{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bertrand's Paradox\n", "\n", "Here is the definition of the problem as phrased on [Wikipedia][1]:\n", "\n", " > Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle?\n", "\n", "[1]: https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)\n", "\n", "The question is easy to visualize and might appear well-posed at first. For example, in the figure below, the green chord is longer that the side of the inscribed equilateral triangle, while the blue one is shorter. If one were to draw chords at random, what fraction of them would end up being longer than the side of the triangle?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "R = 1 # radius of circle" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bu8a7Lnr06IF58+ZpNRrNXsaYbfYlIsRJUTNJiA0xxuRarXbP1KlT9f369eMd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\n51/y50pLS7FixQpxuVz/CmU+onDjuxzRJYjIDpfLlbVo0aK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# example plot\n", "fig = plt.figure(figsize=(12,6)); ax = fig.add_subplot(1,1,1)\n", "ax.set(xlim = (-2*R, 2*R), ylim = (-R - 0.1, R + 0.1), aspect = 1)\n", "_tmp = ax.axis('off')\n", "\n", "# circle\n", "_tmp = ax.add_patch(patches.Circle((0,0), radius = R, fc = 'lightgrey', lw = 1))\n", "# equilateral triangle inscribed to circle \n", "_tmp = ax.add_patch(patches.RegularPolygon((0,0), 3, R, lw = 3, fill = False))\n", "# add two chords, one shorter & one longer than triangle's side\n", "_tmp = add_chord(ax, R, np.pi/3, -np.pi/12, \"blue\", 3)\n", "_tmp = add_chord(ax, R, 5*np.pi/12, -2*np.pi/3, \"green\", 3)" ] }, { "cell_type": "markdown", "metadata": { "variables": { "R": "1" } }, "source": [ "Let us stress here that the circle is considered fixed before the chord is drawn -- i.e. it is the chord that is drawn at random, not the circle.\n", "Without loss of generality, we consider the circle with center $c = (0,0)$ and radius R = 1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem might appear to be one of tedious calculation until one realizes that the answer might depend on *how exactly* a chord is chosen 'at random'. The 'paradox' in this problem is that different ways to choose a chord lead to different results. Bertrand considered three different methods to produce the random chords and obtained three different solutions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We explore them below. Note that what follows uses simulations to explore what can also be shown mathematically -- for a mathematical treatment of the problem, *see E.T. Jaynes, \"The well-posed problem\", 1973*." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "N = 100000 # number of simulations\n", "triangle_edge_length = get_triangle_side_length(R) # side length of the inscribed equilateral triangle " ] }, { "cell_type": "markdown", "metadata": { "variables": { "N": "100000" } }, "source": [ "## Solution A - The \"random endpoints\" method\n", "\n", "The first method is the following.\n", "> \"Choose two random points on the circumference of the circle and draw the chord joining them\".\n", "\n", "This is equivalent to selecting two random points $a$ and $b$ from the interval $[0, 2\\pi)$. Given the center $c$ and radius $R$ of the circle, it is then straightforward to map $a$ and $b$ to two points on the circumference of the circle, calculate their cartesian coordinates and find the length of the chord they form.\n", "\n", "For the purposes of simulation, we repeat the above process $N = 100,000$ times." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# each of the two endpoints of a single chord is\n", "# defined by a (random) angle in [0, 2\\pi)\n", "end_a = 2 * np.pi * np.random.rand(N) # first\n", "end_b = 2 * np.pi * np.random.rand(N)\n", "\n", "# the cartesian (2d) coordinates for each endpoint\n", "sol_A_coord_a = [(R*np.cos(theta), R*np.sin(theta)) for theta in end_a] # first endpoint\n", "sol_A_coord_b = [(R*np.cos(theta), R*np.sin(theta)) for theta in end_b] # second endpoint\n", "\n", "# the length of each chord\n", "lengths = l2dist(sol_A_coord_a, sol_A_coord_b)\n", "\n", "solution_A_pct = 100*sum(lengths > triangle_edge_length) / N" ] }, { "cell_type": "markdown", "metadata": { "variables": { "\"{0:.1f}%\".format(solution_A_pct)": "33.3%" } }, "source": [ "From simulation we find that $1/3$ of chords drawn with this method are longer than the side of the triangle. The plots below show: (i) the distribution of lengths of the randomly drawn chords, (ii) some of the drawn chords. The vertical line marks the length of the edge of the triangle." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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t7o+yzplXTmz7hjsfB+Q+H8fbH7ml5aKteQgoh6K4Ql/kYH8f29dDk/9yNMlv\nwbHQ5HH4MSYSFuvtvuR4MyqgjHdXBPrXINgdjpYkv9ydz6LvDA0Kvo5+2h6teFgUwecPwNuQ1w0a\nnghTwq0u1gOWlEExisPR4GQImsh5Lsozn4meCMxCkwVroUom3d0ZFsc/CzgdudD7xzkuifOtEN87\nNq7JZmiiYgH6D0NtVIHlTLLLmg+M2+K8uG47oYjP4GjbIXG9rwI+Ibv4zddo4FULueffIFC/AQ0C\nJkTfnOTONJLWSgmqk5KSNj39g6C6WrXaTJ8+sdA7CaqT1iwzLgEOQDncUsgBvQi5spnKDvVRxGMR\nArFrUY63FqpK8SmaEHgOgrZaaHLg8Qia68SrOspZ/4Tc0PbufGHGrcjtvdmdJWbkxvadEIhlJj6W\nQC5oYwSAeSiyUArd6AORu70zArvawIvu3BHw+xjQCg0a8uDmGnD1tuqJnKUwqDs0uwbB59moosdQ\nBJhLEFxfEufeEk3sG4ug9UVU1m4J0N+dK6J/t0ETDJvAc1vBieGKWwF82hdaHg+cgBZnOSvad3S8\n9ySK0lxPdqn3gdHfr7qzIEr7fUwWvndHUZQSwOnubG1GXxSTeTT62dCkyBOjn+shsN4XDSTyY7si\n8fuv0cdTkbM9Hjn9DdHg4XHgNgT8/eIaFEMwPh5FZabFqwWaUHp7ioT8vlL8IykpKWk9SkCdBemk\npNUpstOfIid3PtnV9yYgoJyBnOMS8V5LFAPJRxMNZ6Bs7WgUwRiLJvFlJre9Evsc7M6oOGYGvHog\nUHYzzkERggpA1xiflkDg/H+oksWxCMhLonhCW6ADckI7Ild3oDuvm3FstPtg5LbXNeNCBH97xXvH\nw5R74Obdsz1SpTs0+yjOYR5ymNsjsF+CSsldGXWYXzWjD4Lr54FHIiryIXKdy0epu2YIlJcCb8Bx\nTaFHO/iiOHgROL0BjFsEXhK5vxchgN8SwXsuilB8hYD9ZDS42AM4wYxZaJJoZRTpaI+gdxzQDShm\nRpXotxzgM3f6mfEYiqrUjus4L/preFzjeii+MhQ9fWiInlKMjHvhrbj2O0TfHEJ29cdiCMCHo+z2\nLnEeW6LIUKlo655mXODO9yStUcmpTkpK2vT0D3KqV418JKc6aVWZsSsqk1YZ5ZQnx89lCMBmxWcT\n0MS0NgiYRiPHehSC7GUImO4C9nKnfey/E4oOrEDw9gFyrzsguHoGOZaTkav5FZp89wNa8vxQBGmG\ngPlJVE2PvfQlAAAgAElEQVRiJ+RuLzLjMOTO3oAc1KPdWW7G9ShCcgRyU8ejCXNl4+8H1IZKpWF2\nJ/VI2Vnw80goUy72+WO0+VkE++8Dp2QGB6v05a0oGnEwisZUBkYg538pcI67qoiYURTe7AmHnZJd\nYb3EIbCoEcpMH4+gs1z00xjkXGeWJZ8dfXUUgukc5MjvisD4SgTTNyIwvgCB7cDYz0A08bEDAuQ9\nkIN9LJp8eT0qi3cKGli1iOMWRJs6xTndEX3UFOWym0efd0fgfweKyPQyowYC/QHonikZbV5MdnXM\npu4rSwUmFVKC6qSkpE1PCaqTNhCZ8TWKVExCzuFuCHC+RwuiLEET/l5DAHQkgp/nUDxgNALeOuix\nfjUEavNQyTUQGG6PMs2NEUSXR/GLHdyZXaj6x90o0lER5Yq/R3GCXnHco6KNFYCL3MmL8yiKainv\niW7yPeKYNyCntgX6B/AJAvbmqCJFHrw3CvY/HbnXwOU94bYFKH88DjmveyOwHYLy4AcDV7gzL6Ik\n9WO7/ZCjOwm4DOXNVyBn+UcE2re7MzfafQsUrwJLT9exN58DE4dCiWPQojUVENj2QYOVYxHo34lc\n9s+QC1w3+vxhNIGwTByrYZx3R5RlnoEGND9Ffy5HcZHceBVFcZmRaCBwGXLb34m+LY9AOR8NpobG\nz1wUM+mLcu1vosjKorhmH7nTOc55ULRvPIrCvKlz54fYT0Xg+MzgIymrFP9ISkpKSkr6hyniHi8h\nUPwVAewM5GROQKCzArmPnRBYzUTAtC3KF+cX+v7HyFkdgAB0HjDRnSfieLe408OM8qg2dTUEyvPN\naAHsY0YrBKd5yBm+A7moWyOQ2wFBWzHkfOZlzsedfDOWIYAfjZzWcsBl7ow04wMEmx1RrKIEkAMF\nn8IVJ7ESqLf7BW56Fa0EmBmB9gR6mnE6irpUQTD6qRnvIYd+HHJcO7ozJSqb/IDgcRnZiYf3AFeZ\n8Yk7bwHD4MW5cNRxsLwkzKwAXUrDg69GH10Sr+ruLI7lxnsgUJ6BBjST3OltxrYIvMuhTHQPBLXb\noYx3cVSXemK0NQ9NRv0UxUq6ItCtihzjaeipxGB3hpuxWbS/HsrAd0IlD9+Ia3cfAum5wO1oUPA1\niu3sGIOPJnE9u8e9dBEqz/d6tK8meoIw2Iz73bmKpJVKKyomJSUlJSX9gxQVM75F5dAWo0hFEQRj\nE5FLuQ3KLecjQF2O3N3tEEB/jwBtFooR1EIQVhLFM2YC55jRJWpPzzajElrkZReyZfn6kY0lDEYL\nn3R2p7M7P6J4xnQEY0tQJKGPOzMLnU85M05GAFgZTYqcgyYIjjSjEbDAnUEofnIoqoxRAU7Pg69q\nxJ4cbu8HOdsgOM/sfzMzTkARkr7ISS2OJkXug8B2MlDcnSnxtW4IXD9FLv+dyIW9Ms59s8iUfwmH\n7gYd+mavUK9d4Zyz0EItHaNPD4yl4Y9AefUP0MDlYmDLWCSmBoLYncmu+JiHnOyXEeRXiD6y6POP\nEHjfGwfPRdGTTGQmz50PzKiNnlJcTnZA9QXQyYwXEJx3R1U+8uI6tUeQvjDa1hIN1ga4czN6alAU\nRY2GxDXujp4yDAbOjomzSaEU/0hKStr0lOIfSf9Qhdt6J4JGQzBYBMFiRwRE8xDsLEFQmCmxVxbl\ngzshaB2LIgQXIje1K4LGssiZLYcAsjgCw2bx+xjkFI9HmenMiocVgbcDuAj38whUHu57FO94EcFX\nkziHhcixfT32VR25xlVQ2b1XzbgxzqcfAtU2QCNY1Btqd5A7DMCj7t45HN+rEOyNjs+2QYuWzIq2\n7YAmHT6O8sbDkJv/DYLaEWjC51I0ka+RO8+GW9sODSg+RwOM+rCkGNTaDWZU0uGqvATTT0AwXJXs\nk/9H0YClKYpV3IEmlxZBA5u5cU1fQu7+GQiqRyL3ejGKxOyCBkFd0BOJxfFzT+Ra/xJ9/zOKlJyN\nAL5lfL9DnGeX2GZ3BONE/+6DJm2WR7W7X4pr0i/69G50H16EKp3sjdztDmgSaH/klg8DfnDneZJS\n/CMpKSkpKemfIDM6oEfy5ZHT+B0CqRYRLfgcZaV/QpP9RiH42hbB2izgjMhA56IR2iDkXtdHE+Ru\nQm73kyjT3AHli+sh5/T/0MS5M5BzWhnVgJ6NIL+XGZURwH2DgB1Uvu51FB1oEG35GC0CUxbViy6L\nwP7B+KylGUMRgFaMtvZAWfBfoPtRMLOMdp+zEL6Za8ZNaDDxFILTkxDwHZ0BagB3RplxWRxvEBpo\n3Ihc8MUo8rEHAtpS0YdEpOQdM/qhmEMzoDYUXwgVz4EZL+oIM4+GfptBuzEIzt9HgH4YikjUJrti\n5LOZqIoZ5VBWvRKK15wZ578IOcP7oxz0VWgwcgmC3g9QfOcpNPApg+D5vXh1Q/Dr0YbzERQ3j+9d\nQ3Yp9Zoo410eDdR6oPusaHx/MYri3B6TSb9D+fDjot/uQPdQTvR9dTPcfSW0b7JKTnVSUtKmp+RU\nJ/2DFO5oJ1Q7uDSCs7EIZF5DkYFtEXAvQ6DbD1WImI7iH42QG/q1O/cEUO4U289HVUB2Ro/3F6AY\nwb4o/5yHnNKfYn8HIqjfEcVQ7kILnMxB4FcfuMedOVF3+aHYz3g04W9o4ZrGMUnxaQRyfdDiJ3cj\nIKuFoG4pWtjkK7Vj1CBocQXMj38De9wPAy5zZ+kq/XY7cscPRhGYx9z5dZX+bY9iKlPQJMwvUYWM\nWvHzJFTv+1H0RGAucoN3RuDbGA0svoPmTWBwNe25wRQY/RAUPS/O+2s0IbRnXM/D0MDnWneGF2rP\nQQhob4++/xRNoBwf13Emgt/bUByknTvNzbgOOfn10ZOB3ijyMQw50V+i6iUeS6CPQpMzt0H31UHI\nHb8T5ewnooHTy2hw1Rk5+y2jHx+O9m6L7qXe0Y8HRru/QwOcPPR0owUaaN29qda0TpnqpKSkpKSk\n9SQzyqLH9+ch93EpcirvQ47kFLSq4W4IWKaiSMURKDP7Xmw3CwHwODOuRW5kNRTzOAAB5FsIbMsh\nZ/OAOGYt5Gy+i9zfS+O7oAViDIFWCwTyI4H9zbgZ1bceA5zszvXuDFkDUBVF7mc+Arxroj05KHZw\nHHKNFwMOB26XBepqs6H344WBOnQhWlRlmPvK1R87m3FNLAOOGdWjrzILv5wfP7cmW8M5s/T4rwg4\nB6EBxV3xWV60czw8MiP7kH/sFnDv3gjM/+XOAyhu0RlV/ZgZfbOdGXeb0SEGGA2Qy3wgilFsG9ek\nEtmoRy7QxJ3rgClm7IQiOl/GPnPi+z9GWx+I7w4y4woUXTkx+v0r5Hqf4c5TyFXfKo67HIH2BwjO\nm8a+m5hxXJzoDHQfNUNwPQvdX0+je2M5isvkx/fvi0mTm5wSVCclJSUlJa0HmdEUubSNEeQZcopP\nRi5jXQQyXyLHeSfkOl6IwG8f5FDehkC7Zfx9Csr55iH4ySzZea47+yL4vBdloPsi57pHHOcc5LCe\njeo+3xLHy0FAOh0B1O5koSwPaBATLFen41DUpBVyhI9Ag4cTUEyiGwLQfkAXeHYITD40+/X8jrDV\niWbsWKjvOgBT3Bmcec+dGe7chJzz08zojUrCjUOxl++QU/8WAtsJUW+5CMqpZ7LFuyFgfAhB9bXo\nEdJUaHoGHDk227Yu9WBRLpr0R+zvFuQQl4y+/yz2vRxNGj0L6OHOSOSKZxZhyUEAuyUaTO1iRvFo\nw4koC30FcsXLIKCujyC+FIqQPBPXpQPKxR8Tn52JJqbWiz5fjOI6e6JozwUoK90UOfcfAEeZcR+6\nP/ZD98p76B6Zhe6hWe50QRMXi6PSflOBoTGA2KSUMtVJSUlJf7P+e2nypE1NZjRB5d/2RcCWiwDs\nKxS1GIfy001QBKAFcrA/daePGS1RRno7FE1ohABtB7TUeBMEQ0+i3PVUVpalW+kuNkSO6dvIqX0F\nTYC7EwH8YgRZMxEvtAa6ubMiIgw1UFygJsonHxtgPQ9Vi6gSx94DRUtKoEjFNwjkaqEIyHMIEutC\nwZbQeQtWLi9a/lOYsSWaYHlNVCpZCNR35441dO8S5Ia/GW08FLnwm7lzmRn7o2zy87GS4n7RpqFo\nIuVHCHQHovzwJBR9aAbkw12fwQuVUAynJtw4C249w4yf3fk8Vmscj+A8s8LkTBQN+b/4vX1cwwZo\nkFM5+rgqelowNK7X8LguO6Foz3wzmiOgroViL5ei+6KHGdsjx7sdyq1PReB9FQL1wSiC0xDddxeg\nOM4vaDCQD1Ry5xWzlffFr2hQdwm6z3ZAA7l9gBbhaC9C9+3Nce1+Qq55C3eWr+E6bXRKTnVSUlLS\n36zs0uSbZOxwk1fUSD4NZVzzEVAvQznZeQh8nkGTzJohEH0QZaN3j9jF3sjVnIImt5VDsIY7ZyKX\nuRaCpRpowt4FZhyCIDMPgXpJNFltJgKtD5Ez/QRypPvENg8jJ/keM84GtnXnMXfcnYnuPO9ONzQJ\nrx5yMS+Pc6iDstjz4vMmsd/FqMJFMQSwt8CdxWHhzuqpog45ZyN3uywaALRFgHjXGvp2F+TAPxgV\nKd5A0H4bsRy5O+8iyB6MXOi5qFLHMeipwRHutHanqztfIDD9GMVGHoMaleDCIdmjdq8EE+qj6Mle\n8eYUlFe+EjgaRTZGocHSeDQx88Ho2+1QvKJq9E/36KNZcV06I4d4mwDqHZEjfC/KW1+GpmfcAUyP\nKMw+CNSroKcKpZALPzKucwn09CAPDebyo40LgbvjPnkGuebjkAvdAujizpPo3nsN3ZNnA3PdmaNr\nSIvo00rAm5G73ySUoDopKSkpKelvkmnJ8e7o8fz3yKEtg5zbU9Bj+jOQe7kz2RX1dkaA0xcBUDGU\noS6FnMRZqB7zuMiztkQO59nAT+5MRKDWCjmil6PIyZ7A/ShisDmKgZyKIhldUcWMqsAidz5DE/cy\nFR/qmlHcjNZm/NuML6LdA4B93WmGJuN9hGDtDDSQWIBc9qUoYnE/cDJ8vxhuWBnxgIO/gpknxnld\nh8CuEprYd9gq/VrUjIujny50Z2p8dBiaQPgaclGvNOMnFKV4HjnAtdATgvOBF92ZvcplqxD9W4AG\nBiPhvvZQ5Bt9vBg4rwRynW8xLb1eHV3f1gh+GyPHuBkaZHyIrvskBO1FEIjuFO3NVNnYPPpreez/\nCQS/H7jzDlDajFbuvImA9iIzjo62TkXuclmUoW6I7p3KKMZj6EnCofH5OyiXXQdl+hsg1/8GNLF0\nCfBePGXJrMpZG90jsyPLPxe5BY3RE5AGwAcRY9nolaA6KSkpKSnpb1DUTu6FoKUocnRLooljtyGn\n9F0EQYcjB/Fq9Ig+F0FYe+TcvowA61dUh3hLBJ3Po/ztVsgFHgnUNuMWlO1tg2D5HFShYhoCv8HI\ndZyLwGsZgt5L0KS3SmY0iH33RJD8eOz/QpRT3sOd/d15plB5u9Oi3bsDe7lzXJzrTwjuGiGwz4fu\nD8KizfW1IrPgzqfcuRLlobdAUYofUaSldCwogxm10EDlfXcedqcg3s9FbuwdCGhfRsB3AgLEXaN/\nv0GT/n6O/llVVZAz+wVy3nH3fCj4V3aTt6tAn7kIfjuh7POPKPt+BBrEFEVl6nohp/hqFPVYiK71\ny9FXlyFYPTv6eDRyu8vG9SqHqoeAniDsHw783FjhcDZy8lsjuD0awfwv6B5YEn2/VexrFILmDmiQ\nlqmR/gKC8xI6Zy6IvrwV5f73JLtMfL/4fQwC8xyykaV+wF1m1FhN325USlCdlJSUlJS0jhUrzz2N\nwNcRdFRCULoLcoczFSkmIbc3sxDJYQhMJqH88jmx2zLIXWyBJpYVQYBzLFrcpA2KVcwkO8nxRQRp\njZEj2hPlYefF8RchgO2E4OtglAPuEO3/FTm7JeKYxyAo24JC87TMqGPG3QhqOwK/xAqMoLrJeSii\nMkfnfOfl8O+62R679GuoX8eMyu7MR07y18ipvxBNxqtpxhPI4b8UGGPGrqZVIm9GbmtpBKx58fcc\n5LQ/Ej9LxDlVRNVQ9ohSfYWVgeqPUKwCAHfvD01HZje7uAms+AKV5luAYLpF7HcycIc7eWbsjkD3\n/OizydH/Hsf4BjnjrdFgpEi0M5OjHg+cYcaxceDrgYujBjZogLQlGohNRk863o5+a4lgeUTs83p0\nL1yI7q0vUUxkGtnFhvYGDjejiTvvI9gvj+6R2uie7o/u4cyA5W00cMpFA7UfgSdiALTRKk1UTEpK\nSkpKWocy43zkSv5EtipHSeQCboGiAJ8hFzQzSW88gpPX3OkXNYoz8YNMubvSCDbPQBD0JgLqysj9\nrIjiJG+gR/xHIOB6B8U7WqFFXO7NLN9txr8R9GbK8BWDlXWfX0VxhPHAE4UmoH1lxnbArWaMRFVL\n5pCNpxyLXPVMbem2ZKtw7Ac0gqdaw5IMzI6AKy5BUZETY0KfR781RM51RbKTJHdDA5S5aGLfv9Hg\n4CUEl5ls8GbIpW8OlI4SfY9HXKZv9M8k4F4zrnNnbrRnc2BsLMBTEgFz6OFPYM/tYUVR+KkKdMD9\nzeujpF/buJb9EbgOMWOUzm8l6G+OHOSf4/o+jaIqPyOXtzaKtMxCGe2GCGJz4jrfhwYI3YAbo+JJ\nZsXFk9CA7S50z6xAA5mzEOQ2jWN+hwZoA1G+ezK6N3ZGYL8zcqEfifP6mux9/HPsu1gcbzs0CTTj\n4hePa9Ey7oFXzNivUN9uVEpOdVJSUlJS0jqSGe+hahoFyCmeiKIVjkBlFIoeNEUT4T4GPnbnbFR7\n+LTY1S4IZh4jO0mvTHz+BQLGaSj/+wlyF+si2DwU5XuPRznbp8nmZx8G2ppxc6xWuAKB+zgUD1iA\n4hqTgWrudHHn5dVUdJiC4LsVcnY/Q655T6CmO9/HdicDS9x5KhZpqQovLYfRzQvt6wKoYChK8DmC\nvaNR9KALilSMiHN9NdpXHwFcceSq34OqVIyI/rzUnT5R8m5rWOmaE+cyONq7BYrlPBwwD1mnmuiH\nEtmmNs+Fs6dn/+5/rtnPN0Tfv4GeClRG12xLNBA6AQ02Hohza4NgfhwC2Exe/mB0X5yAyt8VoEjO\n7mjy5XQU1TkBucfL0MTIK4CF7ixz53MUPdkPwfpJ6nP2R1BcFA3cDnLn4mjDfnGc5xAk56A8fv/4\nrDiKoqxAEZp60f6BcawF8fuj6D4fjp68bBfX8GUzCj2V2HiUoDopKSkpKWkdKKpk7IUc6mUIijdH\nzt58shnZ2xDElEQO7K2xizHAIjPOI+tS94ptKqPJcBUREL6IJvOVRRGFYghuSqJKG2chGCW2nYNW\n42uDgOdqd65250HkNFZFoF4LOaQjgflmlFnlHEuYcQGKX/Ry53RUWm0XVKVin2gzZlRCDmbH7N/5\nBuc1zu6x/iDwpdH+0qjyxRLkTp8S/fQ1Av4jol21kTPbHuWRL0JwOs2d09wZscqlqYkgsLAmISY6\nGl2jt4BrzXgIQXUmI94fqBcTNLsCW8M1T8fxgfmloFml2NdzZJf07hr9PBdV8tgSxWe2R478TghA\nO6LoxPEIWsei8oS94pr0Rm7z/SgC0wNd5yNjn8MRwPctdG43oqcLR8fxvkaDgwKUvz7ajKpmHIay\n/J+hQcQW0bd1USxpJzQgq4wAvWr0x+eFzqcm2cHjI9G27dEAqEx8t0L0bVU2MiWoTkpKSvobVK1a\nbcwsliVP2thlRmf0aH4pgrKSCPRKonIRxRHojkYuZHVUs/rqzEQ7BHLTUVZ1BJATruqVKGvdAjmC\nJZGDXRc9jl+GIKomWYf1MQQ/k+K4wxDwPOXO97G0dS0zrkKO4lIUXXgbOdBbx34yQJxjxukI5Pu6\nc02m4ka4wWUQ/LUDOphRAbnHhV3uznDN9zCzTvy9BE6+ClWbyERmBkT/PI0m1XVCcYIcd2a78xZy\n6reIc1uC4h6V0YDkLTO6BdBnlLua1Rm/ARq5MwENPnZDDv+Y6K+jI7qyCAH9bQg+X4LNK8L1o7O7\nmnUWDF2Cng4cjFzxDxHI7o8gs0+8VxZd5zEoqrMFWiznZzSYKePOCnd+RvfIFwisf0KTIrsih70r\nguUt0eCinhklzXgLPc3oj1z93iiWkovy27+gJyV90VOAaQj8l8drWLz/SbRzRRx7JzRoGI3uv3Oj\n75cjJ/0EdP9/jgZIS9A9cSmq+HIO0HNjm7yYoDopKSnpb1CqTb3pyIz2qJRcDoKXh1CFj5kIShYg\nB7IuAqCnkSM4DnjRjFZmK7PVe6Hcc8NCh6iMHtvXRXD+IgK3bxEMbo3cwIzjuxeR2XbnTnc+RPGP\n5cBZZhwYNY7bR1uvRvGE6dHuOQho3wFONuNc5MAOdedyd35YTTccgKIm/0Iua1/k0PfMbjKrLdzV\nLPv3Kd/B1TWRS1wdwVyv2NehwEURI+kJdDRjXzP6o+jDDe60Qw7vNnHstmgC3oLo1wFmPApsGZVB\nCms0gl0QND4W5/h4HO8gVJnlIXQNr0cA21Ln1epABLxAflE4dwc04LgK5duvj/NfiAZZDVFmegi6\nF45E+fiFCESXo4odjc3YMYB+MbpPlsexDkBOcyt0vSojOP852pn5j87taHB0BBogTIy274cmJuYh\nmB+BsvLdUP65N9DQnbEIyDODg8qx3wMQbPeNfS1G9+CW6D6cEtvsjQYPpdF92xz92/gGVQXJDKo2\neKWJiklJSUlJSX+RTMtn90S52xUIVBqiVQUroAhHEQS5A1GkYSAqCTcRObtnIof2BJSZPR0t4NLQ\njPoIar5AIDMVgeRRaMJZZQTTO6OKIVuhag/TCjngIBe1LILOK4HLw6029Nh+BgK2XeMc6iM39EcU\nI3hgNbGKTB9sEe2u6c43ZpyFoPJo4DYz5qgvrtsBlleMr/0Cd33kTq+IVThyN+9F7vbnhQ5RBy3a\nMhg4IVxcANyZaEYJBHhl3RmPysXdbVrtsT2K17xtxpg4z2HRn6ViNx+haMXtKA+fhyIb7VDkwVH5\nu3zknJ/m3ibf7NR7odfu2sWXtaHoW+75M+O44xDsT0bX+yAEvjVQzKY/cojLIug+H8HnYSgbfhTK\nxx8S59YEAfQvaLD0ihnT0bUuiVzlLRHQbovusykoxtETDSAqo3tmURx7L2IBIQTPh6N7rnhci4MQ\nXO/nTr4ZPVHt7xwUu2kV55KJpdyLAP/iOIfnUBzoIPRv4hI0ifUgtBDOBq/kVCclJSUlJf0FMuMI\n5DrnIoD5Ajl5eyLA7otc3zHInbwHwXcpBD3dEAyPR5GPJxE0VUHQVQQ5gc1QtKMUqvxxOHJjSyOX\ndRhyWosgKKwNbGdGGzP2NOO2ON61CIpOdl/5CKULcrdnImd2DnJjW6LM7ETksC4249ZVM9ahK+P8\neptxDIoKnIsyvEOBcTBqF3ikfPYru90HlSdHfnw0ypyfA1zrzuexuMtpZgxCru7ewLDCQB3XYDvk\nqp+CFmKpkvksBhXvIAc2k8cuh2I0nYE2ZtyAgLV19P2r0ccTosZ2f+Tq5iIA3hWtZlgFnjwQ9v4u\n25qC+8wsY16ejWA4E/H4BQ1+MhP9hqCJfbPi947oeubE925HcZAKxOqQCNJ3AP5txq8I9BehJxcT\n0f2TjwYBPyCHexCa/Hht/HwdDSyKxncONeNkdyaj++57NPHzYWCKOzdGvAc0QNgD3a+dULRlavy9\nCxrMNEWg3S9+740GkDujUo0tgb3MaBuDjw1ayalOSkpKSkr6kzJjWwTUPyL38SXkynVAGecpCF6m\nIsjIgPYt7vQutJ9SZOMXVyMgKhp/F0Ow+A3KDc+JY9VGUYPLETw1QVBcHuVY90TgdhxaZfFqd1bE\nIZ8yY3czrkCO7DjkYFZF0PM2AstP0KTFZ5G7vQJlZm8y43l3Bkf7N0cO+mwUX6mDQP0Ud7rENtXg\n+ItgRUBU6RHw+TI02LgIQeXEaDvhXB+M4hH7uLMw3s83Y6sAwIw6AaPcmWLG5cgZv73QNjWBie7k\noWgHZjREoO7IoZ2GHNT3EZSOBbqYcSRydE9CA6Aise2lcZ3fgLx2UHQM5GeWAT8r9nFaHONw5N7O\nRFnmAgS6e6LIxA3I0f8Uwf7maPA1FC2U04fsoGcbBLWz0WDqyujv7YFrEHxfhNzuRsjBroTqZeeb\n8S2K13SMY2TKJ7YwY5u4fk8hh/kR+K/IDO6sMGMsmjj5JhoMzUZw3xa516PiWpaLV/Po29bIxZ6L\n7t/TUTnADVYb/KggKSkpKSlpfcqMYiiuMQpBVg7KBJdBQDwNgVUlyFSMoB6wzJ3eZuSacbAZPZDb\n2B45iM8iB/pZd1ohuP0h9tcWAVU1NEHvEgTe36Oc7BUI3g0B13zk0rYDHjTj+nhdjMD5rNhXtWhz\nZeSiZuo+10Sg1xCBVhd3pqNYx6lmvGdacOUyNIi4Js65PYK5L7M9dt9N8M122b8fHQhFj0GwWhmt\nCjkFQfx7qMJJe3fOywB1qAfZhXAwYy8EhQMB3FmAgPfSiM2AoHNC4evnzrfu3IDAsRECvHqx/6MQ\nbC9G0NsQxXL6x9dPRIOaF4DiMLQ17P9mod3fCNOOAB6NxW8qoycAzRGkzo821UUDpCuRe7svGjT1\nRuDdGsFnQWzfEl3Pa9DEwMtQrOP0+Lw10N+df0dfPoXKNdYGbjDjJBTTGBF9thjBfQbWF6AnIlei\ne6hX4T6LJxTV40lES+R8z0QDt20QNM9GcacqKIY02p0r4voUoGv7Qpx3faC8GUXZgGXuG++kGTPz\njfn8kpKS/qAKV+BYh/+NqFatdkxQXHmwTAPW6nd3T6VC/uGKR9bD0KP681Ht4bLo0fhUBE9Posf2\nuciNvQTFOOYiAC+DQG8gApTOAYSY0R3B3N7IRd0PuZYVEXjXQcC7GGVYiyOXtQA51m9GW/aK995B\nC5H8G4FhaeSi7oQgvXjs62cUVymD4OobFB8wBO5nxXZ9Yz9L4716CK7moujGHDNujd+Xm71UCi6Y\nABJ59fYAACAASURBVNNiOXJ6gV+AIh8/IKe8bvThl4C5Z8F5Nf1/GnKwR8T5zwFuLVzdw7S4y81o\nkNIceHvV2Ehs1wK5/c9HW+5H7u13yM2tjmI1XchmrjdDg5BnUEa6Iiy8G+rsCDNjhcNjJ0Lv19Dg\npwXQIK7ZDwh0zwPaudPfjEZo8DQy9t04+rJ49H1u9FWuO/ubURa5vdcjKK4Uf5+GBl8L4zgW514i\n2voIGuycFO97/DwXTQo9UOeihW/Qtc8hO5iYj+6ve1CUZizKuJ9MLPKCIi4NY7vPENB/gvLZ/dAA\n8lk0gMhHbv2p7ly66rXZUJTiH0lJSUnrSNmKH8B/rXyctJGoFXJ3u6LoQQkERN8hwJiKQOcHBNTP\nIkBpity88935CcCMbqiKRaEV+5iJYOUt5Bpfjx6hf4rcyFmxnxUot5uPAPNTBOj5qMbzLwjaL0Hu\n52VoglgllPEtEq88so7lQ9HOYxFErojPD0O53Q4IkMbH8tuXxHFGATcFUFcB5mTL6PV5JAvUmy2F\nbj2Qyz8AAWNpBGLvo4hFe9Py2KudFIkc2LvRQOMF4OBVy+UJ5rki+q46GlCsVEzOPBnB7mgEiB3R\n4OEuBJgZ5/07ssuLZ/p8d+TOP6P+KVUbbp8CpwVUv7gVnFUL2tyMMtArELhXRTGJycCTZjwfTZqE\nJhlujp4yTIk+/xA55zsCz5vxLwT5jp42LEaAe1icw/0oQlQCPXXYFU3SbI8GQE3QILA4itxsh5zm\ndnEtcqOt0zPHjMogmX47J9qWj9zpZ+NYl6BB3Eg0MLoLueiZ1TwXo/u2GhowjEAZ69dQLnuDVYp/\nJCUlJSUl/QGZ0RS5bTMQnG6GgOEllJ2dgcBhbwRmdyJYfR7B6O2FgPpYYLg741Y5zHIEsgtjn2UR\nMDVGcH0HgqVaKIoAAvgGCFzuBy5A8Hksytjuh8BrKwTUg+K7ryKnt2kc620Eoktiv0+iQcKN0a63\n4txuMON6lCnfDLnWd0cco3McG7PSleCNI7Onduj7cNVLCLaGRFtui3bWQFA9pNB5/Zdi0tzHcT6b\nwX9UCSm8XQGKKNRBwIfaRAM0cW48cl1bokl2FyO4rQIMdOea2K4RAr8j4jwPQYObBQhwZwHvwAlH\nQsvoNy8C3dpBwctodP01egKwV+xvERrA7BjnvCL6YiG6jkvQ05BZMWAYge6xqigXfgiC9bYx+CgZ\n++ga5/EAuu/GRB8cgdzxHVEE42m0CFC52E8vNEgZjKC4T/TtUeGMZzQH5fYzqoUGGF2jP4qgiZmt\n0QBhOIqaZNp4OMrOb4Hup6+A/zNjP9PiOuXYwJSgOikpKSkp6X+UGa0QkMxG0Noagcn3qDZzReTC\nzUcgmnGAH0agm4viFpjRGKjlzpv8t0oh93A5gsedEGgtKrTNS8gdnoLc6Bbo/+8FUdd5GYLJGQjm\nHkLAvFW8NwRBVhPkNL6DgOkgd/ZBk+fGISh6FMUDmiPXt3K0qSKCxE+iP26Nn+2BcwTdbQfAouJq\nch2HXhWQa74QAdxH7oxELnsuyoW3BraN/l6T6qLs7n6oQslqFRVOBgDbm3GEGZehwc5lce7nRzve\n/X/2zjvcqura2++kSpfeVBAFVFQUe8GGirGBsXdj7yLW2HuX2GKNvZfYYsGOCnZFRSxgAQVE6b0c\nYH5/vGOxjya5N/deNX5xjefhObDP2qvMOTf7Hb/5m2NistAm7mHXqApyAyZPJ2LiMhPV3S+B63Pm\nTvQ0d4E6V8MFQyDFVNUr9eGRNbHPl4s+qkIrySRc9AmqwnWwfz+P67dG+FwzjqnCPt0Y4fczhPVT\nU6IPJgU7IOSeHNdYA60bj8V598V+b4VjeK84Ry/063dHi9K3OHtwVjz7vSktruc9FaG6BqrlVwDn\n5sz0aIevo18exUTt0Wi34WgTehQtIfUQ3DdAiD8Xk9Wr/1E//pqjhOoyyiijjDLK+B9ESiyP9oSG\nqDpugdAyFZW+pdHPOgzV3AKUGiHUfIpg0S8lmmHJtkv/wXXWQ9gpFta1wu/tBghEd6Ll5Ab0sR6A\n4L0s/EDluwZtCreiGnsJKsGT49wHIqQdhFPwNVDxvTAWYQ5EtXTb2MHwReACBL/nsapFE1QfByBw\n94pzzgE2gKdawOMrVG7pnNHQoCVC1TQEuW5RsaMnJiNdcubPcX8XpES/qJlcvY1aRrv+GVgtZ+b/\nuB1/3KxoSzgSoblVtNmqCIbdUfmdi7aFGfGzPvqQn8eZgb9hstMgznluSpyClTdaAfWgZzvYe3Ll\n0rtOhA+2RwguNmo5ABXj96gsEJyPQPodAvf70a5to32OQS/0OEzg6mJ/rYyVWYpt3YcAj1PZsGYZ\nnKm4GyH5qjjmDrSDzMfx0BktIX3Qh38EQu90nM24LiUOpALVbTGxehd4New0OyLw98Yk5RhU5WdR\n8Wx/UO1aU6JPOqP63gHYJhKf/2+ihOoyyiijjDLK+J/FywjGT1Ipc7cEAsyUOOZbBK6ROL19OkLS\nIQjgt8V77wPOrL4xS0rUS4kzcIFifQSNDghjYxHoGyOgLAKaR2WJtgip7yMk1kiJWnG99vF6J5zK\nXw990UOwJnahcD6LHuXuCN8XIjzXBCYld7+7GStgXIWJxSEIml8DH+TMbVFNYzSwKyz6AC7ch8Xl\njTeucr8a7kPVNEW7/Q29xI0QcK8KW8nhmAAsiyUAD69W0/goVDSXBGamRMNq7VgnJVZIiT4pcUIs\n+twb4W0wKqMdgJ45c1j4hf+ENpxXc+bTaK+joh3eROA/FSC2NC/OswgXo94YbTINuAEunQENw0++\ncFnYdt/ot1HRrzthw3yLqvI5OF42wDKCR8c1+0Y/HI+7FD6CCvlLOMZ2i38Xf1bFhGCveN66OM7m\nR7/PRR95e7Rr7IWzBgnH6ds4nraP+x0YfbBU3NcWCOad0TJzGS6enIkzNlMQujfGz8syCPbjcXz9\nNdqgBSYOA6J/Z8b5H4pr7pQSG/P/SZQLFcsoo4wyfsL4+4ofZfwnRdgAGiEgtEWQWhIBYnuEhGKT\njnYItNNRwWyGEHQjlQVmTYEeKfEags76WKd4ECrLc1FJ7IxKYDdUNR9D28fWwLEpcQwVJXpsvG/v\nuIdWuIjsY7QefJ4zkxBQT0OwPB/hqmfOzEmJ6fEsNyHofY/2lQNy5rQA1J1Q9T0NlerVgPNjwWJf\nXNy4B+w4FgYH7KYMAyZBjW45a2EJZbMpQtXW8YwNUOVuyA/LAd4X13ktJcbEcaci2A0HnkmJF6Jt\nqxAwP0MLRWdU2JshBG8af45MiSvDHjIM2Dol3kaArRvtsgBh8AP0Ca+REufGvY2PMXEHqse9ESrX\nglaz4OgRcEFYJiadBCMfhM5fRpsVJQxrYRI1G2FyLyqLTptGvzVE285b6JU+K97XPXbDHIO2lfVz\nZl7Umu4Q7dMnZyYC5My3KTEDgboX0CNn5id3ZKyPC08PSG7lfne0+1iE60MxWdon2udCnLmovgnQ\n9jjWGuOGMTkl/oKK+bKYUK6M4Dwn/n00gvYDWFFmtbh2HayFvmvOjONXHqVSXUYZZZTxE0al4kdZ\nzvM/LVJiXSy59hWC1n6o6g1FsPoCoagWwtBABIdCxXwVVcXhuMnFQgSV09BHOghV103Q2vE+AuHO\nCBkdqOxQV3hxb0RIfDXOsRaCy3wchNPiWk/iYrEpwLyUaB6PdSHaK95A1fWigKmh8XwjUIFvhuA6\nKSU65MwXCJTrx8+FqGQOj/PsAuwOUxfBO+dXWnGvSdBjAlRsHDmTc2Zyzrwb7XZVtMVu8YznILhN\nQ2BbAxcJbopwtmqc6tM4vh6V8nMbYKLRKF7bCLgvZy7NmdlhZ3kf/cgJ4XFlVKwfjv66KK5fN9pw\nMnBRzpwe6vb86OdrUelfGYF3MnABnLEQusRmO3NqwmlbYsJRbBNfKM3Toh0vR8X2eyw3Nwv9xzcj\ntB+AMLozqtDtor7zrvEs86NdR+BY/RqTnX4pUT/aaqU4/wRg+Sg72D36bqmUaJIz83Nm57j2aExM\nGmHVmMfQL38bWj+OAz6P9QGLqFhq7on665NyZgDadI6M+yTuYU2cFemBKvwWmMQci5+rQ2Gxj/tX\nHWWd6jLKKOO3Fz9jneqU/rUa1GWd6v+/IkDzfYSddlhFYW2Ekw8Q9JZDqNoMQfM5VOAOQUXwO/RO\nn4Sw0BgB+mP0FD+KYlc39KMei9P88xFWhyHM74Mw82WcZzW0D9yNVoWVscrCSIT5N+P6r6JqvSQq\nkkPiHrrh9Pw7CKVrYXLwNiqpT+HCt5XRX7s7wvi2qCx3xkVsRX3iGlgpYwEcXhuuW9tWrDcXPn0I\nlhmPg/3JnHmpWhvXQjDsiJaHNxGcB+NMwJeoAh+Bvu02aBm5Kp7zPvSz/x4tB+vgB2oEAmPNeOZi\nkWdCkP0cIX9NVPh3Q8V0YTxzfeDSnHkhpcWwfE/OTIzk5AlUxb9BG8078d5xmAC1gZvnwoG9K5e9\n7ybYpR2qvQNzpmO0QTNUwndCj/UXOEPRL45dOtq3Zs7skxJ3xn3PwXHyGSZEN+H4PAK927egvWQS\neps/QRtIH1TM/4awezOOhxVyZr9q9/Q3TNoewLH2PfA6KurfIHCPx8/IREwqBmEZwG2APXPmszjf\niZgQLIi+vRCh/MM470EI5BMwiXkGk5gJ/MqjVKrLKKOMMsoo47+P4Qguj6Kq+0cE6vcQatoiZBSL\n7F5ECPwjgs4CrBpxNAL0NQjTXVGdOzfeWxun98+ExXWfxyO0D0Bw+l2c85Kc6YegOTvOAULOJahQ\n7hS/3zVnjs+ZfeK676Ii+j1C5NPx936ohNbHag7T4vWhcY1dEcRPQtBeDpXxYeif3QHBazkYXRtu\nXq3ShP0/h2WaIagm4MyUGJYS96bEbdEmy0S7foqL7Q4CRuXMJTnzULR3p3iuB3NmTtxfUb1kPiYD\nHeMe30Aw7Y8b2nwfN5OirdfE5KUfJiv7IMwtQIW4JVpMqlJiD1S6dwSOCr/3Xgj0Y3EW4M5ok8mY\nEB3m5Q5YAtYL+0IGzuwLi5rj4seU3J6enJmMdbSnIaO1QAX8YkxclsVdDjunRCdMEvaJdnsynnM9\nhNpzoq1noLJ/N842XIcJxunRDmehgvwQKsw1Uf1esdo9jUcF+gkqG9c0wsThGCpboO8WbbR5/Hsu\n8GkB1BHNUPUfD7SIWYpTo83OjHYchzM+w+P+j0iJm6IE4q82SqW6jDLK+O1FqVSX8T+I8A/vhSre\nHASbYjq6ASpzVVgK7mSEm71yZnZKtEe42xgV5ZcQensgRNSLf3dFpa4mAu4mqEqOQXiZiyDyIaqq\nn6LK9z0u5KuNVSQKK8h0tD58FO9pmjPXx/M0R5AaHcefip7qh4FNcuaylLg+zn1Z/P7luI/eCGjb\nIdz1Rcg6IN4/AdX87WGt5+Cd9W2mDjPhs/egbgGfLyM4NcGNVp6M9mgQbV0znqMWlVJ5Of69E5YO\n/AbBc6No17qobDdE8H8T1djxcU9HIIR2iXPNjGPaoLo9AhXS9ePvdRDgJ8e/x2EpuIzq6Rdo49gi\n+r82lUWHk6Pv1kG43gveWQBr94Ic69mu+xwOHY5K/1dos5kXY+FFTE4uR2W52AJ8a0weNsGxeCba\nU5pjEnYoFb//bbiI9tJ43w7xDJPQ3nJIPN9CTES6RtufF+doDhwVnugD0Fu9NML1C9EXe8d9boTA\nXRcTifoIxKOBW3LmcYCU2DnadwImPt1yZoMYk2dgKb3+mFhug0nFKThOJ8fz7Rxl+351UUJ1GWWU\n8duLEqrL+BcjJbojwI1CeH4LlcT7ESBeQRA5AdXOFrjg6vBiF8GU+B2qhq3RxvAMgm4PrKLxLCqm\nE7G6wkRCwUTAPgitFrch+AxD4GsS93BdzoyLafqPEbTWRsVyv5x5KyX6AYNy1suaErsiZJ6GcLZ0\nzjycEjsi0HaLa2+GNpIVEGw2wETgNYSos9FKsBmqxLWB5+Ge6bDn4SzeSrTh1jCjJ4LRTTkzrVob\n10aQmoSJy8FoPzg2ft8LqJszT0VJvSeAw3JmZEpsG226bNzjUAT/uqgYD0PIroMK+BsstmSwBEJi\nUcJucvxpGX0zCdXqCQiYUxBwF2Gy0haV4EXxnCOjbWbFsY2ir1vGMUPg9yfBI2v45E2mw6gXYckV\nbbPFXvDv0FJ0c1zjwBgf7eNZhuF43AYtRg3i2PXQ5vFMPNvrmIw9ih7303NmbpT+WwJBeHbc32xM\nPt7C/4Q+xIRgVM7cnRKbIfRmXOx5RbTz3zAx2QoBemicr3P0x3wE5VHxTGtjwjMnfraM+1sPOCt2\n5jzTtuKceP9c3DBpAari7yDsL66Y82uJ0v5RRhlllPF/jDZtOpJSCqAu4z8lYuHanQhhzRA0/4Zq\nYrFBx+4Igcci3HyJyuHZKdEqKmGcisrx/QhFnXARYH0EqE2pbEf9Whw7FSFqHALKfISkotbz74HH\nY7FcURWhLaq7ByLcFwvfQN/xAYXNANXFpgiPRS1hcuavCPbtc+YNVIMPQzW5XlzjeYTJO1BtXIQq\n9Z+AybDwbdhzdRYD9YrDYcZqCOlNqgN1XLMqZy5GOP8Tgt3y1Q55EaEdVCqPAfaPf2+L/tyZmLRs\nGc+8BJWKHx2p2GgGoo3mRITTLXNmhZzZMmd2y5nDEfAnosXmMaz/9xqq8S/Es05GSL8j7q8q7rkV\nJiVLI4D/Me59U+AiuHlZWDK2UZ/WGI5fDj36eyDEPx/PvxwmBudiIlVsJb41wvCu2L8JGBOb5iyH\nCdUhcexGODvSEzgxZ3fGzJkLos/uw7F9BZXdDg+O59wh2q9b1EvvHW0wExOGKaiif4FjKeEY3gk9\n+5ehV/2TaKfVMAHrjmOzNSYmnaIv+1cbFzVz5nn0ZKdolx3jub6Kdj2NX2GUUF1GGWWU8X+MsuLH\nf2y0pmI7+ATB9hJUpyfid+gC9I/WRo9qK1zo1x5Vw3sQtFdBe8ZCBJrPEdRvR1XuNrSITELV+2hU\nX1P8rEKAb47K4MsIJdVjKfSfvkKlAsjWsHib7guIGssIm3chnDcEFqTESimxA8Lc9inxLiqcX6H9\nYV1UK79DZRe0iFyTM0dEe42Ac7fAKX687893QFX1v5yyz5khCIW7YaWT4vUMDEvuqrgkKsKkxPMI\nf9shKLdC0HwJE5v9MSnqHdeejbMCPaJdjo0dJxdHLJY8IdrwRrR2tMJ+aB7PtTqCamdckNkNgf1q\nTF72j+vtH9f+kMWlDpvOgENfrVzx7lVgVEb7y65xfHMqPvxWCOtN0cpxJJUNfpbB2YYVw9/dE/to\nz7jHZXAcbgEclhK7p8T2ofw/gzMg0zEBmBbt0RWTn01xcetymAx+GffwHnq430YlvhUq2tNQfR6B\nScXJ+Lk5AxXq5pggdkTleRRakCbiZ6cdfx/z41n/glC+ABOM5sAeyY2JflVR1qkuo4wyyiijjB9F\nqNRbxZ/5CMMjcEr6rwjFe+GCv91xodfqqDD/Hv20ddGq0AkraCyDoPU6KpCv4XR4S/TD3ouwszcq\ntn9GEJ6Kat8itD28nxJ9/8H091JUdghsE+fdPCXOCzAdD3wSANYDobwe+qJnoirdGcG18PeenDMz\nUuI+hLueCFM1Ua2sQkDCdpo8Fa7cqdo9XQHzp6LC/4doy38aoVaelBLbpcTVaG/oiNB1MXrJ+6B1\nYAm0c/SLjVj+LlIyqUBQHBfnexk4JWcW/OjYYtHeNdi3DdCPfC2qqzMRrhtg0nMCWj3qIdjvj31w\nN9A3NuQhpcUVLT4EJsDru0CrL+D7DvLlIXPgmdk4ZppjBZeZ0cbrxD1PQajthQr7QgT/pjg+umHC\n0ABBv3ecb+u4935x/Ng4ZjX0PPeMf9cETonJtlnRvh9TqVqzeTxbhzhHszjvN3G/0zBpGRznBiF4\nR0w+51Kx3nRDO8tIVMWvAe5PiUHRRtOiLxJyai2sZrIXzpR8H/f7ckqsF2P7VxElVJdRRhlllFHG\n30exKUptWFy/eBr6Q3dH5XEiKtCTEYQXxDEfIWCshxDwIS5W2x+VvgHA1eEJvhMhYRzC0B/QStKX\nytbNXyKAz0PfKiy2VvwgNkd4eQwhdDtU9h5JiQ9RORyHKud3uABsclyzNsL/7fHaHmgPOD8lhhCb\nxsR5WyNwFVVELoxNZDJsWAVTYyOQhrNh5nmobN6DiugfU6JlzkyI2srLIMh3jvMWgFRsq30BqqJT\nEeA+ifZYCitZ/FOgjrgWF3I2QdV2qzjvZSnxLPB0NSg7AngmZ0aEYr1HtOcNaDHZBJOVT6MNL0ZY\n/zNCbieE1FWiYgYAOfNZbH5yu+cb9Cc4/AK47gaPeLY13N4A9h0Qz/gtjpd5CMrPxPXmIEz+Pn72\njfaagcp2XVTShyDwb4t2jptx8eGOCLF34azIVQi8a+C4fBfHQW0cbxvEa69iUvApjuunou1bU/F5\nV8X5i2RgESZ4LeO+Mqrfc6hsS94aE8xamBxkVOsb4bivg4DfN9pkOvb7MlS81teyuMLKvz9KqC6j\njDLKKKOMahFANQ2hdCJaHRZR8euuh1/uIDCMwt0MD0IVuxOq1g0QUD6mUjP6UuDsnPku1LibEMLf\nQSWuO4LZVghL16OPuAEsBnBwC/IuWMmiK6p/myCAHYwQ+TL6fbcG/pwzz8XzLUQFclMEtDeAzjm7\nd3hULJmHCmwzBNuiVNqeCD2L4n03oMf5brjifPjsyUpL9r0H7lwTVfaPEd5HA0+FdWNetO2IuM+u\nqHLWxMWBRcWLw9CD/hqwIiq1p2Pd5gOpWFr+UYzHfpsN7BYl+KakxLFYmvBPKXELqvDTgVkpcQl6\n16eipaMWJhPrIfhdg/16L3qKOyG4Nor37BCLL6v/qYMQ2Rp4C65tB598DYOW8TYv2B52/x7qrBHP\n2RaBd7N4BqK9psf1RsZ9fYZjZUn0uTdAyL0HwXM+qt2fY2I4HMfcszhGhuJMwEoIrlXx7FMwOVsN\nPdODcLwsF/3TP86xCJOFLnGtZeP+e+JnYhVMgsZhXzZFX/ujmIheg2B9DarXL2B/zsYkc3scB03x\n8zCz2rOvBrRNiQE5awn6d0cJ1WWUUUYZ/4sotyP/j44zEYprIfB9jN7ipfDL/mSEjvmoKtdBxa4B\nKpoPIwSMQQjsjIBSF9giZ2YGUJ+NixUfRsB5CuHkFgTouujh3hFh7ChgiZSYh0rhCISqKThdPww4\nOmemR03ldxE6E/puayO87oiQcxhuYnJ1SrySEsvFTontENSax/P2i3sdi6rzQwhYZ8e1MzAJBt4N\ni+rYhN0XwC0JayKPQGCui0nHy7jobDiC4HaoYH6BCnpNTF6WQ6DfEgF/WwS/duiznQJ0SIk/wQ8W\nPxYqfjMEyncxsTjpH6wlno5K8/II/F/jQsEqtFAcGT9fjmsvGefsQaUm9u+pzDSchnaNqmp/OkZb\nPxFt2gnYBQ7+GIbcA1U1YUQjOLIV3Pgqjp0H43mH4Ng4D0F7FM587IEJ1KJoj7fiXubi2H0C1f71\ncYw1QL/10gj5vao9V9Poow3Rr98VE7nzcBHj2Tmze1QA+Qgh+D4cbz1xbP+OymLGa3FMtEUY74wL\nNr+I93wabXUQWkhOxc/RwPj3yTiuu+Nn8AmcoTgVx95W0S9XR9sOxLHyb4+ypF4ZZZTx24ufoKTe\nT1k6ryyp9+uJsCQMQRVsKixeyLYSKoe1UDGcCzyVMwelxEU4bX8oTnm/gAB6L37pj0E4WQWn3kej\ntaQ+1ofeAAGjTlx7Q4SfKQhQPXF6fvm4/sNx3scQ5jdDz/IxuLiuNnq1v0Sw2h0BtrCzfBnX6Utl\n2/RlEcBGoeL6XTzLsGiLYiVu/TjnqvG7qUBTeKEtbN6q0pJ33gd7dUBlPWHC8Ie4XrE9e3uE0Pn8\nEEKrsLZ312iDHmid+Qy95rMQwk9BWDwpZ06v1ocprtUSGJAzVSnxJFbAGF7tuGaYMGyJXuoece1r\ncXHfDehPPwgXPo5Gi818BMS20QcbA2/kzC0p8QL6qWfEjMcR0WcfxftmYDIyHLgPDr4Dboqa5w1n\nw8i/QptvcXHo4agCP4Vja4t4/sG4eLB+vLYd2lK6EluoI4g+Hu29fdzvIITpfqhm90CbyNrRT/Wi\nPT+hsvHNQwj316DV5XFMej7EcX5//Pwax9M+OF7bIrDPQ3vJeBxbB+LnqDEmil8hcO8cfb0/Avee\n8TyfRT9vEe+7CBXy5viZa4dAfUzOXMO/OUqoLqOMMn57UUJ1Gf8gAqhfpQJXIAhNQGiZgbCwEOHl\nDuywnRFW56KKtz3C+PQ4bsn4fY5zFwveCr/2LISaWQhRy6LdoT8CWD0El2URjDZBqO6HKulZCJmP\noFpYhSD4YLznLITgVbHKyL05c09KXIDAdxVW0TgUoX8cem/nxT0ORgjaEtXQjMDzFXAJzN8Duh8G\nn9a3yTb+CgbtjLaBYuOUycCCovZ0tPdqwPY5c86P+mEjTEI+Q+Xy3Jx5pdrvn0D42yY22OkPPJQz\nX8cmIqcBD+fMq9Xecy7QIGf6p8Sq6N1diP7cg3NmfvT/wQjkkxDWuuI22n9GoD4JvdTnoJVnFALf\n9TijcQMqyCPiXNfnzPCUOD2On4dj7BDgKJjWDtpvALOaeacbPg2v1kWV+FxU+qdh4tQVYfhWhNOp\n0RcX4ri7AROvY6vd7zJok2mGED6OAO5ioWtKvBO/ewDH+JB4ru0wYVgR1expqLKDSePkeF9bKrMl\nz+L47h7nGYLVcAagAn06Jnf3xDP2xM/L5LjHTjibUhM/X1viDNHX+DkqKt50iHv6HCvLLBX9+2+t\nXV2W1CujjDLKKKMMo1CiFyGsXI3wUAMhoy6C8iKEpiGomA1BZfcSopwD2iZWR/h9HeH5eVQBv0OA\nvgGtBMcibIHwUAfh52EElMcRbCbF9c9C4LwWFc/xcd/TcmZW3Pt6OF3eAaFlJkLWW0CjAOqOZ1i/\nTwAAIABJREFU6J99E20nQ9Easj3C24Cc2SRnTsO6w4Xy3RShrj1wAFyzQwWo6y6Cq9+LNrg97mWv\neP4fLCiMjWheTYmjQOU4JS7GhGAyqryNqgN1xEc45X9xgPlNwEEpsTmC29k/AupaCNBVKfEAKu8X\nxXMcCyxKib2j/4YjGD6OwHg5zkh8Q8WGsmU805KoqA7CMdKAisK8CS6iLJTxujkzNxZFTkd4vR2a\nrAx73FV5tNe2hKH1qEDsjGjr+1F1fgnBdB7OgLQDhsd5F2HSdGC00R45MyL6YgHaLiZi4nV9Suyc\nEjVwxqG4/6K6SgO02IzGxO2W6MPN477exvFQO+51OezrvpicrYTjdTwmeQmYmTML4/3344LF1eL6\nVcD7+HnbBD8/+6KP/6k434fxuzUwMXgirn1fXPsJ/s1RQnUZZZRRxr8Y5SYv/7mREo2wnu48hN7b\nccq8DdohuiBkJQSWtRDg2iAIt0HluCaC0IeoPp+KauvrVHaSq4EA0QSYlTMPIyydh0CzMsLbHQjh\n01DdnIpK3h/QHrIbKoJXxLVHpMQJqKLOQdUZnOIfixDfksp2411RDe0b19k7rtUTd7d7uloTtY/f\nfYbq97K2x5Sd4IIOlcM2H5jzKjsh9K6NSuLeuKhx7YC4xZEzLwHjUuLPqPY2xKRhMALr2wHFP3hb\nPMcxCF0HRn+siBaPqcWBKdEK1f61MEkZF+1yCqq5O6HS+3H83AW4NWeuw3HQGOibEodGu4yOthwb\nfXQPenxroM98MwTTawMgSYkm/LBG9yeYvLwFTIDrV4SusRhxUU04oA16wCfHfdfJmTdxMeo8HDtd\nEGxfAc4Mv/xkTOTewxmWXmGFKTzVf815sVr8ISZPryEQT8uZExCSa6IiH+o5jeLYTXEGZTqOu1tw\n7BWVOe6Ov7+IyeU2uDZgm3jWPinxElqVdkMf9hmYzA1G+9F3mJi0wIRvGiYvzaOvh6Ct5GhMcjvE\nsXOAtVJiaf6NUUJ1GWWUUca/GOUmL//R0Q+/E19AQJiOlogqhNmaqLo1QbiZiF/o+6B9YijCdAFf\nXyIw9MSFazujn3UmToXfjCDXLyV64/T5BwhRO6BXtzh+M4SYwQjpnREkJqOHehW0GuxBZWvoDjgl\n/jH6cPdFQKmBgPwx+rl75MzbCCh/QZB6kmo7GgaYnoKq4M4Ilrt4v6fVgUk1PbLZLLj19Xhbsfve\n+whV3dEre3j1Rk+JzphIrA28nzNHxGLJegjOT6OaXxy/ZPTNJ/Gsz8bvJwHLFuXxUmLNUOP3w4WK\nlwWY3oPwVyt+91rA5Hy0jZySM1+kxDKopN6ASuqJ0UcL4t9HA2fkzGMIktchFF6Fyuq61R5zYwTB\nIsYAHQK6F9glV7zP4v9Yhi4L93THcbcZ8G7AcWP0HH+IFpDRCNcfouf5URw3W2PCURU/T8CFkn0B\ncmZi+I/vxmRtJrBScnvwJ1HFn4VJ3SKcMbgTE54L0Wu/ABX71+K+vsEx+GnObIWJxfkIyU/hZ+Cy\n6Is5ca8JF6LuiIlRKyobHq0SP5vFdY7NmU0wIXgx7m85TBj2i3PWppJI/luihOoyyiijjDJ+05ES\ne+FiwXb45T4Dp/fnI0i0RjhYGL97FBdwNUKl8GIEgCoE5ttQXXs4jr8VFeH9sGzY1zkzEEFgMILD\nSgi+4+J6DdByci9CU1H9YwRC0Lh479UIlt+jIvshAs+7OfNIznwUZeS2RpVzq7iXEaGQj02JcxDO\nNojfL4Vl4S5JifMwUfgKQWkYKs8D4aON4IbGlZa8YCy0bB6q/27oCV+ACUlPLBtYOyVWSYk6Udv6\nagSt9YGFKbFOeJvXit8Nwin/IvpE+9+DHuXto68OAlZLiRtT4lJiy+6cuQSTgS9TojECYg/gtpw5\nOfzO2+NivOOicko9TF6exsRoN0wyvsBk5izgnFgAuT5aGB7GRGYCQl+vave8RjxjEcOBeSnRHT3P\nF8JWj8PGwyqHnNQF5m2ICu80BMsuwHM5czawKLby7o+gXezW+XKcs1isuR9QK2fG4EzGigApsQ2w\nfCQUAzDJSlTG1CWYGO6LScODwI5xngU4Bnuh2jwfgbgWKtfgzMzpOPvSPo7tFecdkjMX5sz+mBQ+\ngInXEExOi3KVTfHz1w34S0q8jSr30fG7OdE+tVDJrg+sl9Li9//iUUJ1GWWUUUYZv/VYAaH2DVQH\nv0c4WQm/sKegz7kpLuBrlDP90WtaHy0EwxBs5qEVpAP6cdfF6fhxqEBfDXQN7/BTCAyjUCH8I4LN\nn6nAygUI1IWlpA+qtE3jHucihEyP+6yHKviGKbFvAOxlcb6bUHm9F3gm1M82aDfZDBOEh5ENngbm\nhJ+6NiqU3aJtagFrwiENYWFwRJdvYd+tMUE4GmibM+NQJa9C4NsFldyz4vztgX1z5sqcqULg6oPW\nlNk5MyFnZkcbV++rCdEu32DC0iqu+R7aYqqAJ+OcoLK/BwLfl5g49A4nV3+gfkDewmqlDp/yGemA\nC/aWjL+PiHY/LSUeRNC9PtquqMVdhSp3ETV/tHvj8GjHa9FOM8l/798P6i/0kDGN4cKG0W7DqNQo\nP7LaeciZz+IcHyMc90Co70ulikutlNgyzrF3JBHLVKuW0QRV749yZp1o05fQbnE9jvn1gTYp0RLH\n3CSE68Pjeb9E+N8pkpLlUcE+AcflmpioHARslhIbpsRNmJBU4ZhcCS08n+B4r0JFelDcT914/dv4\n+874GZwTx86J3z/GvylKqC6jjDLKKOM3G7G4rQfC9PoIGMvEv5fF6e9a+KU9EBdDpZRoH0phsQBs\nn/g5Dr3W3RGo38Ep8l0RzOZS2cb5AVSHL0bF9U2Em6Ku9TmoiI9BSEkIx/cCl+bMjgiiy8S97oOA\ndRL6vjdDqH0p7uExBJ+VEZRej+vPQHX9y7jmSFzEOColtov3FKr9R8AZcOAYeK11PEeGv0yBJb5B\nuN0rzkHYMY5HgN4CLQctgJE5c1jOfFf0RRx7BtoGhlbrpu9TonWUwGuBVoyzoi8eQCX5ppw5HgHs\nPuCClOgdVTfWiTb4FhXmr6IvrgFezZn7ql3rcOz7vgh0T+XMfFRSiw14CvX9bhw7K8S/56IN5LJo\nu84p0ZrKhj1FjMPE4XsEzllAfdhnEOz3TuWwyzvAqBbRJ1OAj6tVt6i+sGPpaI/TsALMo1iW8SSE\n2AXon++FszFdwjNeRLHdePdIKtZCO9SuCLo1cUxviEnRB6gQd0WLzlhMDOthgvcBfpbeRotSX4Tr\no6jYlm6JvxeVZl7Az9reObM2FbhuDnyZM7viIsnpCNLFOL8XwX8GjtObgeVSoin/hiihuowyyijj\nv4hyceJ/bgRAhK+Vz1BlLhTJwxGmhyLUDgdG58xchOfdU2JHnC7viBDSFqtJ1KIyNb0OKqNbITjX\nQJg6OTyi5yCorotqY39UpjdAIB+LU/CLgKNy5lyEh5kAOfMIVhUZgbB5FCqru+JGK32obHt+GIL3\nNLRUbIsANjBnLoxnWRvBayJC0WkI3Nuj53c1GDEAnji50pI7T4aeA4AjcmZanGfflBYrzKvE/fWJ\nNtoUGJLSD2wdRayFSulG4Z8GS9RtjSA2AmGrUNDfwN0iJ8WxN0Z7TUHbyiK0XuyJiy9z2APaAfPC\nTw4stkT8DpXh5jirMD/GyakI7FtEn/wtZx7Ffm+OCvIyCJSXY7/vEM/64o+ecScq29nXwUoXDYCu\ncN690HqGh82sDeftggnR/LivH0S00UfAllHx5GVMTJbEBY5fI7TfG+0/H+G3erSIe6iJfuqh8Yzt\n0G7xFIJ7x7j39TB5mh190DWedyH2z2248PEQTHCGALfnzFkI0dPRR/0Njtdiq/T9i6otOTMjzv8B\nKtvPYR9+h4lCayprE8ZHOz6Bn70FmDj+4lFCdRlllFHGfxHl4sT/6OiCCtyXCCGPoYrWiMrCxGXQ\n1rEIGBPVK2qhCnxc/K4m+pQnISx1Rg/y8wjWjyMkb0rFW3peQPkIBIfH0B6xL6p+NVBd7Rv//pLK\nIGyEylwRsxCW+uHCs+tRNb0a1e+W8ZxTEYyeQrvCKUC3nLkXIGcGI8DWRVvIYXHcfghOrYEHYNPd\n4Lvmce0ZcNk3CEUNUqJrtNtQ4NLwDV8br92FQLV7/H27auBcJDm7RVs8BJwfVoIamBi0RUvBWzlz\nQiQU98R7SInlUBVfAbgjZ3ZAm8neWC+6KiXWRSA8EvgiJVaI926LO2keFH31GsL7RFT7F+BswPWo\npK8XbbYIofkWHE+nY8LzR0xs1oQfbDizNo6pTxCS28Jii8sm0HQ1SAdWuvbWevB8ewTQ6jWYi7Gw\nN6rHHaP9vkaw7gj0jMojAwnQjff8PiUuSImzUuJsTBQ2jn5ZMp6zKxXryWkIr8NwrNXEGZ3Gcc6a\nmBxeggr1B0Cd8Mavjz7241JiV0xaRuDahaUxURkS7dwrJdpVe8ax0S7XoMWn8He/jGr1TOz/XfDz\n8CaOr0+BASlRh184ym3KyyijjDLK+K3Gdjil3QohoQF6lesgpC5Ab+x0XGjXE6exGyN4TkZQfQEW\nw99S+N36AHqQD0LFtzNC0Z04bf00WjouRZXveQTY6+K876PSvCWqe52BbikxFmGkRtghlkZoaRz3\nOgXBuBHC3NEIJxvG885AIBwerx1UvUFy5q2U+DSepxeqg7/H5GE8pM+hbjXlde07YJnW6HE+EdXD\nM1CpvwPV0Sdy5tCUOA6V5LswYbgAwf7EONnvUTmvHc9RqOczELpezJnzfnS/w1KifyzAG4PAuwRw\nZHLDl72xPOLOURZvJO7AmMPTe2G0ad/o32Oj3Xuhd7shQvuraJf5OjaKqV3tNoq65m9G/x2LsxFP\noMLfGhgfFUV2juc9GhXuRAWqtwGOgjHrwIZT4I2mnvrU3rDZFVCjZiQZLYG2KS3eGrzYQfP6+F0r\nHJ9f49gbFq9dhlC6E7BCzuwNkBKXoH96P2DpnP++gkYAex0E7alx30ti8rMNWpj64zjcOvr3uGjD\nhfh5OjbutQ3OykClfN/JqPAfkhIN0PvfLdro6+jD16Pd1sKk8Qlcf/BotHGv+NkEZ5tWRp/9Lxbl\njopllFHGby+qWzn+m/8jfomdE8sdFX/5CEg4BCG5PkLkGFQR62FHfIvWgQkIJ2ugOnYkqmFzEaDf\nRw/oiqhUHoJgNgi/9O/DL/hnUHU+DpXHxxGyJuBuhx0RhpujFeV5hIJ10E9a7K63adxzYype3m8R\nyreLn+vG9XsjxDRGW8W6cf5WCEnfoTVgYbXm2Ri93dvGeeeicvk+bF4PXljTw5pPhq8/hfpfxvvn\nIBh/gWrnTKxMsj0quXUR/j5BiL05jlsi2nPzaKN2cVwrVOgXRZ98jjC2MF5rg971GpgkVP9d72ib\nb/CD1Sr6tA6C4KxokyPj/ZfFNb/F2YXCQrIbKqOzok9uiZ97oX95Mo6LFO+/LK7fCWGxSTzbTZjA\nnIgQvWm073KoxB6FkDrePv5ga1ijVaVb/jwYDq+H42oC2neGRv/9LdrxSATPb9EWczqOyQnRn5/l\nzJ0AKfEYzgi8hOPz1mj7A2Jx6uJIiTZx3kloNekT5yt2aFwZx+aO0ZcTo403wiTr6GiTZjgGeqG6\nXoV1xWekxLk5tppP7nh5VZz3CUysbo9z9Y827h79ORvHyJ7R9+OpKOvT0RbzOb9QlFBdRhll/Pbi\nv4HqNm06hu1j8UHFG3/Rv5dQ/fNFSpyCKnBXBK7eCNgbI6C1QtXvPFSJH8YFVd0RWr+JY7/C+ryF\n77UOlS3H2+ICuptD2dwXIeoztAo0Q3C4CJXry3AQbInA8jmC42Rc6LcE1pLuiCr6AJxKvxRL6N2Z\nEg1xGn4yQtOlCCIJp8pfjGsehHCzNdolHkYAHoT+4ao49iFUJt+AwZ2g50Ysto6uewC83hAV0lOx\ngskjOIhXQdWwd9zvLIS8M9BOsUdcf1e0XcxHD/l6qETWAnaOEnfrohI6MJ5nfYT3jxAyQfvBOXFv\nNdE7vjbOImyNVphR6B8+BGG0KargK8Vz14lnbhZ9Mg2BrVYcVw9Ly9VAaG6PAL5C9E1XrMdcWCPW\nxtmIKhxPwxH0UrXjp0V7NUNAfCleXwB7LQN3t/fx2s+DEaOh/r3xvBtgAjaQShyI4/GF+Pem0Qcf\nYYKwDc4SzI772SjuYyxC8oK432Imoln0R9u474UIzCujgv8GlTKCLePPvDhuMiZvjXB2YGS0/2bx\nzEtUuxfi3gbi2J8d51wDE40lcNaiUbRp9+iPonTeXfjZej7arl7c85LAsznTh18oSqguo4wyfnvx\n30D1v1OdLqH6l4mY+t8Bv4BnoiK8CgLv8mgFuR09sa0QLNugqjgQwWIiQmJjhOLlEDJ2RltDbwTF\nEajivoHAfQXaNmYAR+bM6ymxU5zvQoS10ajufU5lI5blEVomALvnzJfhWe4DvJIzg+LZ2iGcjcVq\nCmPj9TNQHa2LyuKtCKKz4prTUZXeHGHySFRBV4UFu8J698A7hQf6OVgwGGpeGc/xNkLUHphsLJ8z\nB6TEXWiF+RYXa94O7JAzV6bE7Tg78DEmFBdEG88B3ola3qREWwTv7tGGrwEPFzsWxjEHAy/nzGcp\nsSmCbheEsD/Edt2kxBJoNWiNVoTBmMCsg/aHXbCixxaokt6FlpI3EPZfQHisi2rxIIS7OtGnf4v+\nmYA2ixnRvrNxFuHsnHk6ZkoG4XbdRyE47hTXHQjsAB+OgU1ugCnx/8DpU+GcZmFdOR+YmDN/iueq\ngWNmtZyZlBIHIki3RTDeB5XkHVDFBSuGXI7J4ok4/hthEtEp3vshqtQt45gh8RxLOAbohEnm2bjR\nzCX4WZkd5xmJCdOz0Wb14l5+h+OtJs7SFH7pexG6+2MyUjt+bobjoibOHDyEMwFLYxWWP+LYao8J\n055xbMbyjtV3tPzZolyoWEYZZZRRxm8qUmIgAsZIXFT1BSp/LXAKvFhvNBCnz99Btfp7VIe/QJho\nh7CxFaqQPRCiDkIAuwchpChpdyBC81AE+RrAzbFZyfEIPF0QXjajAtAvIOzMQkV4DPBASlyB4Jvj\nNUKpPgqhuEYB1BHd0I5yYVzvOJy+fwjB5wFUWWshqDyB8DQZ7r6iGlAvhNVOgZo14j7fiz+DcuY1\nVHnbpcTWqJx2iSobg1CZbpMSLdAG0gftAadGn9yIoDsvniehwl0zXhuaMw9WB+qIu4C9wlu9SfTR\ngniukXGubqhYv4og2B796HtGP7+Biukm0aZro8rdKfphGiZPA3LmTCzHdyaVDUyez5nLc+YOHDvf\nxj3PyJnzMVnpnxLXR38SzzwJQbRrtMlIYDasugf0G1l5xMsawweXRZt0x1mBIo7HcbZmShyCwP1X\n7O+aWD/7IZxhKdr8bATWaZgM7YVjuAuOzRtzXrzBzuMI2U3j/mrgeARhtwEmRF/EMe2jTfZDC1VR\nO3t/nKnYGsfehjhzcGPOHBXjpz6q5N3Q1nInjsWNop3Wiv55PF5vjsr4N3GP3XA8DkOQv55fKEqo\nLqOMMsoo4zcTAXMZrRGF97Xw2l6HU87NUVHbACtlbIFezXnAWlFWrwnC680ISGNw+vl9VKpnx7kn\nospalCG7EYG6JULcUITt2qiuTgK+iY1LvkHYWR6B56E4R2ERqYrzrA0clBLXxvmvjGs8nBL7x3Nv\nizvr3R51mZ9DeOqCFpebEVZOR0A6EVX5h2DGK3B6p0orrvMiDO0d97AL+rTvJ5gi6k3vgPBeF2id\nErWjXNoUBKnr0ct7fVxvC1R5G0VfzA/1/nKcxj842rtXSmwcz1QzJVoFLK+DMHUjguHhCH0dgYtS\n4nFMiIajurkrAvZ7qGxOQSvJGFzcOBfomzNXxGtDgPE5Myb6H6xF3QnH0ZLR10WsGD9HEyXscmZm\ntNlEXIi3CoL/KQikLbPbni8Z994ETnwElo6qHXNqwLZdUTnPmDAUMxObolp7DDA2yv0VfXE4VnJJ\n8ewjcdFgH0zKlqZi1bgWF2xekjOvRpIyIvpsPgJyC7R4zMUEaAOsPLMLAvU78fvGCPNLxO87RN98\niKr8B3GOoThBeHZya/l+8Ywv4gzMkLjOCXHfp+HYLNY/HI/jLGPi2zKeZ0i81jtmKH72KKG6jDLK\nKIOyHvVvKFbD774uqKIWNYJBhbIHVhv4CoFnQ1Ti6mI1i8NSojf6gV9Bj/OuCBM18Qv9bvxS3xxV\n60/RCnIiqpdPI3gcidPeT8T5xyOIXJgSr8U9volwPhsh+joEhbNwuhsEi0lxnYfivOuiEtgg4PRk\nVASLuB8hdmGc+xhU409CtfFGLLG2Omw+F74J9b7hfHiiGwLcIKB/QOamcT0A4rX+mGA8AFweivwi\nXITWMK67H4LuS9Hu/dEecDZ6nacgZJ6FILYscFZKXIfq9s4I03Wi/WsAl+dM36iL/CSxwU7O9MaE\nY9V4zl2obC1/CYLnULSGfFsNnifwj+seP4/jYGHc44Rqv9sVd2q8FrdmT9EuxQY3zeN+52DiVBch\nHxxLvYBHYImv4MqvK6cdsw3c1wb7vE6c90RUZX+Ploqnqt9kzkxGxfotVPTbo1I8B0F6OoJ3jWiH\n56o9y97xngsxCVoNPxdT0CP9En5uDsck8Xa0LI1G6F1IZdHrZEzctsMkbgLWEt83zvGnnDkFk8l3\ncZwvCmvLc8AWMeMxFj+fN2LSdDGVhaRLUVGt98ZE4sa45s8eJVSXUUYZZVDWo/4tRNTN3Q4Vwktx\nOnkYqoRvomLXGJXLBqjYXYfgNxlBrCkCxvfA1NjspBFOVy+FsNIXv+C/Q4vFYITojqgg74aq6PJU\nlLxj4z2z4j7OQ+DoGrf/EAL+6Ljf/ggirahUwXgkZx5GCBqKFpCGCJJ1gZYF3KEFYvW47oh47rHo\nr62P3tZP4OM58P5+lVY8dy60mIWJwA1Yqu5SVPhnpESHak3+GSrwt0abfxjX6YZgNwyTjDFowTgN\nPewrxTM8iAB3UM6cGVaLVzBZmQXcmTN/jrbZIfroA7TaEN7qHvGeT+Ke+uGizOsRvE6I+txtECj7\nR58NqfYcE+KefvCfQ86Mwj5dhONiYly3GXqGi1KBw+OZiXJxV2ASNAzhtDdaMPaO41tggnMzUBd2\nmAh1n6xc+ZStoOpV7Lt9cSx1j/a+F8F1cUS95hU9Fzthv7+YMydgItEcfdPjUCFeHlgpFPDJmLg0\nQf/9Ogi0i6Itj4fF1TXOReW5BVqWilrm+8R7GuNnZz0c4/1wEeVt2N9Hx1qHItGdGX8aIrQ/EnXF\n940/R2Cy8AyO2YPinKvGfb6K6voeUKmH/nNGCdVllFFGGWX8VuIOtBm8jF/GlyFYz0PFrQrV25b4\nJdwKWJQzLyMwfI9w9Se0auyZEhchJFyMALwfKphPohVk+fDYHo+KWTG9PxzV5MNx+n89BIGhCBg1\n0BayEAFlW4SShnFfl2OCUAMh5GHg4JTYHqF9WJyrqLM8l8qmM+egDaE2QM6cg2plX4T/pdGy8hEc\nuCrMj5rM3TIceh0CYWcEmNq4QHM8Qv6LKfFGSryNavhrCJuF3/U+VA8LALsL4X9GPNOD8e+qnPkE\naPwjX/hQBMhT0J/cEpOGBmgPuQl3uzwl+uh+VMYPTu6YWAOtAxfnzOk5MyclesV1rkNrxExg3ZSo\nnRKNEHx/vAthEUWN6ibAhADYc4CXcmZBHPM08LuUaI/gXoUzB29gv89B//1OYX/YHWcLpmLC9TE8\n9DLUDqj/qi0c3CLudW9MKF7PmWdR0d2yuLnkNukDcezcFX3QHz8HYLKzBMJ0h3ieW/GzcUC8pz8m\nUYsQXntiMvEGJoxL4CLTQzE5mY0zC63jHEvhmH8Hk8KiZOPeCORdc2Z4jMNvccblYkwOEhWP95WY\n8HwS6vtzVDzUCzG5KCrA1ELVfDomvZ1TovE/7sKfLkqoLqOMMsoo47cSBSxvhiCwP4LCMaiQjkJo\nqI1f+uNwiv18VEZXwCn7DRAcpiKwjsEv8ady5ikEzEaoJB4Ni6f9X0DAqY3APADV293Qy/oyld3q\nnkcQr4ULIRuhmr4uAvsa6Ae+ClXOonJEH1Q+56EP+XmE0P1QrbwAwWMmwvODKXExQv6qqLjWBXaE\nVy+E11evNN+5H8MS2yIk3RT39RTC3UHx2gSs5VzA9ziEn9EIe6ejAlsLldVjqFTG6IFgXQ/YPiVW\nifdVjxeAzXNmPoL1i9E2+4ZneTrC/oNYkeSrnBmPyvgxmJzsUa2yyCrAhjlzXXJb9QnIRk9j8rQF\nFZX7H8UHmFQU9o+z4nlfLw4IAFwRx8Nrcc9fU1HR56Iv/kOcQdmGys6FUfd52+aww/uVy96/B0ze\nKNp+fUwUyJnZQL2UWCklLsck8ZScOSRnLkKIPRA3j9k52uNQTOgGImR3i2fZAvvxfBxj9xOJJqrL\njTHhGI7q9um4qLEt+p8b4ni6Fr3RfTApugOtQ6cgyHdOib0jIamRMw/Ee57HMfkX/GwuRMB+Lp61\nWEi8BSZVLdDi8hEmKoXXei6OzSb/pA9/svjZoTqltFVK6dOU0oiU0kn/5JhNUkpDU0ofpZReqvZ6\nk5TSgymlT1JKw1NK61T73VHx+rCU0kU/93OUUUYZ/5lR+qh/G5ESmyAMFxUL5iIUTEQIbYvq4FCE\n3qWq/b0BfrFPQ1jtgdPKd6DSPQ0hcVRKXIig0CFnJgLjUmLzuObu6Lc+CuFjEVou6iA8zENfbUdg\no6hw8TLaSHoj8MyP9w6Ocz6CgLIHemq7YmJwHMLlkQjU+yBovIDw0wshrgYqg0fiFP1Qj1vYBPq1\nqLRgvadgh4fiWTdDBfJB9Euvgh7oUaiYP5gzt8S5zkB7yd4IRPVw0eVR6PEejDaBngjUx2HSMA+B\n7mGqRc5MBZqEz3YAqp8zgFopsQcmKOdGfy4LfJUSa8bz1sfNRj4GSIml0H5zbpz+CExbOmRoAAAg\nAElEQVRSvo1/Hxt9tlK0e03+Pl5CIG4U134KVfyXiwOS29E3j2fpkDNPYsJTKPTjUMlