8nJqRM94NECrXxTD2UaS3wzxuTV93xf1+TxmcYDhhoG2hf9JsGPj\naj22mxpxRdKUj7d5BDJv7G8EjYAqiH4Vo4baCj8Wr5a3b2UDw4Hi2+CR+F67D2fqqjVvoNXa6KQ0\nbyKNla9SgX7WOE4ISkSuwvnEV7sTyYj9pn5PkR8MvzvR1ghC6+DS1xiBaD9G6pQuCpHEE6lOis0Q\nymaJh3jaGaFTSheklD6TUrqj/55SSm9JKT2QUvpCSuln+/DXpZTePC+/jXRyLY2K5LV4KpLrd372\nk+XRoNTbfrsaAAASK0lEQVSDlj55Vb3wiTtW50jaWJJnOiAj8o38cLzeXq5OMK1/TRpwApyN5ENj\nPPsL9t2lHuavqpVKVF4HYPh+ST4uhXg8faZjoLbVHRGYpvd2M39/nx5WGxORdLnVBOFG752ONwD4\nAspxn9cBeC6Aq3LOs5TSkY1kOiatRCutp/NBVVudnHz8eYSoHlEdXGVyCasmxkeTkOlqaZT4vB0+\n2CPVLoqjbfM+VSLR9NyFWrZnTpZRH9ZUFp/U+ksZzEulEOajkqumnyd9aN2jOkQSZU0683YQtUXK\n6xM9W4QkNIZdIwGllI4B+EEAvyPBPwng3+ecZwCQcz7dhz+F4S8IjyLqhJo/iofxvw9KJQXPs7Zi\neZ1cFWF4bfCpSO/ljCHKS7fHXarycigB+MrvpOR9OJO0sLj+XaUSrUN0587YLps7S/qOlsKJByjv\nNprAeibNn/nCoOEReWtcJallCYsWxEj68XJnWJuWcWvPtgq7hoAA/DqAX8Kwf54P4NUppbtTSn+U\nUnohAOSc35tz/tUpmY4Zjv37vBcTDcoo70hV84E1VXJyqYKf56mDwHAi+aRflb+aAyUnhNc5kmii\n1ZZx9GqNKVIA/3taxq3t8HlYrT1eR+YZSSP+kzpALA15/3p9vE7RuON7mSEmtOg9+2Ll43s9KtBW\nkMWuIKCU0m0ATuecP22Pvg3AuZzzDQB+G8DvrjfvaLKMPffPtTC/IlOf610yPtlUuogmD/P2AesD\ncYxUNWzeANZBz+9jE0fjRIZs/tf21lZn7RsnNyc1l4A0TKU5jTN2jakTXUTQLkFFaVyqqEkpNRXN\niWhMWtaFoPZeowVyKglshWS0K3bBUkq/AuCfoOygHgLwfgA3ALgl5/xQSikBOJNzvrCSx9fl64Eo\nztggiMTdaHWprZJ+sZYPzmjHi/AJxTAf2MDaerpfkEsZXlf/rGU5WbI8dzKMHOy8bboj6GpmRCYe\nV9vFevkuo9aNE7R20Fc/1/o02q6vvd8IY+OIbYryid7Z2HiZV04NfvPBAgjnr38PIOf8rCjCrpCA\ncs5vyjkfyzlfAeB2AB/JOf84gD8AcFMf7W8DeGAkj2fxT8N9VfZw/V5Tx2orE8OjQRWt7LULw6Md\nD/0e+d8w3mqQbkzNjERyF/sjVcZX+GhCux2HaZVkIrJcleeEqzmal7ZR0/qxCWB4jaqTrn6uGZ8j\nKcj7sLY4aNjY+IvSjZHP2PexODXpe6OozTnFbtsFc7wVwO+nlN6Izuj8L6YmdNHYV5hoYESGP40/\n9tzzqqkjmsaNvZ5P1IZavXzXyutDuCpVk7giqIThhFerayQdeRtcZYn8dBA80zYoMa1YfK0jn7sd\nyYlrTGJ0aW0MmnaMVKZI2sDa9+P9r3F8d3De2NgK7AoVbNGYchSjpqqgEsZwYDgxaoN0XrlTyovU\nnbEya22KJovGJUn4pGP4WD3Gyoom8Vg/RQQ+RQWa8i5cRfP6aHs9nYeP9TOCPLR8l8Q8z3mYKknp\ngjImoW0GTztHxK1ArQNqK4qG6cocrfDRgPfV3Ovi8ZhXFL826dWWovXTMjSNqkFR3FV7puFKTlqH\nSNLROkfSYhTm0PJdItI4+j+S3FzdnWG+R3nUn553TRphP0Xvl+126dGfe1iEsfGqqEk+Wt/zgT1L\nQItg/RrZ8H+kT0erk096V7vGVuwaMfl2sk7YeariDPGk9TB3uHQVhXGiz05qNfVun6VzVSfqG62L\n96tP9tr7110zl2wj8vB3HZGg1q0mjUUEFS00rp6PLSCar+dT+x6Nt63AniWgMczrlJqRERif2JGP\nSbSaOmHUylLjtJcVba+qQbZmz/Cyxganp4lUC42rRx00r7GVmIZpz1MJIiK+KXVUUtK0Hs9VRu9n\nLWfKwjY2Rvh9LL2Tti8EtbZHquiU8qK8FoU9S0BjKlG0CimmGBcjKSOaSC5t+ODyVTVSbcbUyLHn\nGi/6PC+P2qAcK8/tTe5tHZXh1516vcbqD6ztT5bLuH78hGlqUqiW7RJHVH8PVwL1eo591/Raz9pm\nhSLaKa29v3njf5FoRugNYuwFLioPXeFXUfcn0gFdu1Re40YqRc1p0EnQ6137PAUR6dfaqHFq4ZEK\n5O0l3E4W9Yv2veYf5Rf1UUSOUyQkreOUxW4jGHu/i8IUI/Ru34bfNkSTYb2Tbwr5aFlj27TRLoyr\nJ9Gq6aspLAwYr+e8Nuuk9f9eJ2Dabpamq+VVqz+fjdmgXC0G1qo5QL2/NCwi+0jCqKmfY4vIGPFG\neTq5R9IZsVWkFJXTsACs92WNvfxa3ppm3uBnHFfxgKHKoWqET1SFE9k8laxmi6lJAV7HSG3R/xFB\ne3iUj4dpudHB4akYU5e0XlqeE7KrfPPUpikqqOYZOW9GC1CUz1ahEdB5xpSXPEU/H7NVaNyxMqKy\nopUfiO1Xnk+UPqpjNEkie4tPMEp0Y5NsbMLyeS1ORGiEOiy6+gZ5FiF6D4zrkqi2ueYUOpbnPAmz\n9l/bcD5JodmAdhEi8XssLoL4tbRjcdZjt6jVs2afmYoxyaZWlk9GVz2jybqevvK4rgqP5TGvbVP6\nKlIfdxLalawV7AYCWsQkrT1bz6SoTc5aGo87T1WbijHCQeX7lDJrEpuGzeu7SGKLyouufhmrV0Ro\ntbRTFo31joHNonlC72KMie0RahND86vFi9JENoKayB+dYq9N0o0O+sh+4s9VffD6j/XdlP7QuDyc\nqnH8PugINTWWefj7ishn3q5RZBeKyovIajvIoElAewDzVsuxuOt9zjgI4m101VVpYD2r+JgUMJZW\nvZvHznhNUWfnfa9dQEeiW++B1qmYWvfNoElADQCm217mEZOnnWd09dXaJZGxz9Hv0dfqwnKiC+Qj\nScnzZH5+/Ul0/Ui0He91c7uQP9ew2k2LfFZL5/UaixdB06gz6Pm2JTUJaI9jERJPLU1NUohUwyl5\nzovv5U2VIMZO6NfKdHuXxtuIhFmT7DbS7s1iUfk0CahhLuYNtPUSxNQ83TbjK3e0kk8lyjEpR/ON\nbg1wY/K8NngdonIj21St7h4n6qeoLl6HGmrPN7IoLAKNgBoWgprRM3Kmi9L5hI6+A/HBU5/kY5N9\nzJAd5Tsm/WgczVdVyIhsvYwpqNXZ61p77vnU8j/faATUsBBM3fnZaD58Fh28pL3GJ2lESvq5Nqn9\nlgFNMyataL5+t0+UTkmjZg+rYYpqVnu+kyZ9swE1bBmm2hKm2Fr4fCM7X1FdNqNy1Ow1tXhT7T5T\n6zKWbr32m600PDdHxAoaAe0dTNn5g8UZI46xnT9Ni4nf54VvBFON4FPrtlE0AqqgEdDTG1u9nTxV\nAhpLR/i2/lQJbr2Y5z6wFWi7YA17EhvZuVt0/vN2qxgnutUy2vWaonaOhUc/7bQTsJPq0tCwJdjM\nIJ+3W+W2mHnhmq/u7PmO3jxpxa+1Haub12O7drwiNAJqeNpjHklMSatx3eN6Xhm+w+WX0s/7hQov\na148xp0Sf7sJoNmAGhq2EFthj3IjOclmzOVho3arzaDZgBoathBTJk9k99nspHNpiX5QY75ENd+l\n7UYjoIaGDWLqFr2nmZdu3vd59Zl3a+ROwk6tV0PDrsNGJQtP557c693VG/t9tql5nC+0X8VoaNih\nWC+hLUK1Ot/qWZOAGhp2KOadi1tkvttFBI2AGhp2KMakkc1IKpHLQDsN39DQcF6xE3bDGgE1NDRs\nGxoBNTQ0bBsaATU0NGwb9uw2/PXXX7/dVWhoeNrinnvumRSvnQVraGjYErQLyUaQUvp6zvlZ212P\nnYDWFwWtLwrOR180G1BDQ8O2oRFQQ0PDtmHPqmANDQ3bj10lAaWU9qeU7kopfTal9PmU0r/rw9+e\nUvpSSune/u+6PvyqlNInUkrfSCn9guV1e0rpnpTSz0nYi1NKf5ZSejCl9BsppdSHH04pfTil9MX+\n/3f04a9LKb35vHXAsP7r7YvUt+nBlNLnUkrXS15v7Pvi1RL2UN8X96aU7pbwN6eU/q/kf2sf/ndS\nSm8/bx2wSUTt24nv+XwhpXRBSukzKaU7+u+1cbTQvthVBATgGwBuyjn/TQDXAbglpXRj/+wXc87X\n9X/39mGPAfhZAL8a5HU7gJcAuDGldLAP+y0Arwfwwv7vlj783wL4k5zzCwH8Sf99u7HevngVSrte\nj66t6Nv+EgAvBfBjVsYr+zxusPC3Sf4fWnzTzhu8fTvxPZ8vvAHAFywsGkcLxa4ioNzhif7rM/q/\nqg6Zcz6dc/4UgG8Gj7lFmNEJCJcCOJRz/kTu9NJ3Avh7fZy/C+Ad/ed3SPhTAFif84r19gW6Nryz\nT/dJABf1bdZ+2AxWAHxtk3lsN3bcez4fSCkdA/CDAH5nQvSF9sWuIiDgr0XFewGcBvDhnPP/7h+9\npVct3pZS+rYJWb0fwN0A7s45Pw7gOQBOyvOTfRgAPDvn/GUA6P8f6T+/N+ccSVfnBevsi+cA+EtJ\nfhLAc/q2/xm6vnivPM8A/jil9OmU0uut6J/p8/9dqik554/nnN+w4CZuJaL27cj3fB7w6wB+CWvP\np64ZR4vui11HQDnnb+WcrwNwDMBLU0rXAHgTgKvQqRKHAfybCfm8I+f8opzzr/VBkdPUjrbQr7Mv\nqu3LOf9K3xfvkmcvyzlfj051++mU0iv68N8C8Hx0at+XAfwadidq7dtTSCndBuB0zvnT9mjdc2oj\n2HUEROSczwD4KIBbcs5f7lWLbwD4T+jsGevFSXQTmTgG4JH+81d6dQX9/9MbrvgWYGJfnATwXEmm\n7YvyfKT/fxrAB5hPzvkrPfHNAPw2NtbX245K+3b0e94ivAzAD6WUHgLwHgA3pZR+b0Fzai52FQGl\nlC5JKV3Uf34mgJsB3C+DJqHT2/98vXn3IvfjKaUb+3xeA+C/9Y8/COC1/efXSvi2YQN98UEAr+l3\nw24E8DWqG0Hez0opfTs/A/gB5sP8e/wwNtDX242R9u2497zVyDm/Ked8LOd8BbqNmY/knH98EXNq\nCnbbYdRLAbwjpXQBOvJ8X875jpTSR1JKl6BTM+4F8K8AIKV0FJ1t4xCAWeq23K/OOZ+t5P+TAN4O\n4JkA/qj/A4C3AnhfSumfA3gYwD/cisatE+vqCwAfAnArgAcBPAngn47k/WwAH+jGHpYBvCvnfGf/\n7D/0W7IZwEMA/uVCW3V+ELYvpfQp7Lz3vF34/co4WiiaI2JDQ8O2YVepYA0NDU8vNAJqaGjYNjQC\namho2DY0AmpoaNg2NAJqaGjYNjQCamho2DY0AmpYOFJK3+qvcPjzlNJ/p8OkPH9jSulcSunCkTwu\n5dUQwbOPppT8hP7Uut2W+qtLGrYfjYAatgJP9Vc4XIPuSpSftuc/CuBT6Dypa/h5dEc9Fo0/RHf0\n4MAW5N2wTjQCathqfALlVgGklJ4P4CCAX0ZHRDX8AwB39mmemVJ6T38y+73oPNWZ3w+k7tK5e1JK\n/5l3O6WUbk0p3Z9S+tPUXcR2B9BdY4Lu3Nxti21mw0bQCKhhy9AfE/k+dGesiB8F8G4A/xPAd6WU\njgTp/gaA/9cfhAS6IzJP5pyvBfAWAC/u412Mjshu7k+23w3g51NK+wH8RwCvyjm/HMAlVsTdAL53\nMa1s2AwaATVsBZ7Z31P0V+iucviwPLsdwHv60/TvR3ze6lIAX5XvrwDwewCQc/4cgM/14TcCuBrA\n/+rLey2A56G7RuJEzvlLfbx3W/6nAVy2saY1LBK77TBqw+7AUznn63oj8x3obEC/kVK6Ft2VsB/u\nD4LuA3ACwG96egD7LSw6tJjQXcQ2UOVSSi+aU7/9fRkN24wmATVsGXLOX0N3J/cvpJSegU79enPO\n+Yr+7zIAz0kpPc+SPgDgCvn+MQD/GAD6S9eu7cM/CeBlKaUX9M8OpJSuBHA/gOMpJebxagxxJXbh\nNSJPRzQCathS5Jw/A+Cz6FSv29Fd/qX4QB+uab4O4P+QWNDdwngwpfQ5dFeH3tXH+yqA1wF4d//s\nkwCuyjk/BeCnANyZUvpTAF/B8L7qV6LbDWvYZrTrOBp2JFJKPwzgxTnnX95g+oM55yf6C7V+E8AX\nc85vSyk9G939P9+3yPo2bAxNAmrYkcg5fwDdhWcbxU/0hunPA7gQ3a4YAFwO4F9vrnYNi0KTgBoa\nGrYNTQJqaGjYNjQCamho2DY0AmpoaNg2NAJqaGjYNjQCamho2DY0AmpoaNg2/H9IzAG9Ei5TqgAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa60d022128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.subplot(projection=wcs)\n",
    "ax.imshow(image_hdu.data, cmap='afmhot', origin='lower')\n",
    "\n",
    "ax.set_xlabel('RA (deg)')\n",
    "ax.set_ylabel('DEC (deg)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we get the plot with the x-axis and y-axis in sky coordinates. \n",
    "\n",
    "We can add a coordinate grid with `ax.grid()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G9+HRNVmrxB4s8LSK++tE5rNCVFzXCcCybp4TEKwV8eaLa6tFGaVnsszLrna3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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa60d022128>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax.grid(linewidth=0.3, linestyle='dashed', color='white')\n",
    "ax.figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We add a white cross to mark the center position of `'Cas A'`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G9+HRNVmrxB4s8LSK++tE5rNCVFzXCcCybp4TEKwV8eaLa6tFGaVnsszLrna3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u4O9mQ7ppF87a/t6pl63kjssmXYa79qW38aD4D6eeCzVq2De/eyLd8Nb50DraLXgopIzzxH4n1e\nVEfLeWDSVqgvB5OPlOZSStvVXAppO6ntu8mrWuH2bGzLMUDBtezYuZOuHTtWnTGt5a7VhVn9lEBb\neXsvZgvCmPReQe0XEcvB+H5Xe1s9n6fUuPWez9bQURevrY19Bw8mF97N5ISaAGSojPUto5ToZjvT\nrxZerLLA5JWKJK59mXb1tKueHbx+oHtx7ey5c2RZtsqFqC7W41kTSCKa7v2g9yAC9VyGX7mLwx7q\nRTZxXtoCIkdC5S+FsOf+xJVYcc/mJ0dKfapaE1j5T167xvT0dJ2SWFyN5cJsfymexER9BFGiowUl\ny7EonR0fKbBXHTF5eW5FSnhMPP9v9XA+TGVbmp+f59y5c3XPy0TEO6EtC0ApbiM12VPci+dKNpJG\ncVOd6PU0qU6x3JbiWstHarBpYsDaQ6j0fNfu3XWTQ4BlrWKaBPq1mnh+Mll9ggUcK56pftZPyU5q\n5Wu/AmItN/r6hW8XAYQFc3EzllsR0Nq6LgLtO3aws62tTjRS29ld7VXqwUN1stYwhXsRq1bywzyH\ntWPHjz/b917E8vFTXIu3nHpqrVTo6OioC0uJi3dKWxaA7OQRbbQxUvJ6ivyEbAROZWH+medgNHns\nymhXUN1bvUPdSlqrNVRw253qUIg39v1q1HMfFkT8ZIWCG/CcG9QDRZuJo3eAeuWw6uQ5KAuKFpCs\nBREXlmUZM7lC3nMbaj/7b+tugb6T+rbxICvy4w/3TGlIxLM6Jb8wpdLbsVVNPPPzoFaprH6a2S+W\nm0lbFoBgrchQJlJtlMriWpbZ/srqZPNqTcRNpRW7r5+d4Nb72HIhFeDq9eurE97qLjQJrdUqNQkU\nZsUzD7Z+8vt3EqdmdT7eL8laebzPj50UOmgNii9pWFO81vQUNzkzO8vKwsJqXcvGgzWze3HNbgbW\nc/tv87Mg4i2i9r19fVIckwc2y+EpzHKkKU7G1m1laYlrExObzvF42rIA5EHArxR+BYH6VbYsj0Zy\ndRnb7ePaOvhB6usimk/Er7l7W2cNwiNHjqwBLpvWApNl+f21fy8PMF5ksfXXsRt29dbhX75Omqiq\nm8CrRqGn6iR+RFCimn0Huw/LK7X7envp6e6mg0KXY+Ol3tVyfW2mPPtutu0sJ2rJiqaee/JjynKj\nvt88eb1j6lpl2rK3tbTQ199fyoFtFqVUIVuC/KS0q10KIOxK4B3I7HNvqWi0elhrh8hu5LTAU2Y1\nqbnnfqWruvBll3bs7FmqxG99kYin+ngOyK76qpNvD1uOFbdsXFs/Gydl7VO4yrO71MWB6esc500d\n7OZU28fasa+2mr5+HRYX687zsVY1Enmo3rYuZeMpteD5uKkFzfeZBavU+Er1Qyqe5a7sWAFYXl5m\nZqbw+LpbXNCW5YBSVDaB/HMvRnmgadTpNr3Is+m+rEZ6Jlg7QC0w2Xu/zwhghXp/nZrLz4pBelah\n0MP4CeQnhtXVpADZW3wava+f1DbeMsX2Bz3zH4JU+dY6JVDrBKpZxkJ+OJtVZi8TjwMZothqAfV+\nR/YLrl70VNmpf9s/KStoqm99Ws9d+jipsenr5+9rtRoLc3Nr9HebTVsWgFLAoutUo6Q61a7+KYex\nFNkJakUBKFcWW10AJrxMjPNigtdB2UG1//DhupXQ6zQgbUGzXILCvYhoy/GKcd8+VvzQ9XwirjUj\nW6dG2452h7vSi5PTMa+vpfD21vt17d7Nzp07qVBYsx4H3pDnPUmxn0x9pTKtwhzWto2nFCinuKFW\nE1/taa2Ken+fdyNu1FNqrLa1tnLw8OF1F787paYIlpPtHL/SplZl26lW/GkkvjVim/0gKFsFPXfj\nOR3FT3FwNm/lP3rqFEv51w/KxCW7xcGKBV6kS1nfbL0FcCrbfljQmvcx6fxEsptIxfFYxbX14rai\nnEQo6Zom83ClGQB2TUwwvbS0ep60AOZ5ChHLnrNdMeEpTk7vnBoTVqck8uBjOU57nWqf9cS9lFhI\nIk/R/OIiZ8+eLQWtzaItywF5atTIZSuYFwNEfiDazvaT0ubnAcxzBZ5N9zoCryfyq7EffBWgu6dn\ntSwrRvmBZ3UoqXwbcXxKY50JPXfnxT0/0UTWAlUhDVzec9nWBYqjWW26cWC4vZ2dra30U5wxNEO0\npumzP3Zv27K5LuNsU4sR1PdxSizz4yGVzveP56QaLYaevAgN0NbWdlfBx5bbJNJimV3N1ktbJhKl\n8kmxyY1EKs9dKI1dIcvEQA8cNp9tLS11WzU8qCqujSOSBQrqgc+/p7ciWd2Knai2DmXm61S/LFPP\nGc1Sf/SGFzvVFtoyot9fbtvG3mqVtwOvIn7AULvbZd6fMnnYNrXioj8T2pLvg9SC5LnvirtOjcWU\nmOV1Qz6u4ljSeGrZtq3u08x3i5oAZMh2klcIl3WgpbLVzK6Onj1OTaxUfRoNOihWc+tj4ye1L78C\nXJuYqFvRU7omcRo+H8sBKL637Inz8e+jcA92VuyzXJF/D2u5gQJ8LEdVo/5AMZVBou4A8zMzfHp2\nll/O4+mIkGtEEW3MxPecr+17fzKjvbbilI/jgTglbqk/vOiU4lQ8B2YXAS8irkm7vMzY2Nia+m82\nNQGItaAB6U6xQOIbrmyi+4HjOR1/7TmIFJh4UU0TFsp1VWXXhw4dSiqLU2y/5SSsktfmadN5scRv\nyLTikeJ5Ea/MMthoAlmHSAtMokUTT2XUgLaeHrq6uqgBzxHN+fIJGqX+iNrUzntLyyZOirtN9a9/\nt5p7ZvO26dfjfHVdZ+VK5GspbNtGf19fXfy7QVtWCQ3piUzi2oallIfKq5EC1cbx/jN2wvotBh5Q\n/KC25y37ejeqg64vXb68Btz8Km3z8hPDihplg1r5+Hpq8tgJ5f1RvCiTUsSKatQriNU+9khZgZPi\n2bLmZ2ZYXFys4/omTN4qz09k/Xsdl90h78eaX5h8m3oO2gOZvU7VJxU3NR58utX7Wo35Rb9EbD49\nVBxQCGFbCOHvQggfzu9DCOF9IYSXQwhfCCG8Kw9/Zwjh59bL73ZQvVEHplZrH8eLFXagedY9JZ74\nA7JS5m0rCjXq4BqwsrCwZjVWntbTtkz0gHpA9eVVEmF+Qnour5EI4j2SU/lYq6TlDHW/yFpwrwBz\n+ZnQliNsdXHKFiu/eZdEPPvMjoEyU7d9P89d+jaw+fv+9GFlY6KOY6/VmJ6evusA8VABEPAjwBfM\n/TuBg8BjWZa9Evjt28k01QjeZO5XMJvOigNKm+ro1ABejxVO6Y/KRDTLhaRAzq+AFWBoeHgNt6F0\nXv+iON7BMQUcfhX3+fs4NsxPNKi3PFmxw+5Ot+1h01oLol8EbB37+/rYuWtXHYdr93Upr9R1ysnT\n5l820by/lOU+ffv6tvGLA9T333ockif7bNu2bTzyyCO3tUjfCj00ABRCOAB8E/ArJvgHgX+TZVkN\nIMuy8Tx8jvqTQxtSqhFSzl2plVz/XmxSmB2kqRWybEVKgZrCPddg80+BUyMaGRlJ5mUnhueqfDni\nAPzKnxLrUnE8l5FqH2/RUR2s2GP7oExk8gBixcKJiQkmJydXn1cS6SyI+clp96T5Zykwt/nZd8XF\n9T5YCktxVynux5dbtuhZwFteXubMmTOJWJtLDw0AAc8AP0F92x0Fvi2E8HwI4Y9CCMcAsiz7nSzL\nfnEjmaZYcUru11sNUoMylXdKVPMDy6+iKWuQLdNP8vXEQYV3d3Ym2XhrnraTz6e3yuhU3SA94G0c\ne7RFSqxqxHX6YzEsOPl392H+fVq2b6e9pWVNHS33ZPOy4Km6QL1y3dYt9Q6K4+uUGnfqlzLuNNXP\nfrHy47tMCRxCqPssj6/TZtFDoYQOIbwdGM+y7NMhhDeaR9uB+SzLXh1C+KfArwJfs052FYBKpUKW\nZRACIcuKQZ97BYvKxIfU6mPJbir1z/2ZwH6AlU0e3VvFc5k+qZHoZcN2dHWthpWtin6V9vE9l2HF\np7KJt5xI5+vg28c+TwGa54A8uOPCLGhA/BLEcggNOTZbf89BpdKk3skDbaq/bXybT6Oxty0Elong\nkWUZlfxrJwDVSoVarUYIgZb8ulKpEEKgtVaL52HXaqxkGS0tLVQqFQ4dOsTZs2dZWVmhWq1Sq9XI\nsozt27ezsLBApVKhpaWFxcVFWlpayLKMlZUV2tvbuXbtGhuhkLkJ9yBSCOHngX9B7Pc2ok/Y7wOv\nBt6aZdmZEEIAJrMs21mSx01dAu2vf/3ruXr1KgcPHmR8fJyFhQVecewYL4+M0NXVxY4dO7h8+TKD\ng4PcuH6dmdlZjh07xsjICO3t7fT19nLuwgUG+vuZm5tjcmpqNX1LSwuDg4OcO3uWXbt3s61WY/z6\ndR555BFGR0ep1WoMHznCqZERunbupGX7dq5fucLAgQNcuXKFhYUFhoeHOXHiBJ2dnezq7mbs0iX2\n7tvH5NQUN2/e5BXDw5wYGaFl+3b6+/u5cO4ce/bsYX5xkcnJSY4ePcrp06fZXqmw/9AhTp4+za5d\nu9gWAleuXuXI0BDnL17k4MGDVCoVTo2MsCP/MuiVy5cZPHCAa9euMTc3t1rWjvZ2evL33rd3Lzdv\n3uTG9PTq82prKwf27eP06Ch9fX3UlpeZnJzkyCOPcHp0lCzLGBoa4tSpU/T19EC1yuTEBIOHDjE2\nNsbKwgJH87w6Ojvp6upiYmyMfYODXJ2cZHF2lqHhYUZGRuhqa2NXXx9nz52LfbCwwOzUFEPDw5wZ\nGaFSrTJ44ADnTp+mp7eXbSFw49o19g8Ncf78eZaXlxk+epQTIyPs3LmT9rY2lpaX2TswwMjJkyws\nLPBoXlZbRwc7d+7kyqVL9A0MMDMzw9z0NEfz/t7R2krv3r2cO3eOvr4+lpaWVvtAYszhw4c5e/o0\n3T09VKtVJiYmOHToEONjY8wvLjI8PMzoyAjbu7ro6Ojg8uXL7N+/n2vXrrEwN8eR4WFOnjhBW0cH\nvb29XL5wgd179zI7O8vU1NTqeGltbWVwYIAzo6P09vZSq9W4fv06jxw+zOj589RqNQ4fPszp06fp\n7u6mpaWFiYkJBgcHmbp6len5eYaGhrhw7hxHjx3j6tWrjI+Ps2fPHmZmZpidneXQoUOMjo7S2tpK\nT08Ply9fZteuXSwuLjIzM8Pg4CDPPfccmE+vZVm2Izm5syx7qH7AG4EP59e/APxLE/6pDeaR6Vdx\n/z5c15VEHJ++0fPUz5fR6sKrifql/qsN6pJ6P/v8TW96U919lfXrXPau5O/gy2/0PgpvVNZG2g9X\nRjURT/+tJk6bCT9y5Eg2dOhQXT6KZ+tu2zvV9v59Gr0DJeludSyVtVlZ/zcawxXIqtVq9prXvGbd\n8hr9NjIXHwoRrAH9AvCfQgjvISqdv3ejCT1779nblLiVUvzZ+I2e+7xSbLuX672y1+eTeoeyeqUc\n4ipQp3RVman6NvLzwcTxrgReP5Nq30ZmaJuXF+1S4k6Zv4y13C26+ApfWVggW1mpy0f1sApgm6+/\nVtqUD1eKbNqy+HYMlOnFGommlZI43qfNpt2WZQQjwt0teugAKMuyjwEfy68niZaxW6YyhZ0oJWun\nzNU+fZlc79NsNO8yYPRxy3QVVmHp6wrx2/ApELDvoecV91zhdm9XGViKUk6GvrxGIF6mCPaKX3vt\nwc/e1wHH4iJzOQD5+ngwKntHu5j4clPKfJuX9a5upPfa6CKn+1SalO+WjbOSZWs+THg3yI+XLUdl\nDVDW2TbMrsypFT4FPn4193UpA5RU/DKLScqHKcVxAQznfkDVBnGX3TMbngKnMk7H1jnFLabCPNny\nPUdk49j/FGj472PViOcB7c43YKYmdao9fd6NFosyZb7eO7WHzD73YSlab2EVlXE+om0hcPjw4ZJS\nNo8eOg5os8gPqtuhRlxJiiPZSFw/+f21jVfGiXkRwItR9tmJEyca1hEXbuvry/Crqg9LOUqWrdAi\n6+ejeOuJYrZc/1xAkDpWd2JiAmq1NXW1177d/VaSMo7O1r+MC7TvlxLNfJgtM1WPjXDOUN92ul+u\n1bh48WJpms2iLc8BpWi9Rinb/AeN2eNGGysVZn9lXJLIs+s198ynXzb/qkt7e3vp4LJ1s2FlK2cj\nUc5/5O4AAA+zSURBVE+gYzm01OT0JNHO52n3e3ndjC+3rI56P6VvrVZXfV+WE2lSi5YH+fUANfUs\ndd8ovee4/d7CsndPgWSj8lZycTSV12bRlgWgRiJRik22tBHlYoptTk0k+1OZdnCVcUIpAPNUW+c5\nEM3lLs1G8ygblI3K88pZ722dKsMfd+rrtR735ttT5XoOo33HDtrNt7A8Z+q5MF/vsvr7cAugvp6N\n7m162/9lxgpLfjw24mhqRF+i4SNHGuS4ObRlRTBRo9V3vVWoUdqN7CNOraipQaJJa61Mvp7VxPP1\nxAKAi+fPJy02qUnj69XoOpWORDm+Db1CGeoPv0/l26h8X2fPkdr2mL5xQ24aq3W1lqIysUr5p7ir\nVNtDY27R17nsuQ1bb1FMPU+NB1GWZYycOrVOrndOW5YDulMqY283SuvJ1CmAa2SmtXoNrwdoNBn6\n+vvXKJmVthHAsoFnti5l/5YzqdAYuFOcUooTSol2nqu1op3COjo7aevoSLaZF589Z5gCXm/tSnFV\njTiXFGeT4rY2mmeru09xZzaf7u7ukqebR00A2iS6VRm5UeeX5W3TNJLfUxOxTG+xOD+fFGV83fwE\nXE8kK9PF1BLPUu9RxoE1Ekd9eCofH1ZX7vLyqt5jI2J2WZ6WGvWF56o8kKwnNm1EBLV5plwVUuAM\n0Qzf1tbG3aYmAN1j8oO/LE4j+dz+l62QitOoDICZqamGwNFoI6qNnwJGm2ej9y7Tt/gJJlGz0SRb\nT8+RAjrdz87Ps7CwkGwzK4Z5NwfMsxSl+sFyYhac7DuXOYU2ytOLeuv1Uxk3CTA+Ps7dpiYA3WPa\nCKe0Hmg0ApkUMKUASvGGhofryvDWs/UUnI04nDLxJMXdpN6hTHSy+aRAxueveP7MIA90Pb299PX2\nrqlbWV292Lcet2XzW2+B8elT8b24Zeu2nq6trB42j4MHD5bUcvNoyyuhH1QqE1N8mE+TimNZ/ZqL\nNzIy0jB+JRG2kTr79P757VCZWOdpPVG1TBy8fv163EXu4nmgaSQOlh1NomcpriYFAgKWRnq/MjDU\nvS+/7D3KaGJiYp0Yd05NDugBpUZse4rW4wTKBl7ZmS8pLqSM5fenNpbFbSQSrkc1GufvxQdf/0Zt\np7ghhDX7n1IcjD2BUXHsJ6HLylrv6BHfXynwWY9jKOMKfXkpsPL1np/350FuPjUB6CGiRpO30YBL\nyfmiAwcO3FIdUuJfyoTvOY9GE3MjZaaOXF1PlLNxynQhNn53d/fqp5lhLTdj09j3sRZIn2eqnvbe\nOlT6clJgkzqIzHNl63GIvg4pjhDiNp27TU0RbAuQ537swLTHbjZiy1Np11tpvcjhxbhG19anKSXK\n2bqoHOtDtF7dUu8xff06WX6ol41jy0ttcbHk3yP13MYp2wTsnzUSqdYTvVLkRcNUu0g8v5vUBKAt\nRKlBaZWujSbUeix9ozR+hU5NTC8erPfNMEvL7l/xbvVIjJb2drYZESw1mVN72Dy3t5642cgpMAXS\nvg64MKtvux0RtwwEOzo6biO3W6OmCLbF6VZWykaUYukb5el1M14HkrIqrSdS+FW8TM/hRRzF2xYC\nmTuSdb138HVIlZvSTZXV3cdJtVOqLr4OZVT2PNV/PT096+R259TkgLY4bfTs3vWobIUus/z4dCml\ncuo+tZPcT/CNcm3++ezs7CoANeIo1rMmWRGyTGS1ZWyEytrpVuqaSt8o/MKFCxus3e1TkwPa4jQ0\nNLQp+WzU8nO7+ehZyi9JSmE/SW28lPLax+/p6aGnpyd5KJjNp2xC23z9tphUOi92+Xwa0e3oem4l\nf4B9+/ZtMObtU5MD2uJ0/vz5TclnI6tvo3h6VibW6Pl6olFZXqnJ759NTk1RqaSnp9dhlem3fF1u\nRTeznu7Ix9M1pOtTRmVcmaeZmQ1/Wu+2qQlAW5yWl2+VR9k4bVR/tJ6u5Vby3Ihext7XiW/5Z2ca\nAUcZR9VI4V424W/13VLxUnlsxJrpr1P39wKAmiLYFqejR4/e7ypsOnnuZiPK5Bqwa9cudu/eXQoQ\nNqxGGkgagUoKGPy5QCnlOyVhZZSqd+r8ofUAsOkH1KS7TidPnrzfVdh02ign4QHh+vXrG/oSxK2I\nU43SSaeViuO5sPXEzvVE4EaGgDK6F35ATQ5oi9O9OPPlftNGB3lra+uaIygamb9hrS5mvXCbr7Xs\neTeBRlyY0vh8yurm67FRgG5t9ScIbT41AWiL07048+V+03ogIaqaM6F9HBvXTsuUEtin9yKWP7x/\nvS9U+LLWi6e4G4nfCAAGBgbWKeXOqSmCbXG6F2e+PCi03qS9efMm27ZtWzefRvu+yixh9vl6fjnr\ncTRePBPYlH1vzNdjIxwWwNmzZxs83RxqckBbnG51M+qXMnV1dbFz584Nx9/I5EkBwZ1OOg8eNcq/\njZaqx0ZFsD179tx65W6RmhzQFqd7cebLw0Jzc3MsLS1tOP563M5G0qTSrXe/Xt5lHxnYKPCI7qaL\nhqgJQFuc5ubm7ncVHhhaXl6u+yrGrdKtTvCydGVOhuuRQGYjX9xYLw+g+WnmJt19Onbs2P2uwgND\nPT099PX13e9qrNJGvKJ9/M0oU3QvfMSaHNAWp3vh6/Gw0OTk5IaU0PeKNurRvBn5psLsWVF3i5oA\ntMXpXpz58rBQtVqlpaXlfldjlW5li8rt5LtRa9jdpKYItsXpXpz58rBQW1sb7e3t97sa94zWA53D\nhw/f9To0OaAtThcvXrzfVXhgaGZm5oESwe43nWp+mrlJd5vuhbfrw0IdHR10dXXd72o8MLRr1667\nXkaTA9riND09fb+r8MDQ0tLShjajbhXy21LuBoU78Xt4WCmEkL3qVa+639V4IGhwcLAphuXU2dnJ\ntm3buHHjxv2uygNBdzI2XnjhBbIsWxfNtywA3e86NKlJX+rUBKAGFEK4mWXZjvtdjweBmm1RULMt\nCroXbdFUQjepSU26b9QEoCY1qUn3jbasCNakJjXp/tNDxQGFENpCCJ8MIXw2hPD5EMJ78/APhhBO\nhxA+k/+eysMfCyH8TQhhIYTwYy6vbw8hvBBCeLcJ+8oQwt+HEEZCCL8UcptsCKE3hPAnIYQT+f+u\nPPydIYSfu2cNUF//W22LkL/TSAjhcyGEV5m83pO3xbeZsDN5W3wmhPC8Cf+5EMIFk//b8vA3hhA+\neM8a4A4p9X4PYj/fKwohbAsh/F0I4cP5fdk42tS2eKgACFgA3pRl2ZcDTwFvDSG8Ln/241mWPZX/\nPpOHXQPeBfxiIq9vB14DvC6E0JmHvR/4fuBY/ntrHv6TwJ9lWXYM+LP8/n7TrbbFN1K81/cT35X8\n3V8DvBb4TlfG1+d5vNqFP23y/8jmv9o9I/9+D2I/3yv6EeALLiw1jjaVHioAyiLpY0Ut+a9Uhsyy\nbDzLsk8BqVOmZCLMiAzCPqA7y7K/yaJc+uvAP8nj/GPg1/LrXzPhc8Dd/3hSgm61LYjv8Ot5uueA\nnvydbTvcCS0CD7sDzQPXz/eCQggHgG8CfmUD0Te1LR4qAIJVVvEzwDjwJ1mW/W3+6H25aPF0CGH7\nBrL6feB54Pksy6aB/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa60d022128>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ra = position_casa.icrs.ra.deg\n",
    "dec = position_casa.icrs.dec.deg\n",
    "ax.scatter(ra, dec, transform=ax.get_transform('icrs'), color='white', marker='x')\n",
    "ax.figure\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1 Exercises\n",
    "\n",
    "- (*easy*) Make a combined plot of the Chandra data for all energy bands side by side (one row, three columns)\n",
    "and put the energy information in the title of the subplot. You can use e.g. `plt.subplot()` (check the matplotlib documentation).  \n",
    "- (*advanced*) Make a combined RGB image of the Chandra data in different energy bands. Therefore you have to\n",
    "renormalize the data per energy band to the maximum value of respective energy band and combine the data into a 3d array with a shape that is compatible with `plt.imshow()` (check the matplotlib documentation!). You can also try to experiment with the Astropy function [make_lupton_rgb](http://docs.astropy.org/en/stable/api/astropy.visualization.make_lupton_rgb.html#astropy.visualization.make_lupton_rgb). For this you can find a [tutorial in the Astropy documentation](http://docs.astropy.org/en/stable/visualization/lupton_rgb.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Acknowledgements\n",
    "![](asterics_log.png)\n",
    "\n",
    "This tutorial was supported by the H2020-Astronomy ESFRI and Research Infrastructure Cluster (Grant Agreement number: 653477)."
   ]
  }
 ],
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