{ "metadata": { "name": "", "signature": "sha256:2c7e9c3cf2e6e7f10a1cc2dcc719e6251e650ae43663d2cc3c7f27aa779e0a42" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "The Mollweide projection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Author: [Eduardo Mart\u00edn Calleja](http://balbuceosastropy.blogspot.com.es/)\n", "\n", "As a continuation of the previous blog [entry](http://balbuceosastropy.blogspot.com.es/2013/09/working-with-astronomical-coordinate.html), which was dedicated to the different celestial coordinate systems , we will address now a way of representing graphically the position of objects on the celestial sphere. When it comes to generate a plane global representation of the celestial sphere, the Mollweide projection is commonly used. In this article we will see how to generate such representations using the Python matplotlib package. The ability to generate such charts is quite useful, but as we shall see, it is somewhat \"tricky\"." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Imports and references" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from __future__ import division\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import ephem # to make coordinate systems conversions\n", "from IPython.core.display import HTML # To include images as HTML\n", "\n", "# This IPython magic generates a table with version information\n", "#https://github.com/jrjohansson/version_information\n", "%load_ext version_information\n", "%version_information numpy, matplotlib, ephem" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
SoftwareVersion
Python2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]
IPython2.3.1
OSLinux 3.13.0 45 generic x86_64 with debian jessie sid
numpy1.9.1
matplotlib1.4.2
ephem3.7.5.3
Fri Feb 20 14:19:49 2015 CET
" ], "json": [ "{\"Software versions\": [{\"version\": \"2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\", \"module\": \"Python\"}, {\"version\": \"2.3.1\", \"module\": \"IPython\"}, {\"version\": \"Linux 3.13.0 45 generic x86_64 with debian jessie sid\", \"module\": \"OS\"}, {\"version\": \"1.9.1\", \"module\": \"numpy\"}, {\"version\": \"1.4.2\", \"module\": \"matplotlib\"}, {\"version\": \"3.7.5.3\", \"module\": \"ephem\"}]}" ], "latex": [ "\\begin{tabular}{|l|l|}\\hline\n", "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n", "Python & 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n", "IPython & 2.3.1 \\\\ \\hline\n", "OS & Linux 3.13.0 45 generic x86\\_64 with debian jessie sid \\\\ \\hline\n", "numpy & 1.9.1 \\\\ \\hline\n", "matplotlib & 1.4.2 \\\\ \\hline\n", "ephem & 3.7.5.3 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Fri Feb 20 14:19:49 2015 CET} \\\\ \\hline\n", "\\end{tabular}\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 1, "text": [ "Software versions\n", "Python 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n", "IPython 2.3.1\n", "OS Linux 3.13.0 45 generic x86_64 with debian jessie sid\n", "numpy 1.9.1\n", "matplotlib 1.4.2\n", "ephem 3.7.5.3\n", "Fri Feb 20 14:19:49 2015 CET" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "The Mollweide projection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will conduct a first example of Mollweide projection using numpy and matplotlib packages in the most standard possible way. In the next figure we will represent three curvilinear rectangles with $\\Delta RA=60^\\circ$ base and $\\Delta \\delta = 45^\\circ$ in height in three different positions" ] }, { "cell_type": "code", "collapsed": false, "input": [ "r = 90\n", "theta = np.arange(0,2*np.pi,0.1)\n", "x = np.array([0,np.pi/3,np.pi/3,0,0])\n", "y = np.array([0,0,np.pi/4,np.pi/4,0])\n", "fig = plt.figure(figsize=(10, 5))\n", "ax = fig.add_subplot(111, projection=\"mollweide\", axisbg ='LightCyan')\n", "ax.grid(True)\n", "ax.plot(x,y)\n", "ax.plot(x+np.pi/6,y+np.pi/6)\n", "ax.plot(x-np.pi/2,y-np.pi/2);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GXEp0QNvXGwz3Pd95/Q4e2bcPTmfgloBSqVTo88IL2HXxomH28uVl6jdvPlOj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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The lessons we can draw from the above example are:\n", "\n", "- x and y values, which normally will be right ascensions and declinations, or latitudes and longitudes, must be expressed in radians!. The values of x and y must be in the range: $-\\pi < x < \\pi$, $-\\pi/2 < y < \\pi/2$. We can see that the values exceeding this range (eg. $x = 3 \\pi/2$) do not appear in the plot.\n", "\n", "- The scaling of the axes in the graphical representation covers respectively the intervals [-180, 180] and [-90, 90], that is, Matplotlib translates radian values to values in degrees in these intervals.\n", "\n", "- Another significant fact that we must take into account is that, by default, in the horizontal scale of the generated figure, the positive direction is to the right, while when dealing with astronomical coordinates the right ascension increases eastward, located conventionally left on celestial charts.\n", "\n", "- The horizontal scale is centered at x = 0, which must be taken into account as in the representations of the celestial sphere sometimes we want to place the center in $RA = 90^\\circ$ or $RA = 180^\\circ$ \n", "\n", "Considering all these points we will now write a function that will represent a pair of arrays of values (typically RA and Dec) in a scatter plot of points on the celestial sphere using Mollweide projection" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_mwd(RA,Dec,org=0,title='Mollweide projection', projection='mollweide'):\n", " ''' RA, Dec are arrays of the same length.\n", " RA takes values in [0,360), Dec in [-90,90],\n", " which represent angles in degrees.\n", " org is the origin of the plot, 0 or a multiple of 30 degrees in [0,360).\n", " title is the title of the figure.\n", " projection is the kind of projection: 'mollweide', 'aitoff', 'hammer', 'lambert'\n", " '''\n", " x = np.remainder(RA+360-org,360) # shift RA values\n", " ind = x>180\n", " x[ind] -=360 # scale conversion to [-180, 180]\n", " x=-x # reverse the scale: East to the left\n", " tick_labels = np.array([150, 120, 90, 60, 30, 0, 330, 300, 270, 240, 210])\n", " tick_labels = np.remainder(tick_labels+360+org,360)\n", " fig = plt.figure(figsize=(10, 5))\n", " ax = fig.add_subplot(111, projection=projection, axisbg ='LightCyan')\n", " ax.scatter(np.radians(x),np.radians(Dec)) # convert degrees to radians\n", " ax.set_xticklabels(tick_labels) # we add the scale on the x axis\n", " ax.set_title(title)\n", " ax.title.set_fontsize(15)\n", " ax.set_xlabel(\"RA\")\n", " ax.xaxis.label.set_fontsize(12)\n", " ax.set_ylabel(\"Dec\")\n", " ax.yaxis.label.set_fontsize(12)\n", " ax.grid(True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will test the function making a representation centered at $RA = 90^\\circ$ of a few pairs of coordinates expressed in degrees, and checking that they are represented in the proper position:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "coord = np.array([(0,30), (60,-45), (240,15), (150,-75)])\n", "plot_mwd(coord[:,0],coord[:,1], org=90, title ='Test plot_mwd')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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RERpNaNtnLOTPn54DBiAvNxdHDxwAiLj9/kP1+tWuSxesWLKEffW//1lys7NN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\nLlqkM8GlEiKimzQ6XeK4Bx/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gIzWVd4xSWzx3LrIuX+Ydo1SqRUcjPSWFd4xSs9vtuJyR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\nOHQociV4gUJuTg4eHzcOg1q1wuDWrVGlenVZ5LZ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NW6NESLUOWdihQ4jNWfNPaiybN4+3\nQomIjoqCRq3mrWEVlatWRZfevXHnxg0A2TlkO9etw4hJk9CmUyf8vaG4Sd/i4Mr585Kcwa3X67FK\nosU+1yxezFuhRHh6eqJdly68NUrEjP/8h7dCiUhNToZGrY4p6vniesjeRfasx/ZEVIeIOhBRbQDt\nAbwCYKrdTEuAh4dHWkpSEk8FGYnQa8AANAwuNI9S9Eg1t0atVGbnTIiY3Hyr5MREhB06hJbt2gEA\nHj96hPMnT6L/sGHoP2wYdv75J09Nq8lISxPlGn7F4e7ujnfeK2lZS75M//RT3goyEuHhgwc6k9GY\nWNTzxQVk7wD4oGBV/pztDwGMLr1iyXFxcXn0ODmZp0KJICLJdnNfOH2at0KZQ6q5NS917CjqiRRE\nhHcHDUIzf390rF0btRs0wMzPPwcAPLh3Dy3atkX1wED0HTwY927exI0rVzgbF0/3116TZEDGGJNs\n7ptUSYiNRXJikbGBqJHq9+fD+HgDsvPvC6W4gCwYQGgRz50E0LRkWvbBYrHEp0owIAOk280t1Q+C\n2WyGTqfjrSEjIhhjWLV7N6KUSmwJDUXEiRO4dvEiAGDXn3/itbfeAgCUr1gR7bt1w85163jqyogU\nrSDwVigReglfD6X6/fkoMZEAFDmsV1xA5kJEha4+SkRKK17vUNQqVUzKw4eSm+PNGJNsN3fnXr14\nK5SI9NRU7N+2jbdGiZDqGn8P7t+HVHI823XpgrEzZ+L7WbNwKTwccffuYem33+Ll6tXxcvXqiIyI\nwJ5Nm0Q/O1qqs+bu3LiBI7t389YoEWuXLOGtUCKCmjRB9cBA3holQqrfn49TUlzxjB6y4ir1uzLG\nehTxHLPi9Q7FbDLdi75xQwAgF4GReSZVqlfHkHfe4a1RIqS6xp9GrYabhAqUTvjwQ/y+aBEWz5mD\nF9u0wZp9+/Ke0woC+jVvjtCDB9Hz9dc5Wj6bDIkEwAVp0Lgx6jVqxFujREybNYu3gowE0AoCVJmZ\n7gAeFrVPcQFVKoDfn/E877ngkVfOnpXelCIAapUKvn5+vDVsJikhASajEbXr1+etUmaQam5NcIsW\nvBVsokKlSnh9+HDsXLcOq/fsQaUqVZ56/s0xY7Drzz9FHZD16N+ft0KJcHFxgYuLJMtKSpazYWFo\n37Urbw2b0QoC3D08JHe+3Lx6FT5+fg8ynzwxFLXPMwMyIqprdyv7ciMlKclT0GgkVyl557p1GD5p\nkuQStl1dXSFIpJRBQTRqNXx8fXlryIiE07Gx/3jsxzVr8OOaNYXu/82yZY5WkpEYFosFep1O1AWQ\ni8Is0bqMe7duRa8BA1C+YkXeKjZxIzISZrP57LP24ZoDVlqIyODj5xcnxSKrY997T3LBGJA99BfU\npAlvjRKxYcUK3golYsX8+TCKvHxEYTxOSUFCIUGPFMhdGFhqSDWHbOvvv0OKE7RSkpJw5O+/eWuU\niE49e/JWKBHDxo+XXDAGAJfCwwW1UvnMMgWSDsgAwGw2h1+/dIm3howEmPLJJ7wVSsTEjz6CqyvX\ndM0SYTIaoVYVOidIxkFkpqfzVigRg995B5WrVeOtYTPVAwMxcNQo3hoyEuDy2bMmAM8MViQfkKmV\nyvBL4eGSnHec/vgxb4USceb4cd4KZQp3d3dJ1paqHhiIJs2b89YoER26deOtUCK6S2jdzfy4ublJ\n8hyXKilJSbh78yZvDZuxWCzIkOBNh06rRVJCgheAqGftJ/mADMClyIgIcc9FL4K9W7bwVigRUpo5\nlx9Bo5HXs5SRkbEbyqws3golwmQywUtiedcAkJaSgoiQEN4aNnPr2jV4+/gkENEzi789DwHZtceP\nHrmmPnrE28Nmxs2cyVuhRLTt3Jm3Qok4d/KkJNezvH39Og5LME/FYDAgKjKSt0aJkHPInMsv33zD\nW6FEbPv9WUUIxEvN2rURWKcObw2bqVK9Ol4bOpS3hs2cOXbMYjIajxa3n+QDMiIyenp5nQjZv5+3\niozI6d6vnyTXs2zUtClefeMN3ho2wxiT5PCClJFqDtl0iS4WLdUagTLOZd/WrWpBo9lZ3H6SD8gA\nQJmZuWX/9u2Sq8VAREiIi+OtYTMmkwmhhw7x1igzKBQKydXcAbLzgqS6soOcQ+ZcpDhpRcocz1f0\nWEpI8fsyLTUVMXfuuCN7ucln8lwEZAAOngsLc5faWoWMMZyV4NCIq6srylWowFujREhlKZ+CEElu\nhTAZGasgIkme32azGVkZGbw1SkTFAkWPpYDJZMKFU6d4a9hM6MGD8PL2DiMifXH7PhcBGRGle3p5\n3ZZicPPWuHG8FUpEy7ZteSuUiN2bNvFWKBGL58zhrVAiIs8+sw6iaJFiDpnJZMpbHF1KpKWmYsOv\nv/LWsJlHDx/i3MliOz1EiRSv366urhg8ZgxvDZs5sH27Oisjw6oZfM9FQAYAKqVy8+Fdu4qNQGXK\nNuPff5+3Qol4f/Zs3golIuvJE94KZQap1n2rXLUq3p4yhbeGzdSsXRu9Bw7krSEjYgwGA86cOOEG\n4IA1+z83AZnFbN5zaNcus8UivaUtpVjY9mF8PC6Fh/PWKDMoFNL8qEo1p0mKOWSeXl7o2L07b40S\nIdXzW4rs3bqVt0KJkOL3ZERICDw8PGKIKNWa/Z+nT8Etk8mULMWipY8eFrn4u2ipVLUqKlWtylvD\nZnQ6nSTzyKSaZyMjUxxSvIkGpHndBoDGL77IW8FmtIIgyXy9jStWaNRKpdVr9j03ARkRkVqp/Gnt\nL79oeLvYSq8BA3gr2IyHhwfqNGjAW8NmjAYDTh0tthyM6Ni3bRvuR0fz1rCZSxERvBVKhBRzyBIf\nPJBkkLDk228lebMh1ZmKUiz94+XtjVdefZW3hk2kpaYi9NAhF4vFst7a1zw3ARkAENGm08eOKaRY\nJFbGOfj5+2PgyJG8NWzm9WHDENS4MW8Nm1FmZvJWKDMIajXMZuktWvL+7NmSXDZJinlvMs5jx9q1\nFncPj91EZPVF0OkBGWOsMWMsgjGmY4x9XOC5OMbYNcbYZcbY+XyP12eMnWeMHWeMlSvq2ESkdHNz\n27V9zRrJXZWkeLcVc+cOwk+c4K1RJpDiFxaQXYxXikgxh6xR06aoWbs2bw2bkeq5LUU2rlzJW8Fm\nkhMTEXX5Mm8NmyAi/LF4sVatVP5sy+t4VONLBzATwKBCniMA3Yio4NSsaQDeAtAAwNsAlhV1cLVK\ntXj1woWDW7Vv79WxRw8A/xt+yL3IinE7OTEx728Qg4812206dUJA+fKi8bF2+8COHfD28UG3nGCB\nt4+12y917Ah3d3fR+Mjb8nZpt4kIp48dg6ubmyh8rN1+lJiIQW+/DcaYKHys3X71jTdE5WPN9oXT\np+Hh6YlmrVqJwsea7RuRkdCo1akAbFrLjPEau2eMfQlATUQL8j0WC6ANEaUX2Pd7AOuRHZBVI6Lf\nnnFc5hcQcHfFjh0NpDbmLOMcoiIj4e7hgUZNm/JWsYmlc+fivc8+461hE/du30alKlUkV0g4IjQ0\n7wIrFS6Fh+Oljh15a9hE+uPHOPzXXxj17ru8VWzirw0b8Obo0bw1ZETKu4MGaY7u2TPLYrEU2XlU\nGGILyGIAZAEwA1hJRKtyHg8EsAFAJoBRRCQ869gKhWJKxx49ftp47Jivw/4AmTyISB52kCmUqGgR\n6AAAIABJREFUW9euoUKlSqhaowZvFZuQYkAWdvgwuvbpw1tDRqTI12nnkJSQgO6NGmn1Ol0NW/LH\nAPEl9XciolYA+gGYwRjrDABElEhE3YhoUHHBWM7+6yIjIoxSq1sSERqKW9eu8dawCWVWFtYuWcJb\nQ0akNGneXHLBGADJBWMA5GBM5pks+fZb3go2s3bJEsnNwP1lzhwdUyhW2BqMAU7qIWOMTQcwOWez\nHxE9KqyHrMBrnvl8cbi6uc1s363bdxuPHvUpmbXz0ev1MBmN8PGVVsee0WiEm5sbbw2buHXtGoKa\nNJGUt9FohMVigYeHB28VGRm7oFGrJXe9i46KQt2GDSX3OZTidTojPR3lK1bkrWE1D+Pj0bNxY0Gn\n1dYhIpsLXjqlh4yIlhNRq5yf3JoUT/WdMsa8GWN+Ob/7AOgN4HpJ2zSbTKsiIyL0Vy9cKLG3s/Hw\n8JDcxQmA5D7kAKDTapGRnl78jiLi/u3bkpvVajQaJbmeZW6irpS4cPo0bwWbWb98OW8Fm4mPiYG7\nuztvDZuR4nVaSsEYACz++msdY2xFSYIxgEMOGWOsGoALAPwBWACoAAQDqAJgV85urgA2EtF3pWnL\nxcVlRvtu3eZvOn5cMr1kQPYwoH9AAG8Nm8h88kRyidsyjid3Fl3nXr14q9iEFHPITh45gi69e/PW\nkBEZRISsjAxJXZ+JCGqVCn7+/rxVrCbxwQO82qRJiXvHAA45ZET0iIhqEVEAEZUnotpEpCaiGCJq\nmfPTrLTBGABYLJbVl8+e1V85f774nUXE1tWreSvYzK71VhcjlilDMMYkF4wB0swhk4MxmcJISUqS\nXM967N27OBcWxlvDJhZ//bUOwPKSBmMAx1mWzsLFxWV6uy5dftgcEiKpXjIZx3PxzBk0a90anl5e\nvFWs5klaGipUqsRbQ0am1KiUSnh4ekpq+O/8qVNo0bat5PLHZBxLQlwcXg0OFvRabe2CZbtsQWyz\nLO2OxWL5/eqFC8qQgwd5q8iIjHIVK0KtUvHWsIkDO3ZAr9fz1rCJcydP8lawGanlkKUkJSHu3j3e\nGjYRcuCAJJfWkoMxmYJ8OXOmAKKFpQnGgDIQkBGRXtBoJsyaOFHQabW8dawmIz0dN65c4a1hE1GX\nL0tqLb2gxo1RqUoV3ho2MXrqVMl9IRgNBt4Kzz16nQ4KhbQu5wNGjJDc569t5868FWzizo0b0ArF\nVooSFVIbXg05eBBnQ0Oz9Drd3NIeS1qf4BJCRIcEjSZs2bx5Rt4u1hJQvjw0Euu9sZjNSEtJ4a0h\nIzKkuGKG1HLIatevj9r16/PWkBEZCbGx8PD05K1hNUQEF1ceKzqWDJ1Wi1kTJwqCWj2RiHSlPd5z\nn0OWC2OslqeX1+1D16551w0K4q0jIxKuXbwIX39/1G/UiLeK1SQlJKBGrVq8NWRkSozBYEDmkyeo\nUq0abxWr2b1pEwaMHClXu5fJY8Hs2cY/fvnlmCor6zV7HK9M9JABABElWMzmb2ZNmqSRUhBKRJKr\nVCwl6jVqJLnabycPH+atYBNx9+4hKSGBt4ZNSC2HTGq+SfHxuH/7Nm8Nm2jaurUcjDkQqX3Pxd27\nh1ULFhjVSuUUex2zzARkAGAwGBZEXbqUdmjXruJ3FgmRERGSGlMnIkmVwPDz95fc0j4jJk3irWAT\nrm5uMBklky0gSaT2ZVY3KEhyw8JBjRvzVrAag8GA3Zs389awiaVz50rmPCYizJo0SWMxm78hIrvd\nbZaZIctcGGNdylWseDD0zh1vKRTKIyKYzWa4Smhc/cH9+6jToAFvDRkZGZkyiU6rReaTJ6hWsyZv\nFasxmUyS+Z7bvWkT/XfKlHiNWt2QiOx2t1mmesgAgIhOGnS6P/89bpwghWCUMSaZkzQXqQVjapUK\nG1eu5K1hE/du3eKtICNTYqR0/hIRfvvpJ94aNuHp5SWpYAyAZL7nEuLi8N8pU3QatXqwPYMxoAwG\nZAAgaDQfRYSEJG/9/XcLbxdruX39OpRZWbw1rMZkMkmmBIavnx8GjhrFW8Mmbl69ylvBJs4cP85b\nwSaklJOl1+tx/tQp3hpWoxUExN69y1vDJkZNsVuakMMxSKzMzKWICMl8V5hMJkwbMkRjNBjmEFGk\nvY9fJgMyItJp1OqBX3/4oS7mzh3eOlZRoXJlPHzwgLeG1dy8cgWnjx3jrWE1vn5+vBVsYsCIEbwV\nbMJNQtXYpYbJaIS3hCameHl7o9eAAbw1rIYxJqnrw28//iiZXCwAENRquLi48NawiiXffGOMu3v3\nmsFg+MERxy9zOWT5cXN3f69ew4bf77982UdKy3fIOAZBo4G3j7zCloyMTDYWiwV6nQ5e3t68VWQ4\ncyk8HKN79VJqBSGYiB46oo0y2UOWi8loXJacmHj2h//8RzJ9vGazGRaLZEZaJcX65ct5K1iNxWLB\nlfPneWvIyNhM5NmzvBWs5uaVK7gUHs5b47nEZDLxVrAaZVYWpg4ZImgF4R1HBWNAGQ/IiIjUSuXI\njb/+qpHK8NrdmzdxdM8e3hpWc+H0ackEkFM++YS3gtUoFApkpJdq2TSnEhUZibTUVN4aViOlHLIw\nCdWlM5vNUCuVvDWsplnr1pJZaeLOjRuSuiYs/+47SQytEhE+nTRJq1GrtxHRbke2VaYDMgAgosda\nQRgydcgQbXxMDG+dYmn84ovoM2gQbw2r8fb1RVZGBm+N55Lu/frxVrAav4AASVx8pYiU8ptcXFzQ\npXdv3hrPJWmpqfAvV463htW8P3u2JArtrlqwwBx26FCioFbPcHRbZTqHLD9u7u4zqgcGzj9w5YqP\nn78/bx0ZTiTExcE/IAAB5cvzVpGRkeFI1OXLaNqypSSCBhnHEHLgAKa/9VamVhBaEFG8o9sr8z1k\nuRgNhmXpjx9vmTp4sCCFKbhqlQr7tm3jrWE1Ugn8XVxc8OD+fd4aVkFECD10iLeGjIzVhBw8yFvB\nahLj4iQRjEnl2gpkD1lvX7uWt4ZV3L15EzOGD9dqBaG/M4IxQA7InkJQq6ddvXDh2rxPPhF9kr+v\nnx9atmvHW8NqVv74I3Q6HW+NYqlRqxaat2nDW8MqGGOS6sk7sX8/bwWrkUoOmVYQEB4SwlvDKoxG\nIypVqcJbw2r6vvkmbwWrOLRrF+7cuMFbwyqICJ179eKtUSwZ6ekY3auXoNNqpxOR02Z1yEOWBWCM\nVfD28bk+Z+nS6kPHjRP/7ZFEkNKyGDKO4eqFC2jx8su8NawiIjRUEmstqlUqPHr4UFLrLMrYF/na\nal+MRiOGd+2quX3t2mqNWv2hM9uWe8gKQERPBI3m1dkzZmikMt1ZCp5Su2D8tWEDb4XnDqkEYwAk\nEYwB2T3lcjBmXx7Gx+NsWBhvDauRwrVVo1bj1rVrvDWKhYjw+bRpujtRUecFjeZjZ7cv95AVAWOs\nr7ePz19fLVniOWz8eAD/G8bIvViLZdtkNKJjjx55y6fw9nnW9s0rVzDxww9F41PUduzdu3j08KFo\nfJ61nRQfjyHvvCMaH3lb3i64rRUErPzxR7Tr2lUUPs/aDmrSBJ5eXoiKjBSFT1Hbe7duhcVszlv2\njbfPs7ZvXLmC+JgYlKtQQRQ+RW3v+vNP04Ht2x9o1OrWROT0+ixyQPYMXF1dR/kFBKz6+9w577pB\nQbx1ngsuRUSgacuW8PTy4q3y3PDg/n1JLOh+PzoaZpMJjZo25a1SLFIZsjz011+SyHXSCgJUWVmo\nUr06b5XnhsizZ9GkeXN5FQE7sebnn80/ff55iqDRtCGiZB4Okh2yZIwNZIxdZYxdZoxdYoz1yPdc\nX8bYbcbYXcbYrHyP12eMnWeMHWeMFVuwxWQybdKoVP8a+sorQnJioqP+FLuR+uiR6Ksfv9Shg2SC\nMSKC0WjkrVEsUgjGAKBi5cqSWnNRCtSqV4+3glV4eXtLIhiTwuc9l9bt24s+GEtJSpJEYfBta9ZY\nfvz88wxBo+nIKxgDJByQAThGRC2IqBWAcQB+AwDGmAuApQD6AggGMJIx1iTnNdMAvAVgLoC3rWnE\nYDCsVGVlfT2kUydB7JXGVVlZuHjmDG8Nq9Dr9bwVikWlVGLjr7/y1nhuKFehAgLr1OGtYRVS6B0D\ngKYtW/JWeG6wWCxY+YND1oy2K3q9XjKlLkIlUOZk/7Zt9OXMmUqtRtOJiB7wdJFsQEZEmnybvgDS\ncn5vC+AeEcURkRHAFgADc54z5+zrC8DqWyGdVvtDRlra4rc6d9aIuep8gxdeQPuuXXlrWMXuTZuQ\nmsztRsQq/AMCMG7mTN4aVrFi/nzJXKRlyhbnT52SxMQjhUKB9z77jLdGsez680+kP37MW8Mqhk+c\nCIVCvGFGyIED+Pf48WqtIHQjoju8fSSdQ8YYGwTgOwDVAfQmovOMsaEA+hDR5Jx9RgNoR0QzGWOB\nADYAyAQwiogEG9piXj4+S+sGBY3dcfq0j4/Ih140ajXE7ihjPwSNBt4+Prw1imXPli0YMGIEb41i\nkUIOWdTly/Dy9kaDF17grfJM9Ho9XFxcJDEbUMY+SOH7JyI0FBP69xe0gtCTiESx4r14Q1crIKK/\niagJgDcArGfFlFUmokQi6kZEg2wJxnJeS1qN5r0H9+//NaJ7d0GZlVUadYezYcUKucfETty5cUP0\n63FKIRgDgOAWLXgrPDdUqFQJVWvU4K1RLB4eHqIPxi6Fh0si10kK3Lx6VfQ9ouEnTmDC668LWkF4\nQyzBGCCxgIwxNj0niT+SMZaXIUpEpwC4AqgAIBFArXwvq5XzWKkhIhLU6rH3b93a9Gb79hoxdxtP\n+eQTSSz7EXn2LK5fusRb45mUq1gRSQkJvDWKRdBoRB+EBzVpUvxOIkDsvWNA9qoSYl9YXArnJJDt\nKeahNQBYv2KFJILG4BYtRL2A/JHduzHxjTc0Wo2mPxGd4O2TH8kOWTLGGgCIISJijLUGsJ2IGjDG\nXAFEA+gJIAnAeQAjieiWHdtmnl5e31esUuW97adOedeoVav4F3HCaDRCoVDAxcWFt0qhWCwWZKSn\no2LlyrxVJM+hXbvQuHlzyCVaZMTC6kWL8M6MGXB3d+etInnSUlNFvfSUTqeDp6cnb41nsmv9evrv\n1KkqXfYw5UXePgUR9y3BsxkC4Dpj7DKAxQBGAAARmQC8B+AwgJsAttozGMtpg7SCMCstJWXOG23a\nCLF379rz8HYlKT4eB3bs4K1RJAqFQg7G7ETfwYMlEYxJYXFhsa9lSUTYsW4db41imfTRR3IwZifE\nHIwREX5fuFDUvaHrliwxfzZ16hOdIHQQYzAGSLiHTCy4urm96+Pr+/PWsDCvJs2b89aRLAaDAVfP\nn8fLr7zCW6VIdv75J9p364aatWvzVpE08TExqF2/Pm+NZyL2pH6z2YzkxETJlBERK2uXLMGQsWPh\n5+/PW6VQiAgRISHo2KNH8TvLFAoRYem33xqXz5+frs2uMxbL26ko5IDMDigUiuHevr5//Hn4sNdL\nHTrw1ikSsc98OXfyJNp16cJbo0iMRiNcXV1FnZun0+nwKDFREj1lMs830VFReKFZM94az8RgMIi6\nB0+lVCI+Jka09eZ0Wi1c3dxEO2mDiPDtxx8bNq9a9VBQqzvxLPpqDVIeshQNFotlq0alGjL61VeF\nQ7t28dYpktCDB5EQF8dbo0jEHIwBgJubm6iDMQBwd3fHzStXeGvIlHGICPdv3+atUSxiDsYAwM/f\nX7TBGJC9nqZYZ6DrdDrMHDFCu2X16juCWv2y2IMxQO4hsyuMsZe8vL0PT/v004CZn3/uKvYvb7ES\nd++eqHt4Lp87hxYvvyz6WVli5X50NFIePhT1MIzYhyzXr1iBMdOm8daQLPdu30blqlURUL48b5VC\nyXzyBESE8hUr8laRJI9TUjC2Tx/hQUzMCY1KNdzWMle8kL9R7AgRXdIKQvOVP/54973hw7U6nY63\nUpE8jI/nrVAkMdHRyEhP561RJG7u7hD7Mlpipla9emgi1yMrFX0GDeKtIGmS4uPhK9K8MQC4cPo0\nFCKdGW8ymZCSlMRbo0huXr2Kvi++qI29e/dnjUo1UCrBGCD3kDkExpi3j5/fltr16/f48/Bhn8pV\nq/JW+ge71q/H68OHi77LXqZkHPrrL/QZNEj0Q6wyzx+3rl2Dt4+PZBa9l7GN86dOoXK1aqjXsCFv\nlX9wdM8evD9qlKAThIkWi2ULbx9bkQMyB5FTq+xbHz+/D9cfOeItVyi3HbPZDEGjEe0MKIvFItph\nyzs3bqBeo0Zwc3PjrSJTxrh78ybqBAWJ8mZPzJ9ZAMjKzERAuXK8NSQHEWHF/PmmJd98o9IKQl8i\nOs/bqSSI98yUODm1yj578vjxxCGdOglHdu/mrVQoRITwE6IqVpyHoNHgwPbtvDWKZO/WrbgfHc1b\no1AaNW0q6mBs96ZNSH30iLdGkYi5DtnaJUug1+t5axRJw+BgUQZjAPD7okXQqNW8NQpFp9Nhz6ZN\nvDUKRafT4cLp07w1CkWv1+PD0aN1y+bNi9EKQnOpBmOA3EPmFBhjbb28vQ+MmTHD7//mzXMX2xTh\ns2FhaNelizy8ZSNEJL9nJUQrCHB1cxNt0CjmpH6VUinaXmOxI39mS0Z8TAxc3dwgtlVp4mNiMPGN\nNzTJCQlhapVqGBFpeDuVBjkgcxKMscq+fn476zZs2HrV7t0+1QMDeStJCq0gwMvbm7eGpFCrVNj+\nxx8Y//77vFVkygAWiwUr5s/HjP/8h7eKpNBptXD38BD1UKoYObhzJ/49bpzWYDD812gwLKbnIJiR\nzwAnQUSP1SpVt7s3b87v3bSpNuTgQd5K/8BoNGLtkiW8NQol7NAhxN27x1ujUKIuX8Y9EdZc8vXz\nw6gpU3hrFMlzcP10OmJ+zxQKBSb961+8NQplz5Yton3v/t64EcrMTN4a/yAtNRV/bdjAW+Mf6PV6\nfD59uv7jsWNTNGp1V4Ne//PzEIwBcg8ZFxhjXby8vf8aM2OGr9iGMJVZWfAPCOCtISlMJhMS4+JE\nXTtNjCydOxfTPv1UlAvfi3XIcu/WrQhu2RINXniBt4qkuHf7NoIaN+atISn0ej3IYoGnlxdvlTzy\nhigTE0+rlcoRRCS+SLYUyAEZJ6QwhCnWZUXEvgSU2EiIi0NgnTqiy50xm82iDMYA8QZkZrMZCoVC\ndP/LlKQklKtYER4eHrxVJINYr2Nive4/j0OUBZGHLDlRcAjz+L59vJWeQq/X44/Fi3lrFMrGX38V\n5fCDTqfDg/v3eWv8g4TYWCQ+eMBb4x+INRgDILpgLOzwYYzuPQRj+w3DySNHeOv8gzPHj4syB+ru\nzZu8FQrlxpUriIyI4K3xD5ITE/H3xo28NZ5Cp9Xis2nTnsshyoLIPWQigDHW2cvHZ0efN9/0n7N0\nqac8ZChNLBYLDu7cif5vvcVbRTLotFpRDYmIkbDDhzHlzbHQaecBIHh6fYaVf61D1z59eKuJGq0g\n4PSxY+g1YABvFZkSEnn2LGYMGyaosrKOqpXKcc/bEGVBxHdLUwYholNajSbo6N9/b+0WFCSI7Q7Y\nbDYj9NAh3hr/wGAw4ElaGm+NPBQKhRyM2cgakfbCiqkO2aoFv0GnnQ+gEYBG0GnnY9WC33hriR4v\nb2/RBWOpyeJb31qn1YquFqVer8e8Tz4xjOrZU5mckDBOlZU16HkPxgBAPNnkZRwiUgEYxxjb9O6g\nQZs7dO/uu2TLFndfP7+8L4fcYRRnb58/dQoJMTF5rrx9crdbtm2L0IMHUT2nNg5vn/zbBoMBXXv3\nFo0PADx+9AgDRowQjU+Hbt0w/dNPReWTu33zyhXR+GQ+eQzgFoCxyGZ/zmPg7pcQF4cT+/ejUdOm\nonm/IkJCYDQa0UVkn7+Wbdvi1NGjqFG7tih8creP7d37VE4ib59NK1di8TffaDUq1UmdIIwlohSU\nEeQhSxHCGCvn4+e3wtvHZ8Avmzd7iy2fRS6uWDyrFy7EmBkzRJXkfO/2bTR44QX5fycx/jdkOR8A\n4Ok1SzRDlkkJCShXoQK8fXx4q+QRcvAgqlSvjqYtW/JWETViu44bDAb8MmeOcfXChXq9TjeViDY9\nr7liRSEHZCKGMfa6l7f3n0PHjfP+748/eoilMOrSuXMxddYsiKlcR0JsLDw8PVGlenXeKjI2kvro\nEapUq8ZbQ9Qc27sXqxb+Bjc3d0z++F1RBGMy1nEpPBytO3QQVfBzKTwcGrU6rxeRN7euXcOMYcM0\nqcnJF9RK5dtElMTbiQdyQCZyGGMVfP39V3v7+PT5Yc0a7259+/JWEiVaQcC1ixfRrksX3iqiR2yJ\n9OtXrMCYadN4azyF2Mpe3LhyBTqtFi916MBbJQ+xnUdihIhw8sgROYAuAq0gYPGcOca1v/xiMBgM\nH1jM5jVlrVcsP3JSv8ghoieqrKzBqcnJQ6cPHfpo4htvCEkJCby18jj899/QCgJvDXh5e4syGIuO\nisLBnTt5a+RBRPjjl194azyF2IIxMdK0ZUtRBWNpqanYs3kzb42nWDxnjujK4TDGRBOMRV2+LKoy\nIMf27kXn+vWFDStWHNRptY3MJtPvZTkYA+QeshLDGHsZQASA4US0M+exOABKAGYARiJqm/N4fQBb\nAKgADCnpbBHGmJenl9fnjLGPPvzyS/cJH33kwntx5pSkJHj7+opqseNL4eHw8vFBcIsWvFUAiLsA\nqozM84KYPmdbVq/G0HHjRJXWEXPnDuoGBXGvF5f44AH+++67wsXw8AxBrR5HRMe4CokIOSArAYwx\nFwBHAQgA/sgXkMUCeImInhTY/0cASwE0ANCEiJaVsv2Gvv7+f1SoVKnlgnXrfF5+5ZXSHM5uKLOy\n4Ofvzz1XwmKxIC01Vc5LkhB3b95Ew+Bg3hqiRJmVBUGtRrWaNXmryFhJanKyKPJZVUolfHx9uQdh\nQHbS/qqffjItnTvXaLFYftDrdN8RkZ63l5jg/1+SJjMB7ADwuJDnCotGzAB8c36MpW2ciO6qlcrO\n8TEx49/p0yfjg7ff1qY/LkzFudy/fRuXwsN5a0ChUOQFY2K64Vi9cCEMBgNvDQDZC8mHHDjAWyOP\n29ev81Z4CjHVIYu/fx+CRsNbA0D2zc7RPXt4a+Rx4fRpnD91ircGgKevNWIIxgBg96ZN0Gm1vDUQ\nHhKC7o0aaVbMn39GKwjNdFrtV3Iw9k/kHjIbYYzVBLABQA8AawDsJaJdOc/FAMhCdgC2kohW5Twe\nmPOaTACjiMhuSVeMMT9vH595TKGY+MncuR5vT52q4D2MKSbOhoXBYrGgY/fuvFWgFQSIZaYsAERF\nRqJZ69a8NUSJ2JL6xYJWEPAwPl40C3VrBQGeXl7ce+UBYNm8eZj873+Lch1IXjyMj8fcjz/Whh48\nqBE0mskAdpf1PLFnIQdkNsIY2w7gJyI6xxhbi+yALHfIsjoRJTPGKiN7SHMmETnl9o0x9qJfQMAK\nH1/fll8tWeLTZ9AgrheplKQkHN+3D6PefZebg4yMjExZQisIWLtkCabNmsXVQ5mVhaXffmv4c9ky\nM4CfdVrtPCJSc5WSAHJAZgWMsekAJudsBuB/w5KVkJ1HNpmI9hR4zZcA1ES0wGmi2e328fHzW16/\nUaOqc5Yt82nVrp0zm38KsRUevB8djcrVqoH3WqEZ6ek48vffGD5xIlcPIPt/JGg08PH15a2Cs2Fh\naN+1K28NUXE/Ohp+/v6iGALTqNWiOE/0ej02/vorJnzwAW8VREVGonHz5qJK3ud53TUYDNiwYoVl\n4Rdf6EH0l1ql+j8ieshFRoLIOWRWQETLiahVzk99IqpHRPWQnUc2jYj2MMa8GWN+AMAY8wHQG4DT\nE2OI6LBGpWoUFRk5c1SPHhmTBw0S4vMte+RM8l8U1i9fDqOx1OlzpaJCpUqimPZdvmJFvDFiBG8N\nANkz0zavWsVbAwDg4uIimhw7seSQZWVkwI/zDQSQnRz+98aNvDUAAO7u7hgxaRJvDQDZIwG8Z3be\nu3ULp44ezdvmEYwREQ7u3InO9eppFn355Rm1UtlOlV3gVQ7GbEDuISsFjLE/kJNDllPaYlfOU64A\nNhLRd/zssgNDD0/PTxhjn4yYNMnlw6++8ihXoQIXl4z0dJSrUEFUPWYyMkUh55DJSIWsjAz4+vtz\nCwwvRUTgixkzNHH37j3SqFTTiOho8a+SKQy5h6wUENH43IR+IoohopY5P814B2M5ThqdVvuVTqut\nv33t2s0d69TR/jp/vplHIdfyFSvmBWMXz5zBk7Q0pzvk5+7Nm9i/fTtXByB73b3rly7x1pApgByM\niY/VCxdynzFosVjwyzffcJ+9ff7UKWRlZAAAAsqX5xKM3bt9GxMHDBBG9+r15OaVK+9pVKoX5GCs\ndMg9ZGUIxlgTP3//n8BY9w++/NJj9NSpCh5Ln2RlZCArIwO169d3etv5EUMhSSKC0WjkPjOLiLDp\nt9/w9pQpXD3CT5xAo2bNUKlKFa4eYuDAjh3oPWgQ1/yk9MePceHUKfQdPJibQy4Gg4H75wQQx3Xj\n+qVLaNa6NZcRh9i7d/HTZ58Jx/fts5jN5u+NBsMie1YOKMvIAVkZhDHWwi8g4EeFQvHKR19/7THy\n3XcVHh4eXFwEjQYPHzzgWhRUpVQiKT4eLzRrxs0B4D8J4tHDh9yLj6alpkKhUKBCpUpcPcQwZCmG\nYrlqlQpExG0ljtzvJ56fCyJC5NmzXJeuslgsiIqMRPM2bbg5JMTGYsHs2dpDu3ZZiOgnvU63kIiU\n3ISeQ+QhyzIIEV1VZmb2zsrI6Lxg9uyT7WrWFNYuWWLR6XROd3H38MDD+Hint5sfbx8fpCYnc3UA\ngHVLl3IdyuUdjAFApSpVuAdjYoF3MAYAvn5+XJdF27t1K+5HR3NrH8gu4cA79zUjPR0mk4lL23H3\n7uHD0aO1rwYHCwd37lyk02oDcwq7ysGYnZF7yGTAGGvjFxDwnUKh6Djz88893546VcESoP5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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we will represent an array of pairs of randomly generated coordinates" ] }, { "cell_type": "code", "collapsed": false, "input": [ "np.random.seed(0) # To make reproducible the plot\n", "nrand = np.random.rand(100,2) # Array (100,2) of random values in [0,1)\n", "nrand *= np.array([360.,180.]) # array in [0,360) x[0,180) range\n", "nrand -= np.array([0,90.]) # array in [0,360)x[-90,90) range\n", "nrand = nrand[(-86 < nrand[:,1]) & (nrand[:,1] < 86)] # To avoid Matplotlib Runtime Warning,\n", " # staying far from the singularities at -90\u00ba and 90\u00ba\n", "RA = nrand[:,0]\n", "Dec = nrand[:,1]\n", "plot_mwd(RA,Dec)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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zWq345bvvfFp/jdq18dgLL9C6Q4eMuy9d0rz2ySf3t+va9XulSnXTEBr6KxEN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\nd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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just by curiosity, we now ask ourselves how would we see the plane of our galaxy,the Milky Way, in a plot of the celestial sphere in equatorial coordinates RA, Dec\n", "\n", "The galactic plane has latitude coordinate b = 0 in the galactic coordinate system. We will generate an array of galactic coordinates with 0 latitude and we'll convert it to equatorial coordinates using the Ephem library. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "lon_array = np.arange(0,360)\n", "lat = 0.\n", "eq_array = np.zeros((360,2))\n", "for lon in lon_array:\n", " ga = ephem.Galactic(np.radians(lon), np.radians(lat))\n", " eq = ephem.Equatorial(ga)\n", " eq_array[lon] = np.degrees(eq.get())\n", "RA = eq_array[:,0]\n", "Dec = eq_array[:,1]\n", "plot_mwd(RA, Dec, 180, title = 'Galactic plane in equatorial coordinates \\n (Mollweide projection)')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Cfpk3r2zBnDklv69a5Up1uXYIzM/Py5sNLASWKKW8dstrMNQXo5AZDBHECi0x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\neAKoa/wzB9APpY4D9X9SUtT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8DmRZ2+tW3n5+nT+fOTNmRF2WmnA4HJxz+eW2P9ttO3Tg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\nqwgNC1tuNhqnE9E+0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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Aitoff projection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another projection system which we can find at times, as it is also used in astronomy to represent an overall vision of the celestial sphere, is the **Aitoff** projection. Looks similar to Mollweide, but, contrary to this, the lines of equal latitude (parallels) are represented by curved lines, and they are regularly spaced." ] }, { "cell_type": "code", "collapsed": false, "input": [ "r = 90\n", "theta = np.arange(0,2*np.pi,0.1)\n", "x = np.array([0,np.pi/3,np.pi/3,0,0])\n", "y = np.array([0,0,np.pi/4,np.pi/4,0])\n", "fig = plt.figure(figsize=(10, 5))\n", "ax = fig.add_subplot(111, projection=\"aitoff\", axisbg ='LightCyan')\n", "ax.grid(True)\n", "ax.plot(x,y)\n", "ax.plot(x+np.pi/6,y+np.pi/6)\n", "ax.plot(x-np.pi/2,y-np.pi/2);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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nz+3ItQeR+GLnWFT2qorZ/Vagkrr0jZ1LgtFoL6gtlUoRfvAgagcGuiVh42ns\n2rgRrzRtWigDV2jYbDaEhYZi4c8/a29ERZktZvMcs9m8tCAulsE/TDi9YOTfoQxVeXn94FuhQsVP\n//MfVf9hw1zaC600aHJzkZ2ZyUv7k2eR9uABwg8exOB338XODRvQsHlz1K1f3y1r79+2DbWDgpxe\nQPFFxdlbdQW8909fdKvXB6OCJzl9bnditprxR/hMrJjzP8ydswpvNB7isrUct9sunjoFq9UKP39/\nXI+MxBtDXLfu82Cz2XDr+nWnNr92NtejorB41iz94d27iUgkWmnQ6+dSSuP5tutlhwmnFwRCiI/E\nw2Oih1T6xStNm3p88p//qDr37Cl4T8mls2fhHxCAylXdE4fxLHRaLUQiUZH1YdYuXozeb72Fin5+\nAJwf7+TK9HVHTh87hobNmjmlGerTiDh9GiaTySXCpgBXCafIxHMYPaEXLu5MhafEdeUTDuzYgR79\n+rm+DU/8KXyxawxaBnTAD68vgNrz2TF9xUGTm8vFBt6+cQNxMTHoPXDgM8/JSE9H+YoVS712abFa\nrTi8ezd6Dhgg+OtkckIC/vrtN9M/y5fbJBLJQU1u7k+U0gi+7XpZYTFOZRxCSE2FSrXIUyZL7vXm\nm99tPXnSd9upU6ouvXoJ8mKg02qx6a+/uHGLtm0FIZoA+3bVo3EZT2LUpEmcaALsPfOMBgM3znz4\nsMRrH9q1CyaTvYihO0QTAPiUK+dS0QQAjVu1QpvOnV26hqtEWfNqbdBsSBtsjVrtkvkLqPfKKzDl\n5bl0DQAIrtEBeydEQir2RLdPA3H8WmiJzrdYLIiNjubGKUlJOLZvHzeu98orRYomADi+fz9yHbJj\n+UIsFqPXm29y18nIc+e4IptCwz8gANPnzZOeS06WTZ4+va9v+fLhXj4+FwghbxDi5LoZjCJhHqcy\nCiEkUKVWz7Rarf2Gf/CBaNyUKVK+G9gWB6vVCp1W67I6QSXlQWIiqlSr5rT5rFYr1i9dilGTJoEQ\nAqPRiMvnzxcpHqKvXhX0lsHLSkTCGXyybRiOTb5VJjPsnsb2M+swM3QKRnX7CJM7fwex6HGxbrFY\nsG/rVvQfOhSA/abnfHg4uvXp4zQ7sjMz4SmTCaIKOKUUOVlZXJafkDGbzdi7eTPm//STNu3Bg4c6\njeYrAFsppVa+bXsZYEq1jEEIeUXt7R2iVKkuj586deDZpCTZ9HnzBC2atqxejYS7dwHY7/KEIprS\nHjzA9ciXG35BAAAgAElEQVRIp84pFosx+qOPuLtYsVgMqUOV7IdpaVi/bBkA+zZHAe4STY6tK1zN\nnVu33LKOM+s4PUrLgHYIkNXE+jDXZdgVYLPZsHnlSpevAwAD243E/mmXcS4+DMOWd8ODnEQAwIIZ\nM7hsP7FYjMYtW3IZeUqVyqmiCQBMeXk4ffSoU+d8XgghhUTT8l9/hVYjzBZzHh4eeHPECByNjlYt\n3LSpZv3GjVco1eq7hJAR+V0gGC6EeZzKCISQhiq1ejYFXp345ZfSdydPFhdVd4hPHDPRhJSVZjQY\nYDabi6zZ5ErMZjMsZjO2/v03Xn3jDZw8dAjvjBsHwF6126DTuazy8YPERFSqUsXl24EGvR5hoaHo\nPch5rUuehqtinAo4GLUDPy77FCcX33P569iV1bgBe7Bx7cBAzsOzdO4c3FPHYn/EViz4cgO61O3l\nsrWLw8O0NFSo5Pqq58VBqNewJ0EpxcnDhzH7q6+0d2JicvU63dcA/qGUur5p5ksIE04ChxBSX+Xl\n9V8APQeOHCkdOGqU2N090UpKwt27OBcejsHvvsu3KY8RGhKCFu3aoVIV96ZlF5f01FTcvn4d7V99\nFYDdQ3T7xg0uI8lqtUIkEgn6Iv6iQSnF68ua4esec3gXFkWRl5cHQgiX2bZ+2TL06NePE+LnT5xA\n45YtH9saO3svDJ9vH4k3G4/E1FdnQCLix2mx4c8/MWj0aMH1MoyPi0PE6dMYNGoU36Y8k6sRETge\nGoqD27dr78TE5Oi02v8DsIlt4TkXJpwECiGkrsrL6xdqs/X98MsvJWM//VTiWKzSZrMhZO1alzbZ\nLAkWiwWEELcFNpcEnVYLpUrFtxlITkjAhZMnMaCERT0d73ZvXL6M+3fucEG4Vy5ehDY3lxNaT8rw\nM+j12LtliyCFbFlh2+U12H5lLdaNev62IiXhzq1bSL5/v1DxRsD+PrPZbJww2rF+PZq1aYOadesC\nALavW4f2r776XB7LDF06Jq58C1lXM7Dp9zCUU/Bb802n1UKhVAri+vYoeXl5ghF3Ny5fxitNmxb6\nGaUUp44cwc9Tp2rv372bqdNovoA9BkpYFUDLKEw4CQxCSEWFSjWLUjry/alTJeOnTJE8LSYoMT4e\n1WrUcLOFT2bd0qV4Y8gQl7TUKA0mkwlrFy/GuM8+49sU5OXlQSwWO7V9is1mQ57RyHkQLp09i9zs\nbHTt3RsAcOHkSei0WjQNDoZv+fLIzsyEWCJx6Vblro0b0e+dd9z2gefqrToAMFlNCB5fGau/34/m\nNdu4bJ3U5GR4ymTwKVcOaSkpOB8ejsCGDRHYsCEAYM/mzWjcsiVq1KkDwPmlK6w2K37Z9yX2x27F\nkre3ool/K6fNXVIuX7gAnVaL9t268WbD09j01194tW/fQtm1fGC1WnFkzx681r//E99vlFKEHTiA\nn6dO1T5ITEzS5uZOopQKI6isDMOEk0AghCiknp5TRSLRV4PHjBFP+eknz5JU+b51/TpuXb+Ovm+/\n7UIrC6PVaCC0li0FuLOX3LOwWq1ITU4Gn8H7jh6r6KtXkWc0omlwMAB7LSdCCCc8Is6cgUwuR8Nm\nzQAAOdnZkEqlJcp6io2OdluxUMA9wgkAZod8gwTjHSwcvrHY52RlZEAkFsM7v93MycOHUb5SJTRo\n0gQAELp9OwJq1eKe74jTp1ElIIDX1wsA7L+xDd/snoCJTb7CB69P49WWAoTynn4Uo9EIkUjktiLD\nOzdsQOOWLUtUdZ5Sij2bN+Onzz7TGw2G85qcnI8opTdcaOYLDRNOPEMIERFCRsnk8t/avfqqbPpv\nvylq1atX6nkjzpxBnaAgl6XW3r9zB9cjI/H6W2+5ZP7ScP7ECZhNJnTo3p1vU3Dp7Fl4eXvz0uIh\nZO1a9BkypETta/Q6HaxWK+eRijp/nsuuAoAThw5BrlCgVYcOAIDwgwehVKnQsn17AHYvgVKt5oRT\nSlISpJ6eKLgJsFgsEIlEgvwABB7fCnuQmAiJhwcq+vkhx5CF9tNqYPno7ejQxv7aOrp3L8pVrIhm\nrVsDAI7s2YMKfn6cML146hQq+PlxW2k6rRaeMlmJvI47//kHrw0YAIVS6cw/tUiik69g1Ne90Pvt\nQfhP79/hIfZw6/qOGI1GrJo/HxO//JI3G55GanIyzhw7hjdHjHDJ/FarFQ9TU7nt19J4GfPy8rBm\n4ULb7z/8YAKwWafVfkkpTXGiuS8FTDjxCCGkh0qtXly9du0qMxYvVhV8+DiD1ORk2Gw2rkaRM7JC\n3H1nxSgdzq5RVRSUUmRlZEAsFnOFNW9euQJPmYy7Oz5x6BBUXl5o3sa+3XVs/354+/qiIOGB73H4\nwYPwLV+eE4o3Ll+G2ssLAbVqAQD+b8M4+Kor4Ou+s131ND5G5sOHUKhUvPRvzDXmYPK2obDaLFg0\nZAu8Za5p1Pwi4VhN3Rlci4yE1WLhxLgzyMnKwvwffzT9s3y5hVL6W57R+F9Kqc5pC7zgMOHEA4SQ\nRmovr8VypbLFDwsWKF9/6y2Xx4MsmzsXoyZNKtVd65bVq9G9b18IsVHw3wsX4s0RI1xeCbs4nAsP\nh9TTkxMHLwsXT52C0WB4LKDZ1bhrqw4AolOv4q3R7RG1L5NXD4w7sdgsmBk6Fbv+3IBtK06hVvnS\ne8RLy9olS9Bn8GBBtG55lE1//YXegwY997UoJysLW//+2y1xmQl372Lm1Kn68AMH8owGw/9RSlex\nDLyiYcLJjRBCfJQq1RxCyMgpM2Z4jpw4UcSH90an1WLD8uUYP2VKkccKKXvkWVgsFqcGXZcGPmO/\ncrKyEHX+PLr0cn/afMG1xN1ZUO4UTgAw5K9OGNvuU/R5ZbDb1gTs26injx5Fj3793LpuASvD5mPx\nhV/wx+CNaFezKy82FFBWynLk5eVBKpUWaefmVaswYPhw3q61ly9cwPSPPtLGRUen6jSa0ZTS07wY\nUkYQZqDBCwYhhIhEohFyheLuG2+/PerkvXvy9z79lBfRBNgrAI/55BNunHDvHq5duvTYcTlZWdjs\n0FdOSFgsFuzetIkb8y2abDYb1+eOz4B5o8HAxdu4G0IILx9k7hRNADCy9SSsu7jErWsCgEKp5LLp\n+OC9Lp9i/qD1mLz1HWw+554K509DLBYX6jF3LzaWV3ueRnxsLA7t2vXYz1OSkpCTnc2Nu/TqxesN\natPgYOw8d071y/Lldbx9fQ+rvLzWEUKElSItIJjHycUQQhqovLxWV6pSpeGvq1crhVi80mg0Iik+\nHnWCggDYW5Govb0F0T/qaVgsFiTFx/P6QeLIoV27UKtePV6CwIXA3du34YykhrJAniUPbf9TFZs+\nCUNg5YZ8m+N2olOvYsj4Tvjk6+l4v/1Uvs2ByWRCalISF4cmRCilnPeeEILwgwfRNDhYEKEFj5Kb\nk4Nfv/02b/PKlSaTyTTFZrWuZPWfCsM8Ti6CEKJQKJVzFUplxNQZM1odvHZNkKIJAGQyGSeaDu/e\njYjTp3HzyhXu9wWeFL6hlCLtwQMAdg+TUEQTALzWvz+vouniqVMwm828rR917hxva7uyV92T8JR4\noluVN7Bs71y3ruvIufBw2Gz8fJbV92uM0HVXsCnyL8w6+AVsPH+mSqVSTjTl5eUhKyODV3sKcHRK\nhB04gNgbN7BgxgxQStG5Z09BiiYA8PL2xk8LF3puO31aHdSo0TyVl1ckIaRp0We+PDCPkwsghPRX\nKJUruvTurfzxjz8UQm3vUVyO7dsH/+rVEdSoEQD+4oluXb+OrIwMtOnc2e1rP4n01FRkpqdzzwuf\nnD52TJCFAt2Bu2OcACAh+x76L2+Fs1OS4Clx/xZL9NWrqFi5Mq/B0dmGTIxd9waUD1RY+e1eSMX8\nZ9tqNRoc2rkTA0eO5NWOqxERSE1O5i0ezVnYbDZsXLGCzpo2zWiz2VbqdbqvKaXC7HzsRphwciKE\nEH+1l9dqtbd3+7mrVimFUEeoOCz65Rd8MG0aPDyKlyW0ccUKdOvTh6srIqTAbHdy5eJF1KlfXxDt\nXBjuZ/ia7hjZaqLbg8SFhMGsx4ifekARqMKyd0KglL6c74WEu3dxNiwMQ8aMKfY5uzZuRMPmzTlv\nv5DJSE/HzClTDKEhIUaDXj+WUrqTb5v4hAknJ0DsDJfJ5UvGff65bPL06R5lIROtgNK2bVj+668Y\n/dFHkMnlAOwBygXfl5aje/eifKVKTq1h8iKRcO8eAmrW5G397MxM3Ll1C0LdhnYlWyJXY93Gxdg5\n+zxvNmhyc2Exm3ltdWSxWfDV7vcRnxmLVcP3QeUpjG4ClFIsmDEDn0yf7pSkBcdaeDnZ2di6enWp\nSgZQSmGz2QTZ3/NpnD9xApOHDdPrcnP3aTWaDyilWXzbxAcsxqmUEEIqqby89lerVWvZlhMn1NNm\nzhS8aNJptQgNCeHGpX3jfjBtGieULBYL1ixaxO3vm0wmpKU8f2HaLr17C0o03bp+HScOuafRa1Fk\nZWQg2iEWjQ/0Oh3v7UHcHeNUQJ+Gg3FbexPp2lRe1i/gLE9/fwESkQRz+v+F2j710XtcE+QYs4s+\nyQ0QQvDxt98+t2gyGo3cdcxqtXLxSQDg7eNT6jpLjk3R42JiEMljnGBxad2pE47FxCgGjBjRT65Q\nxBJCXufbJj5gHqdSQAgZIlMoVoyeNEk2deZMqdAFUwFajQYGvd4tDSp1Wi0O796NAcOGAbB7KBLj\n49GoefOnnnP/zh0oVCpUqFTJ5faVlJzsbKi9vATbMuRlhI8YpwKm7hiDBn5NML5d0TXRXnQopfhm\nywRcy76EtaMOwkfumnZPz0vU+fPPLNWRcO8eKvr5cTeBK+bNw8iJE91SsZ1Sivt37ggq4aUoTh87\nhk+GDdMb9PrtOo1mEqU0l2+b3AW7+j8HhJDyai+vnf4BAav+OXLE65u5cwUvmsxmM1KSkgDY6wy5\nq6u3UqXiRBMASD09YbP+W5g2LiYGx/btK3ROfFwcvHyE2drB28eHd9FU4OJn2OFLNAHA4GZjsPXy\n37yt74jVym/BZ0IIZg1ZhnY1u2HY368iU/+QV3seRa/TFcoQPhsWhtTkZG4cc/UqLBYLNx7/+edu\na3NDCOFEE6UUSffvu2Xd0tC+Wzccv31b0Wfw4LcUSmUsIaRsBPU6ASacSgghpL9coYgdPGZMr6Mx\nMYItMfAoEadPw2gw8G0GFEolmrRqxY1rBwaihUOPvmuXLkGv03H98ITgEU2Mj8fmVav4NoMjNCQE\nt2/w39h8/bJlhT5oXkba1OiMlKOJuJJ4kW9T8MfMmXybAEIIvn5tDtpW6ILe7zVBhi6db5M4MtLS\nkHjvHjf2DwiAj0NsWI9+/XgtXluAzWbDmWPH+DajWKjUasxduVK2ZNu2ir7ly+9SqtV/EUJe+AwB\nQW/VEUJkAMIAeAKQAthJKf2aEFIOwCYANQDcA/A2pTQ7/5yVAFoA+JZSuteZtihUqoVKlWrYos2b\nFa07dXLW1AwAf/7vfxg+YcJjGWoRp09Dp9Wic8+eAOzeKLlCAXeWeOCrlcjTcEbDZmeQnprqNs/l\ns+Bzqw4Afgr5DBKlFN/0msObDYBwXheA3ZY5h7/BibsH8c/oo/CSebt8zZysLJjNZm6L/+DOnahS\nrRrXsNnx+Vm7ZAl6DxokiNfvi0JOdja+mzjRcGTPnod6rbYvpZTfAEwXImiPE6XUCKAbpbQZgCYA\nuhFCOgL4CsAhSmkggCP5YxBCGgG4D6AlgNHOsoMQUlepUkW169p12JHo6DIjmjauWIEHiYl8m1Es\nxn3++RPT+lu2b8+JJgAQicXQabXc+Ni+fYg6/29WkzNvBAq8KXy1EnkaQrGFfejYeav9GOyP3sq7\nd1QorwvAbsv/9ZiFVgEdMHZtH+hNOqevEXHmDE4fPcqN796+DU1ODjfuOWAAJ5oKbCpgxIQJgoyh\nfBLL5s6FXuf858/ZePv44I8NG+QzFy2qJlcqz3h4eLxPhPSidCKCFk4AQCkt2JSWAhADyALQH0BB\nYMHfAN7M/94CQAm7h8opiESiITK5POqLn3+uu2LXLoWXt+vvnJzFO+PGoUq1anyb8VQS7t3jxElx\n44YCatYs1NqjW58+hbLuDuzYgWuRkdz4/IkTXLXxkmCxWLBsLn+VoZ/EjvXrYTQa+TYDAP/xNI7w\n6W0CgFf8mkJMxIhK5K8sgSPb161DXl4e32aAEIL/9P4d6kwfvD29M/IsJbMpPTUVMdeuceOIM2dw\nPDSUGzdq0QLtHIq+NmvduthtfxwbBMfHxfEuep/FB9OmQaFU8m1GsRk0ejTZfeGCwr9GjXlKtXrL\ni7h1J3jhRAgREUKiAKQCOEYpvQ7Aj1JakAOcCsAPACil0QAksG/vLSrlujKlWr2iYuXKq7ecOKEc\n88kn4rIgni+cPMldNIVub8SpU06x0XGO3gMHFsrYq1GnDqQOgfvb163D3du3ufHtGzeeeDcnkUjw\n0ddfl9o2Z9KqY0e3Bas+C0opFv78M99mCAZCCFqJOuLPdb/ybQoAoEOPHoIRAiIiwoovdqJ6q9qY\nvG0ozNZ/2wIZDQYuYQWwV0Pfv20bN7aYzYXqwbVs1w5de/fmxgV930rLg8REQQdjO/6N50+cgMlk\n4tGa4lG3QQMcuHJF2evNN99QqFQ3CCFN+LbJmQg6xskRQog3gAMAvgYQQin1dfhdJqXUabmv+Vtz\ne9p27Rowb926MuVlOhceLpiWJGWByHPnEFCrFue2X7NoEXr078/VJrp1/Tqq16kjCMEiJIQUT8N3\njBMA3Ei5jPEb+uPUZ/cE87zwTV5eHjLS0uAfEACT1YRR83vCHGfCtoX2G6aEu3fxIDERZSX0QQjc\nv3MHHlKpoHcSHiVkzRr67aRJBnNe3mcWi2UFLSui4xkI3uNUAKU0B8Be2OOXUgkhlQGAEFIFQJqz\n1hGJxW+Vta05x9eh0EXTtjVrBLGNUEDzNm0KxTrYbLZCzTczHz5EnsP22N8LFyIj/d9MoTPHj7s8\nW1EIGXSPwsRBYRr4NYHMQ47LyRf4NoUjNjrapWUr9DodrkdFcePkhARsXLGCG2dnZOBOTAwAQCqW\nYvXkfUjNScbsvXZPbkCtWoITTfu2bkVOlnCLYVevXZsTTWVFfzxh667s7Ds+BUELJ0JIBUKIT/73\ncgCvAYgEsAvAu/mHvQtghxPWInKFYoZv+fJrNoeHl5mtOUop5v/0U5l5E7Xr1g1Crnk1ZvLkQkHq\nbbt0gbdDTal3P/64UGNV9SPCesVvv0GT+28duNV//FFoKzDz4cMS/6+ir14t0fGuhFJaaHtFCPDt\nbQLsQrJ34CBsPbGab1M4jHo94uPiin08pbRQnaOc7GxsX7eOG6enpmLt4sXc2Gw2w+RwE+QfEICh\n48dzYz9/f3Ts0YMbyz0U2LH0HPbGbcaWqNUl/XPcQocePSAuI303j+7di8sXhCPUn0XB1t2rffq8\noVSrIwghVfm2qTQIequOENIY9uBvUf5jLaV0bn45gs0AquORcgTPuY5cqVZvCKhVq8eaAweUlSpX\ndoL17kNI2yZlFaPR6JLtOKPBAKmnJxf8vnHFCrw5YgQXu7Hol18wzqHQ3uZVqzBw5Eiu4XLmw4fw\nLV9eMP/ftAcPcOXixTLf9d0VRCacw/tfDcDF9c/fYqi0GI1AbhaQnQlkZVCkp+jRqIUSNesCBr0e\nYaGh6D1oEAC7MNqyahXGf/45AHtV//3btmHY++8DsAsjnUYDn3LOrQAe+zAaQ1d3wZw3VuHVBn2c\nOvfLRlm79lNKsfi//7UsnDkz16DX96aUlg3l9wiCFk7ugBBSRalWH+rcs2fteWvXyp3VnNbVXIuM\nfGbbEiHx1++/Y/CYMYU8N0Li8oUL0OTkFLo75ovU5GRUqlLl33ozixdj2AcfQJJ/F/z7jz9i8nff\nQSwWc01MJ3/3HSfMzhw/jrZdunDnWywW7twXFSHEOAGAjdrQ9rdq2DQmDLXKFy+7yxFKAYMe0OYC\nWo39qyaXQqch0OYCudkW3L4RCYUyGNmZQEaaHrE3l0Gu+BzZmUB2phZm0xKUq/gFfMoBKi8NtLlr\nYdBPwuEbgMTDjJTERATUquWCv75knLx1GB9MfRMhK86gvl9jvs15IkK/bjkSGx2NajVqOK25uqs5\nsGMHPhs5Um/U68fabLbNfNtTUl5q4UQIaS5XKA5O/PJL78nTp3uUFeVusVhwfP/+MnPXb7PZeG9T\nUtaglGLRrFn4+Ntvn3mc43NLKcWZ48fRPj9FuyD7raDRqc1mw4IZM/DZ999z5zqOrVYrtqxaxW23\n2Gw2RJ47h5bt2nHzZWdmwteh2rIQcLVwohQwmwGzyf4w5X/NM9qFjtEAGPWAQU+x/PpY+CmaoLXH\nFBh0VtyPi4J3uZYw6AG91ozYm5tRsfIIaDVAbnYeEu/+D56yb6DJBXQaI0SiefAp/zVUakChMkCT\nMx9Bjb6CUg3IFCbotSfQqEV3+JQDvHwoVF5mVPCTwtsX8CkHyBXAo5exIZ32o04DP/x3eQuXPUfP\nw86rGzDnyNfY9f4FlFdWLPoEN1OWrlspSUlITU4WVEP0orgeFYVRPXvq9VrtPKPBML0sBY2/tMKJ\nEDLIUyZb9+uqVbJ+Q4eWDcVUhrBarbBarVzrFCFitVq57uRCxGQyufX5o5QiNTkZlavaww9sNhtO\nHz3KeeLSUlKwccUKfPLddwDsAn7xL7/gk+nTnzg2m81YOns2JucfX5zxsjlzOLFoNpvx98KF3FaS\nxWLB+qVL8e7HH3PjSUOWQySaBErt48S7y1C1xkew2QCLxYykewtRJeBzbvwgYQ4qV/0WNhtgtZiR\nmjwbvuW/yxdDZmRlzIZMZh+b8sww5c2GzfYdPDwAiYcJNttcqL2+hcQD8JSZoNPORbWa30KusI/j\nMidDUz8CfWQX4SmzID3lMOo37g2ZApB62pBnTEDV6jWgVAMqL0Dl8FWpBlzhHEy4Z0PfFjaEXpGg\nisCSseYe+RYX75/C+ncPQyISrmfUVVv5LztpKSkY3auXLuHu3SM6jWYopZT/vmDF4KUTToQQ4imT\nfaNQKr/5z++/K/oPGwaxWAyLxYIbUVGF+qgJCZvNhjWLFmHM5Ml8m1Isdm/ahKbBwaheuzbfpjyV\n+T/9hE+mTy9TMQJ8cuPyZXj5+KBajRouW8MxZoNSCr1OxwXrU0qRm53NZT1SSvFGi0z0fac8agcC\nIBRGQzbUXr4Qiexjs8l+PhEBhFCIRIBYTEBEgCj/4SEFpFL714KHVApIPPLHHo97cZ6GwaxH83EV\ncG5ZErzlvkWf4Cbmfgs8SAR+E0Y/Yg6rzYr+U4NRL/AV/D5xXdEn8MSS2bMx4YsvyoQH6sShQ/Dz\n90dgw4Z8m/JMrkdFIeHuXXR9/XVMGT3aEBYaeken0bxKKXValryreKmEEyGEKJTKeRUrVx6/OTxc\n6efvz/3ObDbj7PHj6PTaawAATW4uMtLSULNuXb7MfYzszEynB2oyhEfEmTPc9hjj2fQPBt4edxwj\nP+zKtykc4zf0R79GQzGg8XC+TeHQaoBOtaKwYlcQWrYXVhxMjiEL/f8Mxmddf8DAJiP5NqfMY7PZ\noMnNFVxsVnJCAsJCQ7nkA0copfj1u+/Mq+bPT9XrdO0ppQk8mFhshC+fnQQhRKxUqVZXr117/M7z\n5wuJJgDw8PDgRFP+8UiKj+fGD9PSeKku6yhshS6aKKVIS+Evo+hFwbHfFqPs0bVeH4TFHeDbjEKo\n1MDYz7zx0+f3IbR7ZW+5L5YP3YEZBz7HtQeX+DbnmVit1kJ13ISISCTiRBOfjhGdVluobZV/QMAT\nRRNg/7z94uefPT774YfKcqUyghAS6C47n4eXQjgRQqRKtXp7/SZNBm89dUpZHAGiUqvRoXt3xzmQ\nmpzMje/evo2Eu3ddYm8BZa1GU4HrVchcjYgo1O9KiDi2lRAKMdeuCbZhdOOWXfk2oRCdar+GI/v2\nCO59O+mrWtBrg3BkD9+WPE5QpUb4oecfGPFBD+QahXvjYLFYcGT3br7NKDahISFuqwNXkOVbUHRV\nqVJhwhdflGiOD6ZNk3z/++/l5QrFOUJIM1fY6Qxe+K06QohCpVbva9mhQ/Cy7dsVzgrwy0hPR3Zm\nJuoEBQGw94grV7EiN2YIE5PJBA8PDxbXVEKuRUaiTlAQ5AoF36YUon8wMGMx0FRAyUSUUrT+3B/r\nvzmMwErCijM5sAP4/Qdg7yV7fJfQ+HrHBGgsOfjjrQ3sPSpAbDYbKKVcUs2K337D2+PGwdkdNvZt\n2UKnjhmjza/1dNqpkzsBAb51nAchxFupVod3ff311it27XKaaAKA8o+IpIbNmxdK096/bRtib958\nrrlzsrJc2irB2Qjdy+SIVCoV7AV50axZgvNSFNCoeXPBiaYCrkYc59uEQhBC0KN7P5y4c4hvUx6j\n5wAgN3sFNv0lzC3179/4HbHpN7AlahXfphRJSlKSoNpHFUV2ZmaJz3mYloac7H9rS29ZtarQVuX4\nKVOcLpoAoM+QIWRpSIharlAcIoT0dPoCpeSFFU6EkHJKlersgOHDGy3YsEFeUInZVSiUSpSrUIEb\n9x40CDUcAsu3rVlT7PYHe7dsKdTKQMiYzWZEnBbcDcFj7N60SfAXufenTROsqGOUjI61X8NJAQon\nQoAfFozGX/P8YLXybc3jyDzk+GPwRvz462e4kXiZb3OeicViKRPXvgKO799fZHzW9ago3Ll1ixtH\nX7lSqFfnO+PGwV2dNbr06oU1Bw4olCrVDpFY/KZbFi0mL+RWHSFErVSrT789dmzgf37/XSrED6N1\nS5ei54ABqFSlCgAgPi4O1WrWFHRdobJMfFwcatSpw7cZZZKzYWGoWbcuV99JSAhxqw4AsvQZaPte\nNVxdnwOpWFi1zCgF3uoAvPsxMEA4iX+FWBo6B9tvrcPOSechk7D6Sa7ixKFDkMnlCO7YEQCQGB8P\nn9/Q8UgAACAASURBVHLloFKrebbsX65GRGBo164GnVY7kFIqiKyLF87jRAiRq9Tqw6+/9VY9oYom\nABj54YecaALsbT/u37nDjdcuWQKTycSHacUiIz29UENQoSNk0ZSckFCoMbDQ8PP3RwU/P77NKFP4\nKsqjxit1EJl4lm9THoMQYOoMYO43NwTpdQKACb2+QO3Kgfjt6HS+TSkWyQnCzJ43mUyFvEwXTp5E\n+MGD3O5Hxx49ONEEANVq1BCUaAKAxi1b4u/QULlcoQghhHQs+gzX80IJJ0KIVKVW7+3Us2fj2StW\neApVND0Jb19fKB1esP3eeYdr9Gqz2fD7jz9y8S+UUt4/aE8ePizYeBxHrkVG8m1CkVyNiIDU05Nv\nM55KrXr1BN3vTmgxTgV0btMLF++f5NuMJ9L+VUDicR2hIcKMpSSEYOYbS7Dl6CqcunmUb3OK5FxY\nmCBCAe7fuYNDu3Zx47joaNyLjeXGwR07onPPnrh46lSZahDcqkMHLN+xQyFXKPYTQlrybc8Ls1VH\nCBEr1ertLdq1675yzx6Fq2Oa+CQvLw8b//yTaz2hyc1FaEgIhowZw69hAsNqteLYvn1lpqcfo+QI\nsQBmAaE3t2PjpT+xesQ+vk15Igd2AItnATvOFb8yurvZEP4nFu74GUfmRLMtO9g9SOkpKahavToA\ne1mcqHPnMHCkvXCoXqeDSCx+YdvDhG7fjs9GjMg1GgztKKU3+LLjhfA4EUJESpVqTf3Gjbv/uXNn\nmRJNsdHRJT7H09OTE02AveaUozjISE/H6j/+4MZajQa3bzjnNca3p6skiMViJppKyYlDh4qd1MAX\nQqvjVEBw9Y44s/UYrDZh7oe91t9eUfzMMb4teTpDO41Hk7atsCDsJ75NKRYmkwlGh2Dq58HRmZGW\nkoJ1S5dy4+yMDNyJieHGterV40QTYE9SKoloysrIwMM0wXc44eg9cCBmLVumlisUJwghvPXzeiGE\nk0KpXFC9Tp0Baw4ccGrJAVeTkZ6OFCcUFSSEFCqFUL5ixcd62mVlZHDfJ8bHY/PKldzYoNcXSjl9\nGtmZmdi/bVup7XUHVqEGbziQkZ6Oo3v38m3GM3mlWTNUdWFvuheZ8sqK8GtVFTFp1/g25YmIRMC4\nKSb8+Ol6vk15KoQQ/NRnETZd+guRCef4NqdIsjMycCAkpNjH63U6hKxdy42zMjLw98KF3Liinx9G\nTJjAjStVqVKow0VpkXp6IvKs8OLwnsWgUaPIN3Pn+siVytOEEP+iz3A+ZX6rzkMq/bhy1aqz9166\npCho/skoGSlJSbh26RLnnYm9eRPXo6IwYNgwAHZhRQiBTC6sHldPIyM9Hfu3bcPIDz/k25RnkpOV\nBQBgr9vnR8hbdQDw5a7xeKVyM7zb+uOiD+YBkwloX/0u1hyohVea8m3N01kXthQLl87EqfXxEIvK\nTuaxxWLBge3b8caQIQAAo8GAVQsWYOKXX3K/z8rIQEWWfFFi5v/0k2X5r7/e1mk0rSilbs1UKtMe\nJ0JId5lcPmf94cNlSjQl3b8Ps9nMtxkclatWLbSlVbdBA040AXZhdfrovwGa1yIjEbp9OzfOyc4u\nlsfKXZSvWLHQXZpQ8fb1ZaLpBSe4eidcEGiAOABIpcC7H9fC2kV8W/JsRnSegJq96mH9xaVFH+xG\nKKXYsno1V7DYMZGnoMJ2/SZNuONlcjknmgBAIpEIRjQ5ZnWXBT6ZPl3SpVevmkq1egNxc5R7mRVO\nhJB6MoVi+/IdO+RCTjV/EufCwiASYr+Dp3DhxAkENmrEjRs1b47eAwdy48z0dMQ49EOKPHcOx/b9\nGxCbGB+PhHv33GJrAULPFhGScH4al86exbnwcL7NKBKhxjgB9jin43/vF3QG6tD3gT2bzcgueWFp\nt2HfsluI+WE/IkPn2ia7Oq22UOeGFfPmwWgwcOOFP//MlYohhKBdt27c9UYkEuGz778HIQQLZswA\npbTMtOGKvXlT8A2MHSGE4Lc1a+TVatbsLpPLv3fr2kJ+Qz8NQoi3QqW68s3cudVGfvhh2VEgZZTS\npq0+SEyEXqfjLiDnT5yAKS8PHXv0AABEnDkDiUSCpsH2KoYGvR4eUmmJU+B1Wi0unjqFLr16Pbet\n7uKPmTMx+bvv+DbjmRR8OEilwirg6IhQC2AWQClFq1mVsGdyJKp4VePbnKfyductaNa2Mb6ZU59v\nU57J9zsn487/s3fe4VGV6fu/z0wmvfdOh5AEktAR6R0VEBALKip2XHXdtf/cdV0V/arriiiLBQSU\n3kMPEFqAQEgjCYH0nkz6ZHp7f39McpiDCWRCMue8MJ/r4tInc2bOnckpz3nf572fy9ew8ZOjXf6M\ny+fOITI2lm0hdHO/tY2rV2PR0qXs6xqNBg5dsAuhabk/zUirqjBr6FBlQ13dU4SQzheY3QHUJR0M\nw4hd3dz2LXjqqQDakiYhTWdZwp2e/EGhoZynrlHjx7NJEwBEDxuG/oMHs3FORgbSk28Ugp49dgwX\nz5xh46y0NBTl5bFx29OhSqnEYLNhcSEj9KQJMCVMQk6a2hCqjxNgOneG9hmFjIpLfEu5JR98/QgO\nbo8QrCFmG2/N+ASZ8hSkmhmLFuXlccx4N/zwA2fkZN3KlWioq2NjkVgMxmzE/+Z+a0+98gqnL2NX\nkiZA+KPeHWEwGKhaPe0fFIT1hw87O7m4bGAYJtYa+xSuq10HOLu6fjc4JmbExytXCtcxsB3KioqQ\nnZ7OmeISOlt//RWLn3uuxy8ADg4OnIvT8LFjOa+bJ1mAqSbLfKT07LFjcHFzY9+XeOgQPL29ETd6\nNADTiJa3ry/6DBgAwGTPYO/gQEVSwCe2J+buYUjQCGRWXMKswcI992NHAV4+wNljwEQrDNgSQtCi\nkaFZ3YhmVSNk6kbI1E1oUjXgWlYWiJsRclELGpV1uH4oGxgAyOybINfI4FDiiJOpBzEsdAwAoLy4\nmONs/9Srr3KO22dff52z77brgrU4Fh+PmFGjBFPLdDtUSiX2b92Kx194gW8pnWbI8OH4eu1a578/\n99xRhmGGEEJqenJ/VE3ViUSiR/yDg387euUKVcXgtFJZVobgsDC+ZXQKhVwOF1fXdl9rrK+HSCRi\nC7HPJSbC09sbkTGmZUQJ+/YhMCQEQ4abDGmP7t2L4PBwRMfFAQDycnLg6ePDXvgMBkOXewoq5HI0\n1NUhrHfvLr3fWjQ3NmL377//ydZCaAh9qg4ADmXuxJefv4+TW67ffmMe2fAjwbF9OdhwOOq22xJC\noNGr0aKRQd76T6ZuQrO6EaUlhdBKtFBBgWZ1I64nZUMUyEDtrEKzqhHSM9XQhKng5OcMD0cvGFMJ\nAmND4B8aBE9Hb2hLtOgzaACC/EPh5ewLLycfeLv4wcvJB+6OnhCLxDAajVCrVHB2cbHCN3NnKORy\n6LRaeHp78y3lruerDz/UrV+16rJcJhtHCOkxW3xqEieGYcIdnZyyt5465dpWC0MDtqf2nkdaVYWk\n48c5RnB3ivnfrfD6dbi4uiIg2GQZkrBvH4LDwxEVaxoVPrxrF8L79WMTsUM7d6L3gAHstOHlc+cQ\nGBqKkPBw5GRkQNHSgqi4OMFf9I1Go+AXMdCQOElbqjD9hyikv1vP27WgLdFR6ZRQ6hRQ6ZRQaU3/\nbZTVQalXoFGhwucvn8b8V13g4MdA76CDXCND0dk8iIJF0LlrIde0oOFcLTTBatj5SuDm4A5kAF4R\nvvANC4CHoxdUuUqED+6LwMAQeDh5gVGIEOgfAh93f3g4ecHD0Qvujp6QiLtuVCxvacGeP/4QvOUI\n7dB2/zIYDHh4zBhF7pUrn2nU6hU9tR8qEqfWdirJy99/P+bV99+nanpx448/Ys4jj8DHz49vKZ0m\nJyODTQJs3Dk1lZVwdHaGh6cnAFOjzYDgYIT3NRnfHti+Hf0HD8ag1pWLB7Zvx4DISAyMMj3579+2\nDQOjotj4WHw8+g8ejN79+wMw9boLCAmBf2AgAJN9hJuHBzsCp9PpYGdnR9UFsLMI3cepjTH/CcW2\nZ08j3KsvCCHQGrTQGjTQ6NXQ6lv/20Hc1NgIg8gAYmeERq9GVUEZRK5iwIlApVOi+HI+JH4SEA9T\nXHmmFKIQEfTeeqh1SsguNkMXqIV9gAOcJM5AJuDW1wMeoV5wkjhDkS5HwKAQBIQG4eJxd3hBgUlz\nQuHnFwgXezdIDPbwdPeGh7MXXB3c4WrvBhcHN9iLbVPdllBVXg5HJyeOWbHQ+eHzz/Hi22+Dpm4c\nFaWlmBEVpVLI5RMIISk9sQ8qEidHJ6d/RsXGvr0jKclF6E/AN0PDU7s5Go0GZxMSMPXBB/mWYqMD\nVEolRGIxWxdWnJ8PDy8v9oJ88cwZBIeHI7TV8fvQzp0YEBnJFuDHb92KiCFDMCAyEgCwb8sWDB46\nlI3jt25F30GD2BG1fVu2IDImhn3/zfGx+HgMiIxEmy1I0vHj6NW/P7v/y+fPI7RXL3bELjs9HQHB\nwfD19wdgmgr1DQhg9Rfl5cHb15edWi0rKoK7lxebeJaXlMDd0xPuHh6YOxKYPn8Llr42my3wLSsu\nhoeXFxuXFBTA08eHfX9+bi58/PzY/eVeuQK/wED24Sbj0iUEhYbCPyiI/T5De/dmp60TDx1C/4gI\nhPXpA8CU6EYMHcougNi7eTOiYmPZ72fv5s1448wTgC9gb+8AbboGdsF2cAxygr2dA4yZRjiHu8A1\nxB32dg6Qp7TAs48XPMK94WDniMb0evj08YdXkA8c7BwhK2qCT7A/fPz84CxxgbZJC29vX3i4e8FJ\n4gIniTOc7U3/dZK4wNneBY52Tp0yjjx7DPj8beCg8HtjU0dzYyOy09Jw35QpfEvpNLTdv9rYv3Ur\neWfZskqlQhFBCJF39+cLPnFiGGa0q5tbYkJOjlNQqHCX89rgh2Px8dT0ozu+fz+mPPAAFSM/P6xY\ngeXvv9+pbZUKBewkErbYvk4qhbOLCzsVeXMic3PikpORAf+gIDaRykxJQWBoKDuClpacjJDwcDaR\nuXzuHEJ69UJgSAjmjgSWvHweE2eFIzAkBIDJfyokPJxN1NIvXkRwWBj7/qy0NAQEB7M1a9eysuAX\nGAhvX18ApkTUy9eXTbSqysvh7unJjuA1NzbC0dmZTVx1Oh3EYvEtbzD7D26Ds70L7ps4BfZ2DhAx\nwrwZGY3AML8D2HpqFgZFC9+huzg/H3qdjrMq14YNAHhjyRLVsfj4XXKZrPtqOFoRdOLEMIy7s4vL\ntf9s2BA4a8ECvuVYxN7NmzH3sceouEm2Qdt8tk6nw/XsbHZkROhkpqRg6IgRfMu4q6Chxok2/vr0\nVQSFhuGdz9tfbCEkNBoNCq9do8aGpA3arrWJhw5h2JgxVHU6kLe0YOrgwcqaioqlhJAd3fnZwnzs\nacXVzW31nEce8aQtaQKAqLg4qk6MFpkMa7/7jm8ZFiGRSKhJmgDYkqYeQsg+TjTy5CuDkbBX+EkT\nYLIyoS1pqiovx/Z16/iWYRFxo0dT0e3AHFc3N/y0e7ezo5PTuu5uBmxR4sQwzFqGYWoYhrli9rOP\nGYYpZxgmrfXf7Ju2T2cY5gFLhTEMM0Fibz//45UrHS19rxDoHyFsB96bcXN3F/zSc3OEPFJKO7Lm\nZtv32wPQYoAbNxpQtADXsvhW0nloOl6DQkOxcOlSvmVYhKe3NzuVThMxI0di6V/+Yu/q7t6t3Rgt\nHXFaB2DWTT8jAP5DCIlr/XcIABiGiQZQCmA4gKct2QnDMBIXV9f1n/3vf86ubm4WSuSXitJSviV0\nma56E/HB959+Ss3FkhCCjatX8y2j09D2NCzkXnXmbF+3jopjViQCxk7Jwk9fn7n9xgLh99WrOe7g\nQoema6050upqthUTLbz5z3/aOzg6zmAYZmp3faZFiRMh5AyAxnZeam9OSg/ABYDFDt/2Dg5vRQ8f\n7jd74UJL38orRqMRSceO8S3DYi6dFW739o5Y/sEHVE2F0jTdvOzNN6n6bmnh+b/+lZrv9fEXByHl\nLD0F10+89BJb3E8LlWVlVm9+fqfIZTJOOywacHJ2xhc//+zs7Or6G8Mw3dJxpLtqnP7CMEwGwzC/\nMgzjCQCEkFyYWrqcAtDpYTKGYUJFItE/vvj5ZxdaLjJtiEQiLH7uOb5lWIRGo+F0AqcFmp7YGIah\npt0CjdhqnLqf4WMlUCl9UZR3+22FAE3Xgza8fX1RXV7OtwyL6DtwIEaNH8+3DIuZPncuho0Z42Xv\n4PBOd3xedyROqwH0ARALoArAN20vEEL+SggZSQg53dkPc3V3X/P8W29J2vqK2ehZHBwcMHrCBL5l\ndBqVUonKsjK+ZVgEDdMzbWi1WjQ3tjeobKM7qJNK+ZbQKRgGmDwHOHGAnmOXEILC68Jua2OOo5MT\nRt5/P98y7hlW/PSTi1gsfo9hmN53+ll3nDgRQqSkFQC/ABjV1c9iGGaWk4vLpNc+/JAem1KYTtjf\nvv+ebxn3BAW5uVC0tPAto9M01tfjd4rqmypKSpBx6RLfMiyClhonADi0o1tXRfco46Yq8fvq//At\no9MwDIOMixf5lnFPcOnsWWSl0eWSGtanD1557z17V3f3n+/0syz2cWrN1uIJIUNa4yBCSFXr//8V\nwEhCyBMWC2EYkYubW8F3f/zRmxZDwzYIIWisr6dujt0Sk0MbXedOmgLbuDU2H6eeo0UGjA42IKVG\nDGdht1WkmsO7dqF/ZCRVK7H1ej0ULS1U+ToBptKU8X36KKRVVQ8SQk529XMstSPYDOAcgEEMw5Qx\nDPMcgC8ZhslkGCYDwEQAf+2ilkc8vLwCo1o70gMmR1+1Wt3Fj7MeDMNQlzQBwLK/dvVPZcMSbElT\nz2KrceoZ3NyB2NFiJB3nW8ndzdSHHmL7TtKCnZ0dVUnTpbNnUVVeDgcHB7yzYoWLm7v7N8wdFFFb\nuqrucUJIMCHEnhASRghZSwh5mhAylBASQwiZTwipsVREaxPfLz9fs8bRvK1KY309tBoNG69buRKN\n9fVsnJWayvvSyIrSUqpqWMxxdKTLIuv4/v18S7AIQghaZDK+ZVhEFWXFqrRRJ5VCY3ZNEzoTZxEk\n7KXrGD577BgVD9xtSCQS2NlR1bueRSj3v7TkZJQWFrJx/NatyMvJYePAkBB4ensDAOYvWQIXN7dB\nACZ1dX9CcQ5/JKxPH5+JM2dyfjhm4kS2vxUAPPv665zO0i0yGQx6PRuv+eorKOQ3+vklHjrU426n\nZxMSqFli3EZDXR3ne6IFH8oM2MqLi5F0nK7H9ZOHDvEtwWJoqnG6mpEBaWUl3zI6zdjJBCcOrOVb\nhkWE9ekDJYXXN9qsCQBTzWlPPWyZr/ZOPn0aORkZbHxkzx5OjVVAcDB8zVYuP/Too2zTcsB0TDg5\nOwMwjZa9s2KFi5uHR5dHnXjvVdc62lS4eseO8AkzZnTrZ2enp2NQdDSbza/67DO8+PbbsLe3ByEE\nv/znP3juzTfZqRRZczPc3N2pS4Qs5eCOHRg/Ywbc3N35lmLDxh1hq3HqWQwGINYbSMwDfOl6bqGO\nbevW4ZFnnrnr7z+A6eHdaDSybuSnjhyBq5sbht93HwAg8eBBePv5IWak6cSWNTfDydkZEkn3rBvT\n6/UY36ePoqq8fC4h5ISl7xfCiNPi8L59vcdPn97tHxwVG8sZAn3tww/ZDu4Mw+CJl15ikyZCCMcx\n2WAw4LtPPmGHIQ0GA04cONDtGvlgzqJFtqTJxl2Drcap5xCLgeHjgEv0mIhTy+Jnn6U2aTIajZwp\n6Oz0dKSbrXA8d+IELpw6xcaVZWWQmbUgmjhzJps0AcDkOXPYpAkA3D08ui1pAu581InXxKl1Jd2X\nH3z1lSsfB4yL641GlgzDcByTxWIx3vjHPzgHsn9QEPv/F8+cwYp332VjtUqFH7/4go21Wi2VjtxC\nRKvVYssvv/AtwyIIIdT5TbXIZJwaQhs9A21TMiPv1+PEwQq+ZVhEnVSKA9u38y2DWgghnDKXorw8\nXLl8mY1TkpJw+uhRNv7h8885VhChvXtzpsrumzIFYyZOZOPouDj0HTiwp+R3irmPPw5Xd/cBAKZY\n+l6+R5ym+gcGet4/bRrPMm6PWCxG9LBhbOzh5YV3Pv+cjR2dnPDqe+9x3mOedMlbWvDT11+zcYtM\nhp+/Yb1CoVIqOQei0WiE3qx+q7s4efhwt39mT8MwDGY+/DDfMiyioa4O2ZT5nJQUFFCX7AF01TgB\nwPnERL4lWMTICQySEo7efkMB4evvj5EUOlyXFRUhPze32z9XrVZzjG0Lrl3DxTM3hhHTL17kzKik\nJSfjwsmTbOzu6Yng8HA2HjFuHMxLa6bNnctxFPfw9OQMTAgRsViM1z/6yMXdw+Pd22/NhdcaJw9P\nz0PvrFgx88lXXqFzfLIb0Wq1KLp+HYOiowGY5nR3b9yIpa+9BgBoamjA7t9/x7Ovvw7AtOLwyO7d\neOz55wGYRrxKCwsxMCqqw30YDAZkpaZyhkBt2KAZW41Tz6PTATFeQHKlyaLARs+hVqtRkJuLqNhY\nzs8JITAYDGzpibS6Gg21tYgYMgQAkJWWhoqSEsycP98Up6aisqwMM+bNA2Cy9mlubGSTmxaZDIQQ\nzuKrexGFXI7hAQFqtVLZjxDS6VUbvI04MQwTqNVqJ89bsuSeT5oAwN7enk2aANOcblvSBACe3t5s\n0tQWz1+yhI0NBgPqam44QdRJpVi/ahUb19bU4I///Y9NmmprarD9t9/Y1xVyOWeVgtFoFEQPO0KI\nIJa72hAuthqnnkUiAQZGAznpfCuxHKFcO3Q6HeRmHQ+kVVWcqa/cK1dwcMcOODo6Iio2FlczM3Fo\n507O6zfX2DqY2clEx8WxSRMARA8bxiZNADAoOpozIuTm7n7PJ02AqVxn7mOPQWJv/4Il7+MtcbKT\nSJ574JFHjLQVKRuNRvywYgXfMsAwDBydnNjYxdUV9025MVXr6+/PSbz8AgLw9PLlnNcfXLyYjQkh\n0Jh5n9RJpZy6oprKSvyxZg0bV1dUcOI6qRRH9+5lY4VczhlyNhqNMBgMFv+euVeucD6XFsw9RGih\npKCAbwn3BBWlpbz7z1nKwKgGnEus4luGRRBC8P2nn3bpvXq9npPoNNTV4WpmJhuXFBTgyJ49bJyX\nk4P4rVs7jEsLCzk1r3YSCcdAclB0NOYsWsTGg4cOxeyFCzmxeSLkHxgIofVzvZaVxflOaOHp5csd\nJRLJawzDdNqpmJfEiWEYkYODw+tPv/aa0+23FhYikQgv/O1vfMuwmCuXL3NWOTAMw/paADAtBR07\nlo39AwPxxIsvsnFAcDCWvPQSGweGhHBiDy8vxI0Zw8Z6vR4NtbVsLK2qws7169m4sqyMk5jdHFeU\nlmLb2rWIGDIE0+fORX1tLccTSSGXoyjvRut2vV4vGNM7Qghyr1zhW4bFpCQl8S2hS9BW43Q9O5uz\noogGBkZpkJoknAa6Wq0WzWbfYXNjI65nZ7NxVXk5ziQkYPkHHwAACq9fx54//mBfL7h2DXs3beow\nLi8uRrLZKjBCCESiG7fLoLAwmPsODoiMxEOPPtph3G/QIEyePZuNvX19Ed63LxvfvDjq9//973Zf\ngeAYGBWFyXPm8C3DYqKHDUNQWJgDgE4v7eelxolhmOl9BgzYeeLaNTdal1/SRlNDAxydnalyCzca\njezFSq1SobamBmG9ewMw1Xhdz87G6AkTAJgulMmnTrHTl+UlJTh3/DgWP/ccANNKpvMnTnDjxEQs\nfvbZduOaykpkp6VhygMPsPsrKShA7ChTD2uFXI6GujpWj06ng0athqubWw9/KzbMsdU4WYfsdOD1\nxwmOXzVdrzUaDZRyOWtI3CKToba6ml0pVSeVoiQ/n11iXlFaiuy0NHbUpDg/H6nnz2PBU08BMK3a\nSrtw4ZZxenIyHn7ySQCm8/V6VhamPvggAKC+thZV5eWIbm3ZpVIqoVQo4OPn1+PfTU8grarirOK2\n0bNsWrOGfPHuu8eam5o6ZSbJy4iTu6fn68++8QYvFgR3glarpa6FRhue3t5UJU2AKXFSKZUATKsW\n25IUAPDy8WGTJgAICg3l1HyF9urFJkkAENa795/j1iSpLX7kmWfY2NPHB0PNiujtJBI4u9zodKpS\nKlFutqy8rqYGp48cYeOyoiJODZmlcWlh4S3jsuJizhNyVXk5jsXHs7G0uhrnTtzwdWuoq0NacjIb\nNzc1cUbF5C0tKM7P5/x+5o7AarUaDXV1bHxzzYbBYOD4uFizNs0aNU5txbltGAwGqFUqNtbpdJA1\nN7OxWq1GnVTKxkqFAhWlpWzcIpOh8PqNEZzmxkaOM3J9bS0unzvHxtKqKpxJSGDjyrIyHN69m41L\nCwuxc8MGNi4pKMAOsxHe9uKbt79V7OBYgNLCjVC0GnLXS6VIPX+efV2jVqOpoYGN7R0cOE7/vgEB\nGDt5Mhv37t+fTYoAoM+AAbeN25ImwHS+tiVNAODj58cmTQDg5OzMJk00XrNpTprMrxO0MPeJJxit\nVjuBYZhO2bxaPXFiGMZerVJNnb1oEV1ZE4ArKSkoui6c4erOIpQCSUvJzcxE2oULVtufeSLv4ODA\nutoCpmJK8xWLvv7+GDtpEhsHhYayNQpXLl9GWJ8+nETM0ji8b99bxiHh4ZhtVhPh4+/PMZBzc3dH\nL7PGoRJ7e47pKTEaoTOrs1EqFJxi1RaZDAVmNWpN9fWcv4W0qgpnzOwzKsvKcHjXLjYuLy7Gro0b\n2bi0sJBz46YtLisqwr7Nm9m4qrwcCfv2sXFtdTXHZqCpvp7zfcpbWtgaMr1ej6Jr1zieWTcnmvYO\nDvAyaxzu5uHBPf4CAjBu6lQ2DuvTh5No9OrXD4uWLr1lvPDppzsd94/oh/C+Q5B7xbRgJDgsjJO4\n+Pr7Y5jZVL27hwenca2DgwNvprtbfv6Zl/3eKbRet83PE1pwdXPD2MmTdQA6Nddo9ak6hmGmjmQQ\nrQAAIABJREFUDoiM3JWQnU1XVTjFrF+1CvOeeIJtcmijZ0nYtw/T587lW4ZFtMhkuHDyJHW6aZyq\nMxgM2L9tG+Y9/jjfUixiybSTmPPIMCx5yXbptgYr//1vvP7RR3zLuGfY/ttv+PStt440NTTMut22\nVk+cnF1df3j57bdfeuOf/+x0BbuNO8NgMLCtZWzYuJugMXGile8+ATRq4J3Pb7+tjTvHdt22LnVS\nKe4LD1drNRpPQojmVttadaqOYRhGJBItnDZvHnVHQ1V5OWcVB03QePIRQlBdQVebBxv8YPNxsg59\nBwGF1/hWYTl6vR7S6mq+ZVgMjdftNsxXONKCr78/+gwYoAUw4XbbWrvGaZBEInGLjImx8m7vnNzM\nTCoPZJVS2SX/JL6pr61FxqVLfMuwmJrKSup6kQGmGiWlQsG3jHuGgmv0ZSB9BwHZaedvv6HAYBgG\niZQ2aFfI5XxL6BLXsrL4ltAlHnrsMVdnF5eFt9vOqomTSCR6aMb8+SLaVtMBpm7NNC413/PHH5zV\nT7Tg6+/PccKlBRpX8ABA/tWrnFViNEGbjxNgaolBG30HAlXlTaDtOUwsFuPRZcv4ltElfl+9mm8J\nXcLcw4ompj70kIhhmIeZ2yQpVq1x8vLxOf9/a9eOMXdAtWHDho2uYqtxsi6jQ4DdF4DgML6V2LDR\n/RBCEOvrq2xuaIghhOR3tJ3VRpwYhmFUSuWQNgNBmigtLIS0iq52A7Rj7ilkw8atsNU4WY/AUKCq\n/PbbCY3amhoqR95pxtyHjBYYhkHMiBEGAMNvtZ01p+p6OTg6MjQaezXU1XEaKtKCWqWidurI3FyP\nJi6eOcO3hC6Rf/Uq3xLuKQqvX6ey9tDVLQsFuQ2331Bg1FRWoqKkhG8ZXaLWrHk7TdCaqI64/34X\nB0fH0bfaxpqJ0/DoYcP0VtxftxE7ahSnISMtXM/ORiGFRagAOGZ+NKERSL88S8lOT+dbQpehscap\n8No1Ko8V30AGFSX06Y6Oi8Og6Gi+ZXQJc2NZmjDv5UcTQ0aMEDk5O99yZZ3VEid7B4dRI+6/39Va\n+7sd+bm5eHjsWAx0dMTP33zDeW1c796YNXQo5sTFYZ7Z1GJTQwOenD4dkwcOxFMzZnDsCd5+7jnM\njo3FCSus3uhIe2VZGR6bPBnTo6IwIzoal8+dQ0xr2xChaG+jubERLz78MGbFxGDe6NGc5asnDx/G\nlIgITBowAKu//JL9eWlhIeaNGoUnpk7l3Rri/MmTmBMXhxnR0XjUzEHcYDAIVvvRvXsxKyYGc+Li\n8ODw4ZyWLB5eXoLVfTPmx4e0yqRViDrVajXmjR6N2bGxmBYZiS/ffx+A6Vz8beVKPBAXJ4hzsSOa\nm5rwyqJFmDp4MKZFRiItORl9BgRh+7qlgrmOtMfa777DzCFDMCM6Gmu/+w6A8K5/5vseERCAmUOG\nsD/7/O23MXXwYMyKicFLCxZg3hNPsK/9sGIFJg0YgCkRETht5tx/LD4es2Ji8N4LL/Cm+9uPP8aY\n0FDMiYvDnLg4JB46JDjdnWHI8OFQKhSRtyoQt1ri5OLqOmHoiBG89MZrDy8fH/zr++/x4t///qfX\nGIbBlpMncTAtDdvPnkXy6dMAgNVffIH7p09H4vXruG/qVKz+4gsApqWXweHh2H/5Mqe/k7W120kk\n+Ojbb5GQnY3dFy5g4w8/IL+1bYZQtLfxw+efI3rYMBzOyMB/NmzAv954A4Ap8fh/L7+MH7ZtQ0JO\nDvZt3sxOI/2+ejV+2L4dr334IfaadTq3Ns1NTfjH8uX4NT4eR7OysHrHDlb7P197DesPHxak9vun\nTcPhjAwcTEvD17/9hvdffJEK3ebcrLWpYTOO718vOJ0A4OjoiC2JiTiUno7DmZk4n5iIS2fPCu5c\n7Ih/vfEGJs+Zg+NXr+JwZib6RUQgM+ULuHsKV/u1rCxs/eUX7L10CYcyMnBi/36UFBRg9RdfYHBM\njOB0P/Lss/jt8GHOz8bPmIGE7GwczshAn4ED8eOKFQCAvJwc7N+6FQk5OVh/+DA+evVVti3Lnj/+\nwMG0NPgHBVnFQ6k93QzD4Pm33sLBtDQcTEvDuKlTkXz6tKB0dwZff384u7gQAH062sYqiQzDMIxS\nqYweMvyW9VZWxcfPD0NHjICdRNLu621/WI1aDdfWHksJ+/ZhYWu/p4VLl+Lonj0AALGdHVQKBbSa\nW5qNdhsdafcPDERUbCwAwMXVFSG9e6Om1URSKNrbyL96lW362W/QIJQXF6NOKkX6xYvw9veHb0AA\nJBIJHnrsMRzduxcAIBKLoZTLoZDLO/y7WYN9mzZh9sKFCAoNBQB4t/YUO5eYCB9/f4T17i1I7eZN\nihVyOdsLLf3iRfgFBQlWtznpFy+iV//+rFZP78dwNTMJYjs7Qelsw8nZGQCg02phNBjg4eWFhH37\nMHnOHDTU1QniXGwPWXMzLp05wzbGtrOzg7uHB65m7IPRMACAMK4jN1OQm4vY0aPh6OgIsViM0RMn\n4tDOnUjYt4/t3Sgk3aPGj/9TGcj46dMhEpluzbGjR6O0sBAtMhmO7t2LuY8/DolEgrDevdGrf3+2\ncTcxGqHVaKBSKiGxt+dFN8DtrydpPQ+FpLuzDBk+XI9bFIhbawTIR8QwkoDgYCvt7s5gGAZLpk3D\nQyNGYP/WrWwyUldTA7+AAACAX0AA6lqL9vpHRECv1+PRiRPx9PLlvOk2p6y4GFdSUhA72lTjJjTt\ng2Ni2Ln79IsXUVFSguryctRUVCAyJobVGhQayiZ/S197DR8tX45ta9dyOqVbm6K8PDQ1NOCxyZPx\n0IgRbDPb6vJy+AUGstsJUfuRPXswdfBgPDN7Nj5euRIAUFNRwV7kAGHqbqOmogLBYTfWwkvsQ2Ev\nccDTy5cLSmcbRqMRs2NjMSIgAGMnT8bAqCj23KutrhbEudgeZUVF8Pbzw9+ffRYPDBuG9154AUqF\nArKmGmg0HgCEcR25mYHR0bh05gyaGhqgUiqRePAgqsvLUVdTgydfflmwujti+9q1GDJ8OPJyciCt\nrGQf1gDuefr4iy/ikfHjIRKL0WfAAL7k4rfvv8esmBi8s2wZZM3NGD1hAhW6b2boyJGujEgU1dHr\ndlbSEezj768B4GCl/d0RO5OS4B8UhPraWjw5fTr6RURg1PjxnG0YhoH5FOg/vv3W2jI7RCGX49VF\ni/Dlr7/CxfXPZWVC0P7Ke+/hX2+8gTlxcYgYMgRRcXEQicW4le9YUGgotp48aT2RHaDX6ZCVmopN\nx49DpVRiwdixiBszBq5ubvDy8Wn3PULRPnP+fMycPx8Xz5zBW089heOtU7m9+vVrd3uh6G6jo+ND\naDrbEIlEOJSeDllzM56eORPnEhMBgFOozPe52B4GvR7Zqan4ZNUqxIwciX+9+SZWf/EFGAYw6KcA\nEMZ15Gb6R0Tg5XffxVMzZsDJxQWRsbEQ3dTxQYi622PVZ59BYm+PV959FwDanYJu+z3unzYN96ek\nWFXfzTz5yit44x//AAB889FH+Oxvf8P//fpru9sKSXd7BIaGilzd3PidqgMQ7B8UZN1uwu2w8ccf\n2cK1W/UuarNM8PHzw6AhQ5DZ2vrDNyCAfZ+0qgo+/v49L7qVzmrX6XR4eeFCzH/ySY7zNp/a22j7\nHR4YNgxKuRxfrV2Lg2lp+M+GDaivrUWvfv0QEBKCPLOl8ZVlZQg0e1rhC/PvPyAkBONnzICjkxO8\nfHwwasIEXM3IQEBICCrLytj3CEG7+Xdu7kU2avx46PV6NDU0IDA0VHC6O+Lm71inLYNOp+VRUedw\n9/DAlAceQNbly4I4F29HYGgoAkND2cUlcxYtQlZqKvwCAtFYL2zti597DvEpKdh26hQ8vLzQZ+BA\n+AYEIP3SJSjkcsHqNmf7b78h8eBB/NcsWbr52K8qL0dASAgf8trF19+fTUofff55ZFy8iFNHjsA/\nOFjQutvDPygIdnZ2vTp63VqJU1BIeLi1Rrc65KlXX2UL1/xbp1Rudk5XKZWs/4RSocDVjAwMbH06\nnD53LnauXw8A2LF+PWZYsSVIZ7QTQvDusmUYEBmJRUuXormxkX2NT+1ttP0OB1JT4ejsDK3WdMPb\n/PPPGD1xIlxcXTF0xAiU5OejrLgYWq0W+7duxfS5c62u9WbMv/+ZDz+MlLNnYTAYoFIqkZ6cjAGR\nkZBIJCi8dk1Q2s2/c5VSyR4zbS0/vHx8MHTECOTl5AhKd0cMHTECxXl5rNamhq2IGHof37LapaGu\njl29pVapcDYhAVFxcZg+dy62/PwzKkpLeTsXb4d/YCCCw8JQeP06AODssWMYGBWFaXMfgqLlnzAY\n+LuO3I46qRQAUFFaisO7dmHeE09g+ty52LFuHZobGwWru42Thw/jp6++ws9798Kx1T+wrKgI0+fO\nRfyWLdBqtSgrKkJxXh6EZCht/mB2ZPduDBoyBN6+vpg0e7agdbdHQHAwjEZjh7VFVpuqC+nVS1AO\nktLqaswbORJymQyMSIR1332HhJwc1EuleGnBAgCm4ep5S5ZgwowZAEzTS8sXL8a2X39FaO/eWLVt\nm6C056SnY/fvvyNi6FAkHjwIkUiEj779FpNmzRKM9jbyr17F35cuBRgGg6Kj8WXrkK6dnR2+WrcO\nS2fOhMFgwOJly9B/8GBetd5M/4gITJw1C7OGDoVIJMJjL7yAAZGRyEpNxfv/93+C1X5o507s2rAB\ndhIJXFxd8f2WLQBM3/m8J54QrG5z7Ozs8K9Vq1itnt7LMPXBpXzLahdpVRX+tnQpjEYjiNGIh596\nCuOmTkVUXBxenD8fm9aswYDISN7PxY74+Pvv8eaSJdBqtejVrx++WrcORoMBv347HZMHDUSvvvxf\nR9rj1UWL0FhfDzuJBP/+8Ue4e3iw178lU6cK4vrXxl8efxzJp06hsa4OY8PC8Nd//Qs/rlgBnVaL\nJ6dPBwAMGzsWMaNG4ZFnnsGDixdjemQkxHZ2+PePP96ytMHaui+cPImc9HSAYRDWpw8+X7OGrVUV\niu7O4h8UBK1W69fR61bpVefq7v7L2599tuyZv/ylx/dlw4aNewdbrzrrMzIIOJAK+NPXBMKGjU6h\n0+kwyNHRYDQaHQghf7L479RUHcMwsxiGyWUYJo9hmHdbf9aXYZiLDMMcZxjG81bvt7e3701jqxUA\nSDx4kG8J9xy5V67wLcEGRdh61VkXiQTQCr+s7E8o5HKUFhbyLeOeoqayEllpaXzLsBiJRAInFxct\ngHZHnW6bODEMIwawCsAsAJEAHmcYZjCAVwA8AuAzAEtu8zFeNLYsAQDPDlZJCZ2yoiIYjUa+ZXQJ\nWtvEnEtM/FPdGQ0YjUbWKNWGddBqtSjKy+NbRpcwGBKh1/GtwnK0Gg3KKe1XR2vC5+jkxHqZ0Yab\nu7seQLuJS2dGnEYByCeEFBNCdAC2AJgHQA/AtfXfLU8jAkiEZEpnCXGjb9nrT7Aknz4t+Hnkjpiz\naBHfEroMjd+5wWBAnkBce7sCjb3qDHo9CihNVsViUJk4efn44L5W013aoLV5uIeXF/oNGsS3jC4h\ntrMj6KAOvDPF4SEAyszicgCjAXwJ4HcATQCeaOd9NyDEzs6O90V19xSLlgqzYPZuhtaLskQiweyF\nC/mWcU/h5OyMaQ89xLeMLuHuNZnKqTqasV3PrY/Y5P/V5cSp3bkHQkg5gEmdEUAIsbvZhIwGjEYj\nTh89ikmzZvEt5Z7BYDCgIDcXA6M6NG21YYMlMwWYN+okvHwm8S3lnkHWZKpzog2dToeSggL0j4jg\nW8o9g1KhQMalSxhr1gidFsRi8R2NOFUACDOLw2Aadeo0DMMYMlNSoFap2C/wfKvLr5BjYjTC09tb\nMHosifdu2gT/4GDB6OlsPGLcOBTn56O+tlYQeiyJc9LTsezNNwWjp7OxwWDAnj/+QHB4uCD0WBKf\nKZqErMuA2M4Ujxhnej0lSdhx8unjqKuuxAOLnxKEHkvi1PMnUScF6qT8//0tibVqNQwGA/pHRAhC\njyUxrdfzuDFj4OHlJRg9lsRqlUoE4E8r6oBO2BEwDGMH4BqAqQAqAVwE8Dgh5Oot32iGl69v5k+7\ndw+5uW2JjZ5jx/r1tuFdK3MuMZHK6TqtVosTBw5g1sMP8y3lnkGtUuH00aOYMW8e31IshtbjnGZs\n13Prc3+fPrLy4uL7CSF/WubdKR8nhmFmA/gvADGAXwkhKywR4O3rm/rD9u1xtpPNhg0bNmzYsCF0\nxoaFtVSVl49ub5CoUz5OhJBDhJBBhJD+liZNrchampu78Db+sfk4WR+bj5MNS2gbZrdh41a0yGQo\nKy7mW8Y9RWVZGa5mZvIto0so5HIxgJb2XrNKrzqdTldi3seGJrx8ffmW0CWkVVVQKhR8y+gStPo4\nXT5/HmqVim8ZXSIvJ4dvCfcUapUKZUVFfMvoEucSE/mW0CXkMhlqb9EgXciUFBTwLaFL2EkkcPPw\n4FuGxRgMBshbWhwB1LT3ulUSJ4VcXlRTUUGlG6PQmxF2RFFeHupbm13SBq0+TmKxmFrTUZpH+Whc\nsaNSKqm9GdJKUGgoho0Zw7eMLpGSlMS3hC7hHxiI0F69+JZhMfVSKezt7RWt3pV/wiq96hiGeeHh\nJ5/877cbN9JpIWrDhg0bNmzYuCfISk3FkmnTCpsaGvq197pVRpwAVFWUllLoNQsci4/nW8I9B61z\n4jb4wVbjZKMzFF6/Tu1UOq3Qev+sqayESCTqcF7XWolTZU1lJX29KAAEBAdT2X+MEEJtL6xiSnVX\nlpVR+53bapysS1NDA6SU1tvQWuNUUlBA5bVco9GgorSUbxldwj8oiG8JXUJaVQWDwdBhY0OrjTjV\nS6UUes0CQ4YPp7L/GMMwSE9O5ltGl6C1/YedRAKDoV2/NMFjq3GyLnVSKbWFyiKRtW4b3cvk2bOp\nbDjbUFtLbT3c0BEj+JbQJaSVlUTR0tJhZ2Vr1TiJJPb2iouVlY5ePj49vj8bNmzYsGHDho2u8MK8\nefKEffteJYRsbO91qzw6EEKMLm5uuVmpqdbYXbdiNBpxePduvmXcU0irqkCrfYUN62OrcbLRGbLS\n0viWcE/R3NSEpOPH+ZbRJTIuXQKAyx29brUxV7VSefZKSgp1E8wikQjhffvyLaNLFOfnQ6PR8C3D\nYrRaLbX1H7ReKGw1TtalrKgIKqWSbxkWU1VejvzcXL5ldImKkg5LVgQNzedmr/79+ZZgMbLmZjTU\n1dnD1GquXayXOKlUF1KSkuTW2l93EhkTw7eELlFbXY2G1ma5NBHaqxei4+L4ltElJPb2fEvoErYa\nJ+tSeP06tFot3zIsxmg0wsHRkW8ZXWLm/Pl8S+gStJ6bHp6eVHo4ZaWmwtXNLY8Q0mHBqlVqnACA\nYZgIX3//Syk1Na5W2aENGzZs2LBhw4YF/PT11/jvxx+vUcjlL3e0jTWXR1xvbmqSNDU0WHGX3UPh\n9etIvXCBbxn3FGmUrgi0YX1sNU42bkd2ejrUajXfMu4pdm1st65a8KQkJcmVCsX5W21jtcSJEGJ0\ncXW9duVyh/VWgiU4LAxBoaF8y+gSmSkpfEvoEk319XxL6BLJp09TabKXn5sLvV7Pt4x7huvZ2XxL\n6BKnjhzhW0KXkFZVwZ7CafSrmZlU1qkSQjBs7Fi+ZXSJVhufWyYqVjXkUMjl+04eOkSdg7ijkxO1\niZO0qopK07fJc+bwLaFLeHh5Qaej7hBHWWEhlQkfQGeNE62Jk6ubG98SusTk2bOp9J+qKCmhMuFj\nGAa9KSwMLy0shKypyQjglhX5VqtxAgCGYUYEhYYmni8rs9U52bBhw4YNGzYEw7rvviPf/OMfW1ua\nmx+/1XbWTsFTmxoa9DS2pbiamWmrpbAytLZ2sGFdbOeljVtRU1lJrYUCrfz2/fd8S+gS8Vu3tshl\nsm23286qiRMhxCi2sztwYv9+6uaOBkRGIorSJfJnjx3jW0KXoLHVDQAc37+fbwkW0yKToZxSnxsa\nuZaVxbcEiyktLKRyilGlVMLFlb5JjrTkZMhbWviWYTGEEMx74gm+ZVhMi0yGK5cvOwJIuN22Vp/0\nlctk2+O3bqXuaLCzs4O7hwffMrqEvYMDlXVONNauAIBvQADfEixGp9WirKiIbxldgsbjpIDCERCx\nnR28fH35lmExvfv3p7JGVa/TUZnwMQwDGlurnTl6FM6urpcJIbf1m+SjWu5YTlqag6y5mYdd3zk0\nNnEdNX48taM3NBIzciTfEgCAkyzr9Xoo5DeuB2q1GvVm5qiOTk4I69OHjVtkMhRcu2Gc29zYiJyM\nDDZurK9va0sAAKivrUVKUhIb19bUcKZapVVVOJNw40GuprISiYcOsXF1RQVnpK6qvBwJ+/Zx4qN7\n97JxZVnZLeObt68qL8ex+HjO/k4cOMDRc/LwYY5e85Ha2poaXDh1ivP7Xj5/Y8VyY309zFcMNzc1\ncUaVWmQyFOfns/Gk2bNRVV7OxhqNBuZWLXq9XnDL50PCw+FH4UMBrYy8/34qr9s03iMB4PCuXcrm\nhoZNndnW6okTIUTh5OJy8QSF0xkKuRzrvvuObxn3DEajkXPz5BO9Xs8ZNlcqFCgtvNE8u6mhAekX\nL7KxtLqakxiUl5Rg76Yb52RZURG2//Zbh3FpYeEdxzs3bGDjmspKnDJLDJrq65Fplvgo5HLO76O9\n6UZOCIHRaGRjsZ0dnF1c2NjB0ZEz0ubi6sppVeTm4YGBUVFs7OHtjehhw9jYy9cXcWPGsLG3nx9G\njR/Pxj7+/hg9cSIb+wYEsPH5kyc5Mbv9hAmczxsxbhwbe/r4IGbUqBt6vLwQGRvL0dsvIoKNnV1c\nEGLmgmzv4MB5qhaJxbB3cGBjo8EArdkycq1Gg7qaGjaWt7Sg0Cwxbbgp8ayuqECCWeJXUlCAHevX\nd2tsfnzcHJcVF+Pgjh1sXFNZyUmEmxoaOIm0UqHgJIJ6vV4QzuiN9fW4eOYM3zLuGRrq6rBpzRq+\nZViMVqvF8fh4EYBOJSZWXVXH7pRhHokZNerXvcnJ1K1tJYRQ+RQQv3UrZi9cCDs7O76lWERWaip7\ngzUajeySYrVKhTqplLX0b2poQF5ODkbefz8A043n0tmzeOjRRwGYbgTnT5zA4uee6zhOTMTiZ59t\nN64sK0PGxYuYvXAhAKBOKkVBbi57c5Y1N6O6vBwDo6JQWVaGkoIC9IuIgH9gIADTU5jBYBD00uKc\njAwq2wudP3mSqum6qvJyODo5CXo6Q6/XQ6vRsMmxSqnEzvXr8eQrrwAwjUBWlJayx4u0uhr5OTm4\nb8oUAKYHgfSLF9nzrzg/H6nnz2PBU0+1Gxfl5SHtwoUO4/KSEuRlZ7M2JfW1taiuqEBUa7KrUiqh\nVCjg4+fH+T3qa2uhUasRHBbWM19UD7F30ybMffxxKu81NN4jD2zfjvdffPFyc2PjiM5sz1fiZO/o\n5FR3MD3dre/AgVbf/71IeUkJfP394ejkZJX9aVqfsEPCwwGYEpvstDSMmzoVgOnmcerwYTz2/PMA\nTInJ6SNH2LiitBRnExLw6LJlbJx0/DibyNRJpcjNzMT906YBMD3B11RWot+gQQAAnU4HvU4HJ2dn\nq/y+5qhVKlSVl6PPgAFW3/edcHjXLsxasIBvGXc9acnJCAwJoaruhhCC69nZGBQdzcv+NRoNlHI5\nm2w2NzaiuqKC1VNZVobr2dmYNGsWAFO3h8xLlzB/yZJ244Jr15B1+TJbxFyUl4drWVmY9fDDAEyJ\noLSqiu2ZqVapoNFo4OHpaZXft+DaNfZaZqPnWXDffS2p58+/SAjZ0pnteUmcAMDJ2fk/S156aflH\n334r3EfwDigvKaGyeeGt0Ol0aKyvZ0dImpuakHHxIibMmAHANFR/LD4eS156CcCNmhTz+MSBA3ji\nxRcBmJ70rly+zF7IlAoF6mpq2OmbtuOOticTGzZs3H0YDAbotFr2wbK5sRG11dXoP3gwANMIdP7V\nq5g8ezYAIP/qVeRkZGDuY48BAPJycnA1M5MT51+9yo5QS6uqUCeVsiN0Wq0WRqMRjpQ2TG6P+tpa\nODk7c6bwaaA4Px+zhg5tUatUfoSQTtm082alqlapftzy669GGu3kzx0/LrhValqtFmXFxWzc3NiI\n+K1b2bi2pgYbf/yRG69ezcYtzc1INSt2dXBw4Di/BgQHs0kSAASGhPwpbkuaAMDHz49NmgBTjYh5\nzQvDMJ1OmratXdup7Wzcm9h8nGy0R35uLqdu7FaIxWLOaLyHlxebNAFAWO/ebNIEAP0HD2aTJMBk\nV3NzPH3ePDa2d3CAg1mSVF5cjDNHj7Jx7pUrnJqyq5mZOLRzJxu3TX22oVapoFQoOvW7WYtzJ07w\nLaFLbFqzRsswzLrOJk0Aj4kTISRfLBZnHtm9my8JXWbxc891+0gJIYTT8kKpUCDx4EE2bmpowFqz\nwvTG+nqOyZhKqcR1s1U8Ti4ubL0BAPgFBGDMpEk43Pp9+wUE4KnWegUA8Pb1ZYepAdMqK/NEh0/G\ntU7H0cSZhARUV1TwLcMiivPz0SKT8S3jricrNZVvCRZjXlhOC77+/ogYOpS3/ZvXk3p6e3Om3voO\nHIjpc+eyccSQIZizaBEMBgNWf/klBg8dyo5WAabFFP5BQWxcUVrKSQqz0tJwZM+eG3FqKmdVaXVF\nBXraePqhRx+lbrRJq9Vi888/G1RK5Q+WvI+3qTqA7iLx22E0GtFQVwdff38ApsQmfssWthi5RSbD\n1l9+wfNvvQXAVFy8d9MmNpnRaDQoLy7u1nluQgg0Gs1dNTwsVBrr6yGmzPvryuXL8PH3p66QljaO\n7NmDmfPn8y3DIkoLCwXzIHW3o1aru/0aLa2uhqyxkR1Fy7h0CbXV1Zj20EMAgPSLF9FYV8cW3xdc\nuwaNWs1OLRoMBohEoruutMLSovA2+E6c7J2cnau3nznjZb40WYgQQqBUKFhDsrKiImwmCuwjAAAg\nAElEQVRftw5vffIJANPQ6drvvsOr773HxvFbt+KRZ54BYDrwZE1Ngl5JY8OGDRs2bDQ3NkKlVCIw\nJASAKbFqbmzExJkzAQApSUlQKZUYP306CCHYtGYNRk+ahP5mFh5ChxCC2bGx8tzMzGWEkNu2WTGH\n13bRhBCtVqP515fvvXdbp04raEHioUNs7ZLBYMB3n3zCxnq9Hlt++YXdPiAkBMPNfGEcnZzYpKkt\nbkuaANMculCSplozPxlaWPXZZ3xLsCFQbDVONm5m4+rVaKyv51uGRbTIZJxyDT7x8PJikyYAiB01\nik2aAGDEuHEYP306AECjVqNvRATH5fzCqVMc369zJ05wDGSrKyrQUFfXk7/CbTl99CjKiooaAOy8\n7cY3wWviBAAGg2FNSlKSztx1t7tQKZWcIu6fv/mGNWUjhOC7Tz5hXU4ZhoGntze7rVgsxhv/+Ac7\nNCmRSLDszTfZ1+3t7TkHEk0cMitCpIUX336bbwkWs3PDBjQ3NfEtwyLMC1BtdD+1NTXU9QRct3Il\n3xIs5tFlywTzoNpZEg8eFFzBd2dwdHLC2EmTOPYaYyZOxH2TJ7PxfVOmYIyZQa1cJkODWeeCU0eO\n4PK5c2yceuFCj9ZkEULw+dtvyxUtLe8QQiy2Oud1qq4NO4nkL2MmTVrxR0KCRZVllWVl8AsMhEQi\nAQCs+eorPPnKK2zmu/a777Dk5Zfh0Oroq1Iqu93Xh0azLxvWoUUmg4Ojo6BNL2/mxIEDmPLAA3zL\nuGvJz82FnZ0dZ8Wq0Gmoq4M3hT3qbPQ8PXX/axstbEt+j8XHwz8oCENHmEqREvbtQ69+/dhuBHq9\n3iJz58RDh/Dao4+WKFpa+hJCjLd/BxdBJE4Mwzg6OTtXbj11yqvtiwFMKwd8/P3ZQrl1K1di/pIl\n7Je5f9s2THngAV4r+XesX4+xkyezRo82eo7mxkY4u7qyibINGzZs3Ex9be2fHMRt9Azff/op/vL/\n/p/V93tzJ4Yje/agV79+iBgyBICpU8bgmBi25kqn07H3DUIIZg4dKr+elWVxbVMbnU6cGIaJALAO\nQByADwkh35i9VgxABsAAQEcIGdX6874AtgBoAbCQENLhvIWdRPJa30GDvt545IhD29zqsfh4jJow\nQdArk/R6PcRiMXWjTo319SgpKECsWb8uoZOSlARHJycIfSGBObYRyZ6HtpYrNEHj8bt+1Sosfe01\nvmV0GoPBgKTjx1mzYZqwdKTHWhBCQAhhW3TFb92K6GHD0GfAACQePIi/PPZYsbylpV9XRpsAy2qc\n6gH8BcDX7ekEMIkQEteWNLXyCoBHAHwGYMmtPtyg1/9cXlSkMG8UOe2hhwSdNAEmrw7aLiyAyVeE\nti7WI8aNoyppAkzmnTT5ORXl5aFOKuVbxl1LZw0ZhcL3n37KtwSLoSlpAkwNtmlqv2OOEJMmwFSz\n3JY0ASaPqT4DBsBoNOLzt9+Wy1ta3u5q0gRYkDgRQmoJISkAdB1pbednBgCurf86el/b52vUKtVb\n7y5bJqfthg7QV1TLMAyGjx3Lt4y7nkXPPMNZnSJ0GIaBUs77IleLoGm0ibbi3+UffMC3hLsedw8P\nDIiM5FuGRWSlpbELrWhi+7p1pKqsrBjArjv5nO5aVUcAHGMYJoVhmBfMfr4KwA8AngPw+20/hJAN\nlWVleZt/+qnLmSBfaNRqyFta+JZhMUKocbOUi2fO8C2h04jFYr4lWETv/v1tRoc9CG3TMTQdv9Kq\nKhTn5/MtwyJovP4CgLSykqpFL4CpPOXfb72llre0PH0no01A9yVO4wghcQBmA1jOMMx4ACCElBNC\nJhFC5hNClLf7EEIIkctkS1e8846GtumC0RMmwNWNPgP0pOPHqZs+0FLW31CpUFD5dEYLNh+nnoE2\nK42aykqOpYzQIYRg5b//zbeMLkHjytvP/v53tdFo3EgISbvTz7pl4sQwzKsMw6S1/gvsaDtCSFXr\nf2sB7AbQ5YpjQsgVIyG/fPLmm8JwArMQ2p4gxk2dimGUTdndT1nvuuvZ2ci8dIlvGZ3G3LjORvdx\n5fJlyJqb+ZbRaXb89hvfEixiyPDhVCVODMPgtQ8/5FuGRdB2f2sj9cIFHNi2Ta2Uy9/pjs+7ZeJE\nCPmxteA7jhBS3fpjTi0TwzDODMO4tf6/C4AZAK7ciSiVQvFhwt69KpqmZNr47fvv0dzYyLeMTnNz\nEZ2N7id21CiMMHOZFzq0LXagpcZJo1bD0cmJbxmdxtzw10bPQNNUKAD8uGIFdLpblisLDr1ej78v\nXapQq1TLCSHd8uRiiR1BIIBLANwBGGGyGIgE4I8bhVZ2AP4ghKy4Y2EM80h4377rjufmutDk22M0\nGqlMRDJTUjBoyBDWLFTo5F+9iqryctb234YNG/cmBoMBf/zvf3h6+XK+pXSalKQkqh6m2qDx/rZu\n5UrjNx99lCKXycaQbhoys2RVXTUhJIwQ4kEI8SKEhBNC5ISQQkJIbOu/6O5ImlrZ0VBXl7rq00+p\nSm9pO6ja8PDyQrWZFYTQ6RcRQZU1gVqtpq5wlRZsNU7dCyEEeTk5fMvoNAzDYN4TT/AtwyJoW13Z\nBm33t9LCQnz1wQcauUz2bHclTYAAetV1RGuh+ONrvvpKffn8eb7lWMy5xESqpux69euHXv368S2j\n0zAMQ1UvKnt7e+Skp/Mto1MYDAacPnqUbxl3FUqFgtPkVMjUSaWoN+sjJnREIhE8vLz4lmERtK2u\nPLx7N98SLEan0+GlBQsUOp3uI0JItz4JCDZxAgBCSIVapXr65QULlC0yGd9yLGLw0KFQUOaHA4A6\nU0xpVRXfEjqFSCTCnEWL+JbRKcRiMVzd3bvt83Q6Hee4kre0cFYZNtbXc7rCS6uqOOdOVXk5x+qj\norQU5teD8L59OXFlWRknrq6o4HxenVQKlfLGIt/mxkao1Wo2VqtU0Ov1bNwdD6o6rRa+AQF3/DnW\nwC8ggNOQVcjUVFZSVbBM2/W1jbA+ffiWYDH//fhjXVlhYapOq/22uz9b0IkTABBC9ijk8m3vvfAC\nVavsvHx8EBwWxrcMizl77BjSkpP5ltFpslJTUVlWxrcMXlEplZxEpLSwkDPamXrhAswd+Y/Fx6Pw\n+nU23rdlC2dqZt+WLRzH/n1btiD/6tUuxwl796KkoICNk0+dQpXZ3ywrNRW1NTVsXHDtGkd/WVER\nWsxWo1WVlUFhlkjdHFeUlEBuljiVFBRwPu/alSucEZW05GTUmiXgp44cQVlRERvHb93K+X32bt5s\ncVxbU8P2zdq7eTPyc3M5rxdcu8bGZxISUFFaysY5GRloqKtj49qaGk6ieS+TsG8fNYsZCCFY9dln\nfMvoElGxsXxLsIiLZ85g7X//q5S3tCy+U8+m9hBEk9/bwTCMs7Or69XPVq8Oe/jJJ+k4S1qRNTdD\nq9HA19+fbymdhsb+VEKGEAKj0QixWIzj+/djQGQkXN3d2Y7zScePI6RXL/Tu3x8AcGD7dvQfPBiD\noqMBmJpZD4yKYjuB3xwn7NuH/oMHo8+AAQBMLvbBYWHwDwoCAJSXlMDDywturaNIKqUSEnt7wbZL\nsBTae9W1XYPbzrn62lo4OTuzzcuvZ2fDNyCAPV7OHjuG3gMGILRXLwDA3k2bED18OPoNGgQA2PPH\nHxgyYgQnHjpyJPoOHGjafvNmxI4axU7NpyUnI7xvX/j4+SElKQk+/v4I6dWLOoNDGqDt2lqcn89e\nl2ihuakJUwYNUtZLpYsJIQd6Yh9UJE4AwDBMrLOra9KRzExnmoYNFXI5zhw9ilkLFvAtxUYXaZHJ\nIBaL2RtZ+sWL8Pb1ZR22D+/ahfB+/RAZEwMAOLRzJ3r178+J+0VEYGBUFDIuXYJIJEJAcDCb2DTW\n18PJxQWOjo48/Hbtk5eTA4Zh0H/wYL6l3BYaEqdDO3di9sKFfMsAcGO6qG0pfFFeHrz9/ODh6YnM\nlBTUS6UYGB2NkPBwAMCujRsxbOxY9ga6c8MGjBg3jk289m/bhmFjx7Ij7Pm5uQgMCaHSENjGDRrq\n6pBx6RImz57Nt5ROQwjBywsWqM4kJPyukMtf7Kn9UJM4AYCDo+Pf+0VEfLwnOdmFlmXztFJSUIC6\nmhoMv+8+vqV0ir2bNuGBxYs7HEUxf9LLv3oVjs7O7BN7wr59CAwJwZDhwwEAR/fuRXBYGLtq7+yx\nYwgOD2ef2KvKy+Hi5ib4BtR3QnNjI1pkMvY7snFn5GRksIn03YZKqYSdRII225jL58+jd//+8PHz\nAwBsW7cOYydPRljv3qZ47VrcN3Uqe2wd3rULw8eNg19rDZi0qgqePj63HPGK37oVM+bPp8I+RafT\n4dDOnZj72GN8S7nr2fLLL+Tff/1rsUIujyKE9Nh8NlWJE8MwIhc3twPT582b9O2GDY40DXkCgFar\npWb4mxCC4vx8dvpHSBBCoNfr2Qt1dno6mhsaMOy+++Do6IjEQ4fg6e2NuNGjAQDH9++Hb0AAYkaO\nBGAafnZ1d6dq+tSGjbuVpoYGOLm4sEnQ8f37MXTkSDaR2vTTT5jywANss+xNP/2EiKFDMWzMGACm\n8zkoLEywSZRapUJDXR01Na96vR4Mw1BnzpmSlISnZsyQq5TKUYSQq7d/R9ehKnECAIZhXF1cXdPe\n/PjjPi/87W9U/WV//OILvPzOO9R5YViborw8GI1Gtkbj7LFjsHdwwKjx4wGYimfdPDwQO8rU2Uda\nXQ1HJydqRoCuZ2ejqrwcE2fO5FvKXQENU3VCx2g0Yt3KlVS4hRuNplrftuvo6aNHETNyJGtJsH7V\nKjyweDH7YPTHmjV4cPFi9vWGujp4envbrsMdsGvjRoyaMIGq0ebykhLMiY1VyZqaFhJCDvX0/qhL\nnACAYZheTs7O6T/u2OFJ0/wrjRiNRuReuXJH0wwqpRIatZrtI5WSlAS1SsX2nDt/8iQIIbhv8mQA\npuXmEnt7+Ad22B6xQ6TV1V16nzUhhEDe0sIWawuVw7t34/5p0wRfqyL0xGnXxo1Y8NRTfMu4JbQc\nk/W1tfDw8rJoYYNGo4GdnR07grL7998x9aGH2Aetn7/5Bo8+/zwbn0lIwKgJE+54BEupUKCmslKQ\no/Z3Ewq5HA8OH66oKCn5WKNWf22NfVKZchNCSlRK5QOvLV6sMl/2Sws0JasikQilhYW33Ka+thZF\neXlsnJacjMRDN5L+gmvXOMvRh40dy2nUO3bSJDZpAoCQ8PAuJz9njh4VvH8WwzCCv0EBwLAxY6h4\nKhdy0gSAiibatByTCXv3Wnz9dHBw4Ew7Pfzkk5zR6Rf+9jdO7OXry1n5tvrLLzn2Dxt//JHTr60j\nPblXrsDF1dUirXxC032pDaPRiNcefVQpraraq9VovrHWfqkccWpDbGf3rF9AwKrDmZnONLlI52Rk\noKyoCDPnz+dbSqeok0pRXVGB6Lg4AEBWWhoqSkpY/WXFxdCo1axPjY3O0VhfT5X7uY27E1lzM5yc\nnUFTT1A+aWpogIeXFxiGASEEK//9b7z24YcQi8UwGo1Y/cUXePX999nXDQaD4K0/1Go11v73v3j1\nvff4lmIR//fBB7r1q1ZdUbS03EcI0Vhrv8J/nLwFBr1+nay5+Zfn585VmhsACp3ImBjMmDePbxks\nzU1NyDZrB5Kfm4t9W7awMSEErm5urIlgdFwcJ+kL693bljR1gX2bN7P1Gja6jq1X3Z1xaMcO6P5/\ne+cdHkW5tvH73U02my1JaAkJvYaOlCAiTZoCBwEBQYriERQR61GPoh92BFFQpAgCijQp0ktC7y20\nJAQSSgLpjWR733m/P3YzJ0FKyu7OBN/fde0Fs5ud99k2c89Tq9DxU2hCqlfnPVKEELw9Ywbv0ZJI\nJBj9yiv83zocDiz9/n/RI4vZjOU//shvU0pF4emRy+V4/b//FdqMcrFt7Vr62/z5RUa9fqAvRRNQ\nxYUTAJiNxveSExJOTBs92lyV2tkX//B88aOx2+2lOhFn3L6NDStW8NsOu72UK7tpixalSmdrhYWh\nYdOmOHnwYKn9iJktq1eX6kYtRl6aNk30obDVv/zCxF0lWLV4sejfv9GvvML3KBMry+bNE/37WMyO\n9ev547q/v38pL448MBDjpkzhtw16PZbP+99EEG1REXZv2uQzW0uef6pSlfrh6Gh8NHmywWw09qOU\n5vl6/SodqiuGECJXqtUHBwwb1uGH33+Xi/1kVJKl33+PcVOmeDQWXlhQgO3r1mHim28CcIXaEs6d\nw1ODBnlsDbFzd28ZRsW4k5+PkOrVq1xpsljIz83ly+oZFUen1VaZqtnK4HQ6kZ+Tw7deyMvORszW\nrZjw+usAXO9DQW4u31Ousiz/8UeMnDgRwSEhHtmfLzhz9CgmDhpkNBuN/Smlp4Sw4ZEQToC7TYFa\nffy5CRNafLlgQUBVUc8cx5Xb62C323Hq0CF+wrZep8Ofv/6Kyf/5D4C/j3DwBna7nYkSD2C1WnHh\n1CnRJzgzHj0sZjPiz53j23wwKocvjolajQbJCQn8Z5Z6/TounTmD4ePHV2h/FTn/CElcbCxe6NPH\nZDIYnqWUHhDKjqrzjj0ESqnBqNf33vzHH2nff/qp/eHPEAclv7QlRWzJ2DfHcfjpyy/5bYlEwpf2\nA4A6KIgXTYBLMHlTNBUnElYFriUmoiDP557cMhMQEMAEaCVhOU4VQ1tUhPC6dYU244FUlc/28sWL\nOBoT4/V1gkNCSgndRs2aYdi4cfx28uXL2LVxI7+dlZ5eamB1MSXPJVWF5MuXMa5fP7PJYHhBSNEE\nPELCCQAopRqjwdD9t59+ylk8e7ZDaHvKQ+LFi/jpyy/57UXffstPvJdIJHh7xgxeDEmlUrTr3FkQ\nOwFXIuFrH3wg2PrlIbxePWSJPC+r85NPCm3CA1n47beiSGCtaiybOxcWi0VoM+5LWEQExDz30+Fw\nVJkTe5sOHdD3X/8SZO2SF8mRbdpg8KhR/La/TFaqPUvs8eP4bf58HN+/36c2VpZbN27g+Z49zWaj\ncTKldLvQ9jwyobqSEELqBiqV56fPmVNzwuuvi/KXt/3PP9G1Vy9+0OvRvXsR1b07AhUKgS0rH1XN\n1StmxDo53WKxiGoAcVVBzO+bWL9rVY2qePwrGVI8tm8f5IGBiOreHYA4v7NZ6el4NirKpC0s/I/N\nZvtFaHuAR8zjVAylNMNsNHab+f77hb/99JMoSu3++uOPUk0gez39NGqVaPLYc8AAXjQ5HA5UlQrB\nw3v2IP7cOaHNeCgcx6GwoEBoM+7L5YsXcXDXLqHNuCdiO5BWFcT6vjmdTiyaNUtoM+4LpRR38vOF\nNuOhUErx89dfC21GmSmOYJRMDejRvz8vmgDgzJEjuHzhAr99IylJ0IbCt2/exNAuXUx6rfZzsYgm\n4BH1OBVDCGmoUCpPvPr++7Xe/uwzf29fYTmdTr76KHrzZjRo2hQt27Ur934ybt/GuePHS8WuGZXD\nbrdjw4oVGPfaa0Kbcl/EnHAv5gHVYhy5YrVaIZPJROvVEfN37fLFizAbjaVO6IzKUVhQgOjNmzH2\n1VfL9bzLFy6gRmgonwu3f8cORHXvzs/98yZJCQkY3auX2WQwvG+z2RZ5fcFy8EgLJwAghNRWqlTH\nn//3v+vN+PFHmacOZE6nEwadjv8CHYmJQVBICDo8/rhH9l8VcTgcou+Qy6gYYh5QLUbhtGTOHLz8\n9tuiFZuMiuN0OiGRSEQrir1JblYW1MHBfN+vPxYuxHMvvujxeZYXz5zBhP79zUaD4RWO49Z5dOce\n4JEXTgBACKmuVKsPPz18eLM5K1bIK9KTxmq1oiA3F3Xq1wfg+mABeF0oZWdkoEZoaJU4AC+aNQuT\n3ntP9LaKOS8hKSEBjSMjRf8eMqomCefPo22nTkKbcU/E/LssyZ/LluGpQYMQFhEhtCkPJT011asF\nAFarFf7+/pBIJHzoctonn1Tqczx58CAmPfus2WQ0Pk8p3elBcz2G+L+lHoBSWmjU67vFbNlyccpz\nz5nLMp7F4XCUyknKSktDTmYmv93h8cd94l2y22y4cEqQHl/lZupHH1WJE/7vP//Mj48RG37+/vcs\nH2YwPEHJY5jYWDJnTqlhumJlzKRJVUI02e12nDtxwqtrBAQE8CKJEFJKNBkNBiyZM6dc+9u7bRte\nGTLEaDIaB4lVNAH/EI9TMe4O41vbdOzY47dduxQlxwxQSpFx+zbqNWwIwNXxNzkhAd379RPI2qoL\npRQmo1G0k8FZRVHFyM3KEuUJQ2yhutysLISGh7PvWDkR++/SaDCI9pgmVkp+plnp6TgaE4Mxkybd\n8283r1pFp0+ZoreYTH0ppaKuOPpHeJyKoZRajHr9vy5fuLB9aJcuxutXrvD9aYo7OBdTKyxMdKLp\nzNGjyM3KEtqMh2K327F++XKhzbgvYj44i5kTBw7AZDQKbYbo2b9jB/uOVQAxv2fnT57E1bg4oc14\nKJRS7Fi/XmgzeEp+phH16pUagJx46RL279gBSinmffaZ/ZMpU+5YTKYnxC6agH+YcAIASqnDqNeP\nTUtJmTWsa1drsViSy+UY+sILAlv3YNp17gyb1adDoCuETCbDv99+W2gzHkphQQHWLFkitBn3ZNva\ntb4J2XEciNEISW4u/FJS4J+QANnp05Dv3w/51q0onD8fqqVLoZ43Dy+mpuLK7Nn8Ux0OB9YuXcpv\n2+12zP/qq1LbJcu1vbVd7G3y1Xolt1f/8r8KaYfDgSMxMXzlJsdxSEtJgRhY8M03omximpOZiY2/\n/y60GQ+lU7duom9UC7iEU8v27YU2476UFFKtH3sMj/fqhddHjjQvmzcv2WwytaOUXhHQvDLzjwrV\n3Q0hZHigQrF6zooVgf8aPVq8lztVGK1GA7vNhpqhoUKbck/EWmZvt9shlUofnGRps0Gi0UCi1UKi\n1YIUFaHg9m3Ulkgg0WhANBpsO3cOI0NDIdFqAY0GM5OS8JlCAYnBAKrX4xuzGf8XGAiqUsGhUGCm\nyYTpjRqBc2+vzcvD2LZtQZVKOP39cXnpUtQvLAT8/EApRUFe3j92iC2lFJrCQlSrUQOAq9oq8eJF\nvqu/3W7H7k2b+Asyq9WKZT/8gDemT7/ntsViwfJ58/DGxx/zj+/duhVDRo/m95+TmckXqJQHsX7P\nOY4Dx3GirMallCL1+nWPDdRllCYvOxsTBgwwZdy+vc+o179AKRV/gpubf7RwAgBCyGOBSuW+ye+9\nF/zuF194vdeTpzgSEwOVWo1O3boJbcoDMRmNOLZvH54eNkxoU0QNMZshuXMHkoICSN3/Su7cwbEz\nZ9A7KAj+hYWQFBTg24QEfOLvD//CQsBsxucyGT4JDwdCQsAFBWGZRoOJ7duDVqsGZ1AQrlosaBYZ\nCRoSAhoSAi442HVTq0GVSlCFAihHBYy2TRsEzZkDMnCgF9+N8iGmHKfES5fQ+rHHPLIvp9OJrPR0\nPu/SarUi+q+/MHTsWACA2WTCygULMOXDDwG4cnBWLVrEb1ssFpw5cgS9nn4agG+Gfz9KZKWnIy0l\nBV179RLalAfidDqx4Jtv8PaMGUKbUmYuX7yIFwcMMJmMxjkWs/kLWsWEiGiFEyFkKIAvAXDu2weU\n0oPux54B8CMAKYBllNLZ7vsbA/gTgB7ACEqppoxr1Vaq1fu69+vX5Kc1awLlgYGef0FeQOzJlFWJ\nv/74Az0GDEBoiW7ulcZmgzQvD9KcHP52+vRpdJXJIM/PhzQnB3OuXMF/bDYE2mxw1qyJmU4n3mnR\nAtLQUHA1auD39HQM694dgXXrwlmjBriaNcHVqAFnzZqgajXg488/7c03EaTRIGTVKp+u+yDEJJxi\ntm4VzUWC3W7H1jVrMGriRACAXqfD+uXLMenddwG4vMEbf/uN3zYaDLh05gye7NvX67YtmzcPL02b\nJtomnFWNqnQuiN68Ge+++KLJYja/xDmdm4S2pyKIWTgpKaVG9//bAthCKW1KCJECSAbQD0AmgFgA\nL1BKrxJC5gBYAKAJgJaU0oXlWC9QqVavrdugQf+V0dHK2nXqePw1eYu0lBSERkSIdsRDMTeuXoXD\n4UCLtm2FNuVvWCwW+Pn5lS1kQCmIVgu/jAyYk5Ohys9HQFYW/DIysPTECbxICKoVFECi1eI7hQKT\nGjaEok4dOGvXximHA+06dIDEve0MC4Ozdm3QoKB7iqD0W7fgsNvRqFkzL7zq8uOXlISwvn2RmZ5e\nLk8VQxiO799f5iIXq9WK2zduoHnr1gCAO/n52Ll+PV6aNg2Aq9I4+q+/MGHqVACu34xeq61QqNZk\nNKJkVbNYsNvtOLBzJ54ZPlxoUx7K9StX0KxVK6HNKDMcx2HBN984Fs+apTObTAMopeeFtqmiiFY4\nlYQQ8gSAeZTSru7/f0Ypfcb92EcAQCmdRQiZBWAVXMKpNqV06X13eu91iDww8FN/mezjBevXBxa7\nuMVOdkYGMm/fFn3yIsdxuJmUJP4fu9UKv/R0+N26hZwLFxCq0UCdkwNpRgaWxMXhBaMRtQiBo149\nLCcEQzt2hKJxYzjr1YMpLAzSBg3gDA8HV6PGIykuwlu1wp0VK2Dr2lVoUxg+pqRno+jOHZw5epQX\nGXeXm2s1GtzJy6tSOUImoxF38vK82jTSE9hsNhzctatKCDzA9V2ZNmaMKe7MmZsGvf4ZSqn4y8Mf\ngKiFEyFkGIBvAYQDGEApPUsIGQngaUrpZPffjAfwOKX0TUJIXQCrAWgAjKWUmiq4bu9AhWLzS2++\nqXr/66/9xZi4yPAMednZUKrVfH+WtT/+CP377+OrGjVgb9UKO6VSRHXsCFWzZnDUrQtnvXpw1K0L\nGhzs0zBZmZLFfYTl7beRq9GgwcqVQpsCQByhOkopDu/Zg6cGDRLUjmKsVisCAgIEtUFbVITrV67w\nF3Tb1q7FjaQk/OfLLwG4qloNOh3qN24spJkML3P+5ElMHjbMZDGZlpmMxvcppZzwB6oAACAASURB\nVHahbaoswh+FHwCldCultCWAIQBWkYcEcSmlGZTS3pTSYRUVTe79HDabTC1XL1oUO+LJJ41VoXdS\nMTeSkrBzwwahzXgoV+PjEb1li9fX4TgOdvv/fqdbVq9G6vXr/HbipUuluhWPfecdTJ05E1xwMPLX\nrUPU/v3Ad9/BMHkyLAMHwt6mDWhIiM9zi64lJuJIdLRP17wf8nHjEHDwICDiiy5fY7fbUcuT+XGV\nwOFwYMWPPwptBoKrVSvlBR8wbBgvmgDXb/NOfj6/nZSQgN2b/pfyYtDrYTZV+DBeZvQ6HZbNm+f1\ndSrLnfx8rFokqlm3D4TjOCyePdsxrn9/fWF+/hijwfD2oyCaAJF5nAghUwFMBkABDKaUZpd47CaA\nLgCaAfi8RKjuYwBccYK4h+2RygMD/89fJvuwKoXunE4nKjKPz9d4YzbVmaNHEVK9OiLbtAEA7Nq4\nEa0ee6zcOULBX30FxcaNyD18GFz16h61scpDKSKaNEH+X3/B3qGD0NYwHlFuJicjOz2dz9E6f+oU\nrGYzuvXp4/G1qsKcPEopOI6rEsf2u0JzQyilt4W2yZOISjiVhBDSBEAKpZQSQjoC2EgpbUII8YMr\nObwvgCwAZ+FODveiLVUydGc0GHD75k20EnFDNMB1JSULCIA6KOihf2syGmG1WPjeOYd270ZIjRr8\n3EBNYSGUanXlq3UohX7KFJzatw9Px8W5KtgYPCGffAJYrdB8/73QpjBETEFeHmK2bOGbglYGSils\nNhsfgjx95Ag4p5MXUum3bkGlVvPHhoeRlpIi+jChxWzG9StXRDuY+V48iqG5uxGzxB4BIIEQchHA\nTwDGAK7O3wCmAYgBcAXAem+KJveafOjuuSeeMFaVIayBCgUKS7jCxQohBLHHjt3zsWuJiTh95Ai/\nfTU+HnnZvCMSTw0aVGrYckj16p4pcSYE6l9+wcj+/RE6ZAiISIaP6rRabF2zRmgzYBw3DmuWLQOc\nTqFNwanDhwVdP/HSJVw8c0ZQGwBXztCujRuFNqMUNWrVKjVmozIQQkrlbXXt1auU98lmtZYK/e3b\nvh1JCQn33FdhQQGuXxF/k+r01FTUrCINZh0OB37++utHMjR3N6L1OIkRQohUJpN94OfvP+OT778P\nGPvaa5Kq0jsDqBohvMsXLiArPR0Dhg4F4KrMCZDLhWu1wHGo8dJLQFYWCrdvBxVBCXVeTo5n+01V\nENqmDQLnz4fFC6GT8iB0crimsBByhULwdiAmoxEcx0ElAu+oGI41lFLY7Xa+Y/qO9evRom1bvqpX\nrN3UAXG8f+XhRlIS3nj+eWPmrVvxBr1+DKU0TWibvImYPU6ig1LqtFqts0xGY+eZH36YPLp3b2NW\nerrQZpUJSikWffstnAJ7CIrHdBRzIykJ29at47dr1a4Ng07HbweHhAh7QpJIcOf333HM3x/J3bqB\n6PXC2eJGDKIJAIJefhlKEXi/hK6oC6leXXDRBAAKpVI0omnRt98KbQYIIaWEUadu3XDl0iV+e/fG\njUi/dYvfvpaYCJvN5ksT78nuTZuQkpwstBllwul0Yun33zv/1bGj6WZS0kcGvb77oy6aAOZxqjCE\nEH95YOAnEqn0wy/mz5ePnDjxYUV//0hsNhuS4uP5+V3ZGRlIOH+e9yjdC7PJhECFwlcmlg2OQ/Up\nU+B/+TLy9uxxtSMQmDNHj+Lxnj0FW1+amYnQNm2QnZ0NiEA4CIEYPANpKSnw8/dHRL16gtohdqxW\nK6RS6X2b3J48eBCtO3ZEcEgIACB6yxb0GTxYtF4pobl14wbeHDPGmHrtWrJBr3+eUnpTaJt8BfM4\nVRBKqd1sMn1uMhie+Pytt1ImDBhgKpl7I3a2rVtX6mrLUzgcjlJtBhx2O6wWC78dXrfuA0UTAF40\nOZ1OZGdkeNzGCiGRoPCXX2Dr2BFcr16QFBUJbRGcDoegE++ddepgfq1acKxfL5gNgLA5TgtnzhT0\nMwCAnMxMUeTB5GVnC/5e3E3JY0hAQMADJwN069OHF00A0LRlS14UO51O/P7zz157fcvmzhWFt6ss\ncByH33/+mRvYvr05KSHhM4NeH/VPEk0A8zh5BEKITK5QfOknlb719eLF8qFjx4re++R0OuFwODzS\nJG/b2rV4evhwyAMDQSnFtcRENG/dutKzk+x2O3auX4/h48dX2kaPQSkSnn8e9S9fRrWjR8HVqiW0\nRYKiWLkSyg0bkL9rl2A2CJnjVJVmhHmbtUuXYsykSaIq679w+jTUQUEemVagLSpCcLVq/P+3r1vH\nj5+pLBazGVVhRmr6rVt4Z9w4Y3JCQqpBrx9JKa0aMUUPw4STByGERClVqg1tO3euNevXX5UNmzYV\n2qQycTM5GXabrcwz5A7s3Im2nTohNDwcAJCZloaIevX+OScQShHyf//n6vMUEwOne3q9UORkZiIs\nIkKQ95+YTKhTrx6yL12Ck4WKfEp2RgbC69YV2ox/LBaLhc9tS09NxYVTpzB07NiyPddsxokDB9D3\nX//ypokew2azYfncuc75X31lczqd39is1tnuCvd/JOK5NHgEoJTGGg2G5hdOnvz6mXbtTHNnzLBb\nSoSpxErDpk0fmKdx+cIF3Lpxg99u9dhjpbok16lf3ycn7YUzZ5bqAi4YhEDz9dfQT5uGhM6dwcXG\nCmpOXnY2Ei9eFGRtqlDgzsiR0IugU7WvuX1TuOhE8YgXoTm2bx+sVqvQZpRi65o1paYDeIuSBQH1\nGjXCMyNG8NsJ58+XaqNyNzabDS3atfOqfZ7i9JEj6BMZaVz47bcnzCZTW6vF8s0/WTQBzOPkNQgh\n9VVBQUuVanWPOStWKHoOGCC0SWWCUooLp0+jZmgoGjRpAsB1ggiLiBDclSzGsMidRYsQPmMGyMaN\nsD71lNDmCAJ39ixODhqE7rm5gACJ0kKE6jSFhTh/8mSV8Rh4i7jYWLSPihLajFKI4ThBKYVBr+eb\n+p4/eRJKtRrB1apVGS9hfm4uvnznHfP+HTtMZqPxVQBbKBMMAJjHyWtQStP0Wu0zuZmZz0957rnc\nSUOHmnIyM4U2674YSpTZnztxolSeQoMmTQQXTQBKHQwP7dkDrQgStGtMnQqycSNqjR4NhQiaDwpx\n9S/p0gUjGzWCfO9en68tFCHVqwsmmsTk4RGLaNq1cSPvjRZaNBXbUHISQrPWrZFy7Rqk7uT0G0lJ\nok0GdzqdWLVoEde7aVPzgR07lpqNxoaU0s1MNP0PJpy8DKV0l8lobHR8//75T0VGmn/94QenwyEu\nL+fN5GScdlcmEULw2vvvo16jRgBcVx1i/L107NpVHGE7ANannkLuvn3Y8uqr0H/+uWDDbx0OB377\n6SdB1jZMngz1r78KsrbQfZx8ybkTJ3Dx9GlBbVgyZw7EloLQol07z0wM8DD5ubkAgKDgYAwaMYLv\nwaYtKsKdEv3sxHJOiD93Ds+0b2+c/fHHcUaDoYvRYHiHUmoQ2i6xwUJ1PoQQ0lwVFPR79Zo12321\naJFSqKHBRoMBqxcvxmsffPDQv71w+jRkMhnadOzoA8sqRmFBAQIVCsF7P5HUVIQOGQL7k0+icMEC\nQIQHcm9B9HpciohAh6tXwVWRUERFObp3L7r27v2P7e/jcDgeWNbvKzLT0lCnfn2hzbgvlFKsWbIE\nY1999aGVhotnz8a/33nHI1XOFSEvOxvfTZ9u2blhg81qNr9FKf2DeZjuD/M4+RBK6TWDTvdkWkrK\n+KkjR2aO6tHDeCUuzidrr126FCajEQCgVKnKJJoAl2enWDQ5nc5SIT2xYLfZeI+ZkNBGjZB36hSk\nmZmw9e4NSWGhcLb4+JhH1WrUGDwYAQsW+HRdwPd9nIKrVfO5aBL6HJaTmcnbIAbRVFhQgMsXLght\nxj3RabUAXN778VOmlKk9w+v//S8vmrRFRVjuo2ILo8GAuTNm2Hs1bWretXHjUovJ1JDjuJVMND0Y\nJpx8DHWx1WgwNLpw+vRHz3Xrpnt73Dizpxs92mw26EuMLhn8/PNQVHLOmtlkwvYS41HEQlhEBJ4a\nNIjfFtLtTdVq5G/bhuS6daHv2BF+164JYsfebduQWGK8hC9o+MUXqPHbb6AlBiLn5eSUGrx6NT4e\nKSXek5OHDiH+3Dl++9CePbhQIhRVlu2Sw1rL+/yThw6Vep+uxscjLSWF387PzYVWoyn1On2d10Mp\nxY9ffCGoeDoaEyP4uCbgf7/t6jVr4ulhwwS25u/ExcbiaiUvhoOrVcO/336b305PTfV4I2CHw4G1\nS5fSbvXrm1b89NMus8nUyuQayit84mgVgIXqBIYQEhyoUHxKKX3j5bff9pv68cf+JZMKK8q+7dvR\nol071PNijyGdVosgEYweKYnT6cTiWbPwxvTpgieJqpYvR8jHH6Pg999hKSHsfIUnqouKu8sXf4+O\n7t2LQIUCUd27AwCOxMRAqVKh85NPAgDioqLg378/Ws2cCQC4fPEilCoVGjVrBgDIzcqCLCAA1WrU\nAODqhSOVSgXLT7GYzQAhfGl5TmYm/Pz9UTM0FICrrFyhUqFJZCQA4OCuXahWsyY6PP44v129Vi08\n1qULAFePs7CICN5Le/vmTaiCglCjko1SxVApJjRHYmIQFBLCv/diQafVQh0U5LXPp+jOHWTevu2R\ndIniNhYzpk0zagoLk/Ra7euUUmH7qVRBmHASCYSQeiq1+gcikfzrw5kzA8ZMniwpz8nkZnIyrsbF\n4V/PP+9FK0uzb/t2NGvVClWl0acQBJw4gbPPPouwceNQ+8cfAQG6Kpc86eZmZcFms/FC6OShQyCE\n8AnWJw4cgJ+/Pz8DL/X6dQTI5fwctIeewHfswMbXXsOozEzgETvRZ6Wn4+zRoxg2btx9/4ZSCo7j\n+L5o1xIToVCpULdBAwAuT2BEvXr8STB6yxbUa9QIrR97DIBLqIZUr85XZAklmDiOw/J58zDpvff+\n8YLtYaxatAij/v1vnw163rpmDdpFRaFx8+blet7lixfx2bRpxqT4+CKjwfAGgB0sJFcxmHASGYSQ\nDuqgoEWq4OC20+fMUQ4eNeq+MXKr1crHxe12O/z8/AQ7yFmtVpgMBt6TIBa2rVuH1h06oGmLFoLZ\nQDIzoRg5EopatVDwxx+gJeZheZobSUnQFhWh0xNPAABijx/H2qVLMXflShBCkHr9OqRSKeo3buwd\nAyhFtRYtYFqyBFYfVbv5qo+TJ8cU3Y+E8+cRUqMG6jVsiN2bNiHj1i30HjgQzVu3BuD6PBs2a4Za\nPphNp9fp4Anvd2VY8M03ePWDD0SViE8pRX5ODj85QWhbbiYnP/D4lnr9Or7/9FPzgZ07bXabbbrT\n4fiVUiqOkuQqChNOIsQ96K6/KihoXvWaNetPnzNHNWDYsFICiuM4LJkzB1M+/FAUV4QGvR77t29/\n4NX4PxqbDdXefx/6HTtg++svSCrodk9PTUVWejrvEYqLjUVBbi7fU0hTWAgikZQaVspxnE/nh6kW\nL0ZgTAzyt271yXpCzqrzJvf63DJu34Y6KIifmbZ51Sp0fOIJ3ut79tgxRLZpwz9eXrLS03nvIuPe\nJF66BJvVKoqQIcdx2L1pEwaPGvW380BaSgrmzphh3rN5MwdKf7BaLD9QSnX32RWjHDDhJGLcAmqQ\nKihobq3atSNe+/BD1RO9e/MdvcXM9StX0Kh5c1FU4BSTnZGBozExGP3KK4LZUDRvHrI+/xxd5s2D\n8eWX/xbOMhmNyMnM5N3w1xITcf3KFQweNQqAq+KG47gKefaKf+veFtrEaATq1weOHgV1e0qqOr4s\nfa9MeC71+nXUCA3lcw/XLFmCfkOGICwiAoDrNxAaHn7PEUsGvR4Hd+3Cs2PGVNz4SpJ6/TriY2PL\nPPPNV1xLTETjyEhRHc/uxeULF3D75k0c2r3bsnP9eiel9CerxTKHUqp5+LMZZYUJpyqAW0A9q1Sp\n5tYKDw/9aPZs1YChQ0U1hfxursbHI1ChEF3+k6+9L/fC/8oV1Bw9GvZ27ZDw6ac4evIkL+ZyMjOR\nnZHhlavZrPR0HNu71yfC8dqrryI4Lw9hPvI6eZv1y5f75H3Lz81F9F9/YcLUqV7Zf/TmzXjiqad4\nj9QfCxdi5MSJla649RQcx4EQIgovekn2btuGPoMHi1o4paWk4MfPPzfv3LiRSghZZDGbv6WUCtcT\n5RGGCacqhFtADVEFBX1XvVatOh/OnKkaOGLEAwf0igGL2YwDO3fyXhOxsHLBAgwbP75UWMvTUEpR\ndOcOqtesCQAoyMvD7o0b8dLLL4ObMgWb9+zB6JgYOHzUYNRXycaSoiJENG2K7IsX4fSyp+ZRC9X5\nMiE8/tw53L55E0NGjwYA/Pz113j9o494gWC3271e8bh++XI8NWiQKHKGiklLSUFuVhZfPSpmUq9f\nx4+ff26O2bKFAzDfYjb/QCm9I7RdjzJMOFVB3AJqoCoo6LugkJAGb/3f/ymHjR9PfFXVURFu3bgh\nOu+Tw+GAVCr16EmK4zicOnQIT/btC8AV/ti9aROef/nle/69fM0a1HznHWj/7/+gnzbNZ1V3vuj+\nHPLBByA2G4q8PAbmURBOQnXjfpAH1uFwYOn33+P1//4XhBDYbDZk3LpV7mquh+ELcVZesjMyUK1m\nTZ9VylWEhPPnseCbb0xHoqM5juPm2azWuSwk5xvEG+th3Bd3E83dBp2ubVZa2rCZ779/PKp2bfP8\nr75yFN0R54VGSdF0fP9+nD95UkBrXJSsQryRlIQd69dXaD+bVq509QOCK38oQC7n84lUavV9RRMA\nWMaNQ86pU1CsWYMTHTpA4uFGd/fjaEwMEs6f9+oa+nffxZ7lyyEp0QDTG3hTNB2JieE7QXsLSikW\nz5rlswaX1xITcS0xEQAeGLb28/PD1I8+4n8jnNOJ1BLNSwsLCir0O87NysK6EnMNxSCa7HY7Fs2a\nxW+H160rStHEcRwO7tqFoY8/bni+V687B3bs+MxiNtexWiwzmGjyHczj9IhACGmjCgr6xGG3D3tu\nwgS89uGHcjEnkZe8whZLcz+n01mmsOdff/yBnk8/zZeE52ZlITQ8vHKvweFA1jvvoPOGDdAsWACT\nD/txeZP80aPRqFEjGEqclKoSyZcvI7JNG6HN8Cg3rl5Fw2bNKu3hslgsuH3jBv/+pF6/jsKCAr4V\nxv0QUx5TyWOPWGbw3QuLxYKtq1bRn7/5xqgrKsrW63SfA9jI2goIAxNOjxiEkHB5YOC7AF7v1qcP\nmfbpp8qOXbsKbdYDWfjtt3jl3XdFdYW3bN48jHr5ZQSHhODAzp1o0LQp3yvFaDBAqVJ5ZV3Z2bOo\nOX48brdtC9ny5V7t+VSMtqiowuXrD0N6+zbCO3ZEVlISuEp2z74fVTVUp9NqoVKrfVKskJeTg1ph\nYV4VKzabDfk5OXz1YeKlS5DJZGjWqhXW/foreg8ciHARDYDetm4d2nTsyHeFFyNFd+7gj4ULHcvm\nzrUTQmJ1Gs0XAA6xxpXCwkJ1HoYQEkUIcRBCRpS47xYhJJ4QcpEQcrbE/Y0JIWcJIQcIIR45Q1JK\ns80m04cWszn8SHT09PH9++cN7tjREL1liyhmTd2LNz7+mBdNhQUFHp/LVF6uxMWhU7dufNJ4l549\nSzWY85ZoAgBbly7IvngRV+x2GFu2hHz3bq+tVcy+7duh8dJAYmeDBjCNGYNA9wiWqgLHcV6febhr\nwwY+xOttDu3aBbvdu84JmUxWqmVDw6ZNoXI30BwzaRKK7tzx2vesLNjtdj5ECQBDX3hBtKLp1o0b\nmP7aa5Yn6tWz/PrDDxv1Wm2UtqioF6X0IBNNwsM8Th6EECIFsA+ACcBvlNK/3PenAuh0d2koIWQO\ngAUAmgBoSSld6AWb/AAMDwoJ+czPz6/RxLfeChgzebI0tHZtTy/lEfQ6HeLOnkX3fv18tqZBr0dW\nWhrfnTkvJwch1avz3Ypv37yJcydOYMSLL/rMJgCQHziA6pMnw9y9O7Q//giuenWfru8pJBkZ+L1Z\nM7yckgKniCqnHsTRvXsRFBLCz6CrigjZeiM9NRVnjh7FyJdeKnUfkUj48TN38vMrPcOvvDZpNRq0\n6dDBZ2uWB4fDgQM7d2LZ3LmG+HPnQIBfLGbzXEppttC2MUrDhJMHIYS8A8AGIArAzruEU+e7S0QJ\nIbMArIJLONWmlC71sn0dVGr1u3a7fWSP/v25f7/7rvKJ3r1FkWtwP6I3b0bTli3RtGVLj+63ZCVP\nWkoKbDZbmcey+HK4MTEYkPv667i+cyf6rVgB8/DhXl0v4fx5tO3UyeP7rfbee4DDgaL58z2+76pE\nTmYmCCF8Q0pvkZ+bi+jNmzHh9de9uk5JDHo9FEplmcVa9ObN6NC1q9feC0opfvnuO0z+z39Em7sE\nuHIk1y5d6li5YIGNczpv6jSa7wBsopRahLaNcW+YcPIQhJA6AFYD6ANgBVwDFDe7H0sBoAXgBLCE\nUvqr+/667udoAIyllJp8ZGuwRCJ5UaFSvR8UHFx90nvvKUdMnEi82c+oolBKYbfbee+PxWyGPDCw\nUvvUFBZix/r1FT6pRG/ejNYdO/KDcn1BwPHjqPHKK7C1b4+in37ymufm0J496NG/v8dPNJK8PES0\naIHsS5c83tepKuU4Hdu3D1Hdu1f6OyxG1i5diqFjx1YolM1xHH7++mu8+emnlfKScRwHm83Gh/5t\nNpuo5twVw3EcTh48iOXz5hlPHjwo8fP3X2/U63+klMYJbRvj4TDh5CEIIRsBfE8pPUMI+R0u4VTs\ncQqnlGYTQmrBFcp7k1J6TEBz4baLAOihDgr6j81uHzBoxAg68a23AttHRQlt2j2hlGLZ3LmY+NZb\n5S5hXjRrFv79zjseT0A3GY24cfUq2nXu7NH93gtiNiPoyy/x4/z5eGPWLJimTgVE3vy0JIH//S8u\nxMWhZXS0R/frSeFkMZuRcP58lWh8eDd7t21DRP36PgtFaTUaZN6+jVbt23t831np6Yg/dw7PlNPD\nGr15M5q3aePxXlOeQlNYiI2//cYtmzfPZNTr8416/RxK6Ro2Q65qwYRTJSCETAUw2b0ZDKA45lUT\nrjynyZTS7Xc95zMABkrpDz4ztAwQQsL8/P0nyWSyt2vXrSuf8PrrqmfHjiW+zEEoLxm3byMpPh79\nhgz522NGgwE2q5Wf6eatfA+Hw4FzJ06ga69eHt/3/fC7fBk1pk4FMZtRuGQJbF7oOk4pxZ/LlmHM\npEkeC+USnQ6pDRui2YEDsIs0zyQrPR1Op9Oj3sRLZ8/CXyZD68ce89g+74Wv23rcSEqCSq1G7Tp1\nvLL/woICvuP+/TxHOZmZuHT2bLkFli9xOp04ceAA1i1dajy4a5efv0y226DT/QDgJEv0rpow4eQF\nCCG/wR2qI4QoAEgppXpCiBLAXgBfUEr3CmvlvXEnuPdVBwdPsVosA7v26uUYO2WKqs/gwaJ0eRfk\n5aFmaCiA0gfXIzExaNG2rddzSe7m2L59CK5WzfseKEqhXLkSx999FzUHDkT9X34BdVcweYrsjAzU\nrlPHoydj1eLFUGzahLz9+/824PhRJSczE2ERER4XNRzHYfGsWZj68cc+EUx2ux2//fQTJv/nPz7P\nizx95AgkEgm69OhR6ndu0Ovh5+cnytDn9StXsGHFCvuGFSvsHMdlGHS6BZTSdZTSAqFtY1QOJpy8\nwF3CqTGAze6H/ACsoZR+K5x1ZYcQEgRgZFBIyDSnw9Fy6NixGD1pkrxd586iSyjPSk/HmiVL0GfQ\nIHTq1k0wOyilsFos/IHc214AUlAA5QcfIDgmBpqZM2F88UWvjG3x2OtwOBDRti3yv/sO9nt4CiuC\np0J1ZW2AWlZ84QHyRQ5PydfhiRzDyuBwOPDrDz+gacuW6PXMM6K7mCssKMC2tWvp6sWLDVlpaQ5K\n6e8Ws3k5pTTx4c9mVBWYcGKUCUJII3+ZbKJMJns1uHp11bgpUxTPTZggEUtDO4vFAj8/v1JJzWuX\nLsXgUaO81tyxLCyePRsT33wTgQqFV9eRxcbC/403sCY3F8+vXw+bB5ueUkrx05df4u0ZMzwiBBwb\nNmDLW29hVEYG4IEkdE8Ip9ysLBzavRtjJk2qtD0AsH/HDoSGh3vc83g1Ph45mZl4auBAj+73fmxd\nswbtu3RBo2bNfLLevdi2di2ievRARL16/H3Xr1xBg6ZNRSGcbDYbDu7ahXVLlhhOHT7sFxAQEK3X\n6X4BsJ9SKs7meYxKwYQTo1y4E8q7KdXq1xx2+4hWjz3mGDlxYtCAYcP4ESS+YvHs2Xhp2jQolMp7\nPm61WiGVSuHn5wdKKXIyMwXtXFxYUIDCgoIytz0oNxwHsmIFIj77DJY+faCZPRtOH4cqywSlCO3T\nB6ZRo2CYOlVoa3jEMvrnQZhNJsgDA71mp8loREpyMtp4IW+urFitVug0Gv54YjIa7/sbB1zNIq/G\nxWHgiBH3/RtPY7fbcebIEWxft86ya8MGSP38ruo0moVwjUFhid6POEw4MSoMISQQwGB1cPCLVoul\nf4t27WwjXnxR/cxzzxFf5xY9DJvNhh1//unzJpYlsZjNiD93Dl169PDqOsRgQPC332Ln/Plo++qr\nCPnyS9AHnHjKA6UUV+LiKp3o7J+QgLC+fZGVmOi1USy+RltUBL1Oxzd49BTL5s3DhKlTERAQ4NH9\n3ov0W7fgsNsF9TDFHj+OajVrlusC42HiyhPYbDacOHAA29euNcds3Ur8/PxuGfX6351O5wZKaapX\nF2eICjZyhVFhKKVmSukmnUbzrM1qrRYfGzvh+08/3dyzSRPToA4ddMvnzaNZ6ekeWy8pIQF7/vqr\nQs+VyWSlRNPN5GRsW7vWU6aVCXlgYCnRdDg6GudPnfL4OlSlguabb9DjwgXUTU9HRPPmUC1dCnhg\nhAghBOmpqeA4rlL7sbdti5znn0fixIml7s9MSys16uT4/v2wWq389tY1j7JWRAAAFMZJREFUa0qN\nKdmwYgUOl2hvsGX16lKPH927t9Tz01NTS40eslqtOLZvX6VeSzGJly5B7eEEfQAYP2WK10ST0+nE\nT19+ieIL6HoNG/pcNKWlpGDTypX8dlT37uX2ypYUTasWL4ZWo/GIbRaLBft37MCbY8aY2lerZn1n\n3LjL29au/dRkMLTQFhW1dDgcs5lo+ufBPE4Mj0MICQDQVxUUNMFusw1p0KSJc8RLL6kGjRwpqdeo\nkdDm3ZOTBw+ieq1aaNG2rWA23LpxAw2aNPF4GEYWGwu89x7+vHYN45YuhfnZZ31W0ZZw/jyatW7N\n989a+v33eOHVV6EOCgLR6TAnPBxvbd8OWd++AIDtf/6JAUOH8gnICefPo0W7dnzfrpzMTNSqXZtP\n4i4sKMDV+Hg82acPAFeuUs2wMP7xyxcvIrJNG/75OzdsQL9nn+Xt+f7TTzF03Dg0c3emv3vg9Jmj\nR9GpWzefdp6+fPEicjIy7tlmwxMUFhRA6ucHoRre2u12/Llsmde6mlssFshksgq3H7GYzTgcHY2t\na9YYD+/e7Rcgl1/VaTQrKKWbKaWZHjaXUQVhwonhVQgh/gCeUqrV45wOx/A69evT59wiqixXtht/\n/x3d+/Xzem6S0+mEQa/nTya3b95E3YYNPVpl9TD2btuGJ556yiteC1AK/127UPPjj8GFhEAzezas\nHqg+/OzNN/HWjBn8zLHf5s/HsHHj+P5ZZ44eRfsuXe7beFS5Zg3UP/yAnNhYUTbzPHvsGDp16wap\nVApKKeZ/9RWmffIJvz3zgw8wYepU1G/c2GNrerq6724O7tqFDl278p+RL8hMS0ON0FDI5XJQSqEp\nLPTJ+hfPnEGt2rUfGj41Ggw4vGcPtqxebTi2d6+/PDAwXltUtALAVkppjtcNZVQpmHBi+Az3wOEe\nCpVqHMdxI8PCw8lzEyYoB44cKW3WqtU9PS1CjUw4feQI6jduzFfy+HpgqlajwcYVKzDpvfc8u2On\nE8pVq7D/gw/QNDISdebNg+0hneJLJk2vX74c3fv3Rx332JTzp06hVfv2Fa8apBRhvXvD+PzzMLzx\nRsX2IRAcxyEuNhYdHn8cgCvst+yHH/DG9On845TSMomgn7/+GlP++99yd8QvCxdOn4a2qMhnlXjF\nlPzNRG/Zgp4DBng9D+luLBYLstPT7xl+1Go0OLx7NzavWmU4deiQf6BCcV5bVPQbgG2U0nyfGsqo\nUjDhxBAEd6PNboEKxVhCyEhZQICi59NPo8/gwYrQiAhEde/ulZNIRVk0axZeefddnyTo3ov01FT4\ny2Se69Jss0G1YgWCv/kGtg4dUDBjBmjnztBqNKAch5Dq1QH4phzdPzERYb17I/viRThF0t7CE+h1\nOmz87Tf8++23AbiaNRbk5qJh06YAXD2JvBECtNvtuHzhAi/ohGDXxo1o3ro1mrVqJZgNd2M0GhF3\n9ixO7N/v3Ld9uyH12rVAhVJ52i2WtlNKC4W2kVE1YMKJITjuFgdNAfQLrlbtOZPR2D0sIsLWb8gQ\nea9nnpF16dmzQoNDvYVep8O6pUvx6vvv+2zNwoICZKWlebxM/E56OhxLluDA/Pl4a8AA7B40CBF9\n+3q8MuxhBH/xBWTnziF/+/ZHtqO4Qa/HpTNn0L1fP5w6fBiawkI0iYxE89atPbqOTqvFjatX0dGD\nvbweRuzx4zCbTOg5YIDP1nwYlFIkJSTg+L59dP/27foLp0/LAxWKWxazeZvNat0D4BSl1CK0nYyq\nBxNODNHhDul1lPr5Pa0OChpmNBjaRLZpY+7/7LOq7gMGSNtHRfk0Wfdh3LpxAxdPn8bw8eN9tuaO\n9evRom3bcl/R22w25Ofk8KG2q/HxUAcHo16tWlAtXozgOXNg7dYN2unTYfPB4OIShiG8UydoP/4Y\nprFjfbeugOh1OqSnpvJDctNv3YI8MLBC/dDuTmr3NkJ858tCVno6ju/fj4M7dxqP798vAaVaCkQb\n9fqdAA4xrxLDEzDhxBA97hl/3eWBgYNkAQFDbFZrnaju3a39nn1W/WS/fmgSGSl448KS+RznT50C\nIcSnV/y///wzRr/yyj1zjUradv3KFZiMRrS/T14TMZmgWrYMQXPmwN6qFbTTp8Pas6dPvECy2FiE\nDhmCrISER6a3U3nIyczEnfx8vkfWg8abxGzdiqYtW6JJZKRPbDMaDNi+bh1emOyaae7rnL/7odNq\ncerQIRyJjrYe3LXLVlRQQAICA4/oioq2wtW5+5bQNjIePZhwYlQ5CCGhcLU7GMI5nQNkAQGBvZ55\nBk8NGqR4sl8/n3cwvxuO46DX6fgKvZOHDqFew4bwZiuGkh2lbTYb0lNT0SQyEoUFBdi5fj1eLG/i\ntc0G1apVCJo1C86wMGinT4dl4ECvC6iQDz6AX0YGCtat8+o6VYGDu3Yhon59tGjbFkaDAYX5+fx3\nyNsNHyml+OuPP/DchAmQSCRwOBwwm0zeq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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will generate the image of the galactic plane using the Airtoff projection" ] }, { "cell_type": "code", "collapsed": false, "input": [ "lon_array = np.arange(0,360)\n", "lat = 0.\n", "eq_array = np.zeros((360,2))\n", "for lon in lon_array:\n", " ga = ephem.Galactic(np.radians(lon), np.radians(lat))\n", " eq = ephem.Equatorial(ga)\n", " eq_array[lon] = np.degrees(eq.get())\n", "RA = eq_array[:,0]\n", "Dec = eq_array[:,1]\n", "plot_mwd(RA, Dec, 180, title = 'Galactic plane in equatorial coordinates \\n (Aitoff projection)', projection='aitoff')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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6UAQyGIKAUcAMBj8iItFAW6BTYnLy5REREV1zc3Iand2sWU6nSy+N7di1a9wF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\nbtbM5H0U9Vdexb5+DaVSaXS7Iks3IY94+RIvg4IYq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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "And as an example of use of this projection system, we can compare the previous map with the coverage map of the data release DR7 from the Sloan Digital Sky Survey (SDSS), which is available in [DR7 SDSS coverage](http://www.sdss.org/DR7/), which is presented in an Aitoff projection centered at $RA = 180^\\circ$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "HTML('')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "" ], "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This image shows how the SDSS survey avoids the area near the galactic plane, in which are concentrated the majority of stars in our galaxy. Naturally, since the main SDSS target is the photometry of extragalactic objects." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "The Mollweide projection preserves areas " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A main feature of the Mollweide projection, which makes it particularly useful to represent the global distribution of objects or figures on the celestial sphere and get an idea of its density, is that while not preserving shapes and angles, it is an equal-area projection, ie, areas equal in the celestial globe are represented by equal areas in a Mollweide projection. The Aitoff projection does not have this property.\n", "\n", "To visually verify this fact, we will represent a series of rectangles of equal area. By rectangles we mean in this case the bounded areas between two meridians and two celestial parallels. We will proceed as follows:\n", "\n", "First, calling theta the arc of a meridian that defines the extent of a spherical cap centered at the celestial North Pole, we will use the the fact that the area of said cap is proportional to 1-cos (theta). This fact is derived from the formula for calculation of the area of a [spherical cap](http://en.wikipedia.org/wiki/Spherical_cap) , together with some elementary trigonometry.\n", "\n", "This fact will be used to establish a set of values of the angle of declination *dec* corresponding to parallels such that he area between these parallels is the same in all cases (this implies in particular that these parallels will not be equidistant)\n", "\n", "Finally we'll subdivide these strips into rectangles delimited by meridians spaced pi / 6 radians (30 degrees). The resulting rectangular regions will all have the same area. \n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "theta_1 = 30./180 * np.pi # 15 degrees expressed in radians" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "# Create an array with values of theta (angle measured from the N pole)\n", "# That delimit equal area strips between celestial parallels\n", "theta_a = np.zeros(7)\n", "for n in range(0,7):\n", " theta_n = np.arccos(n*np.cos(theta_1)-n+1)\n", " theta_a[n] = theta_n\n", "theta_a" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "array([ 0. , 0.52359878, 0.74946887, 0.92969779, 1.08817621,\n", " 1.23435819, 1.37336376])" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "# Converted to declination values\n", "# Measured from the celestial equator\n", "dec_a = np.pi/2 - theta_a\n", "dec_a" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "array([ 1.57079633, 1.04719755, 0.82132746, 0.64109854, 0.48262011,\n", " 0.33643813, 0.19743257])" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "# And finally we represent six rectangular regions of equal area\n", "\n", "fig = plt.figure(figsize=(10, 5))\n", "ax = fig.add_subplot(111, projection=\"mollweide\", axisbg ='LightCyan')\n", "ax.set_title('Example of equal areas \\n (Mollweide projection)')\n", "ax.grid(True)\n", "\n", "for n in range(6):\n", " rec_n = np.array([(n* np.pi/6, dec_a[n+1]),\n", " ((n +1) * np.pi/6, dec_a[n+1]),\n", " ((n +1) * np.pi/6, dec_a[n]),\n", " (n* np.pi/6, dec_a[n]),\n", " (n* np.pi/6, dec_a[n+1])])\n", " x = rec_n[:,0]\n", " y = rec_n[:,1]\n", " ax.plot(x,y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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vPDJySHZWVus777rL2WfgQGu7rl39Fm1h5rwP31NxcdBoNKhcvbpf2vaSk5OT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4AAAg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\ng3z4a3ASlQAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the figure above we can see how the height of the rectangles in the Mollweide representation tapers to offset the increase in width as we approach the celestial Ecuador, so that the areas of all regions are identical to each other in the figure, like they are in reality." ] } ], "metadata": {} } ] }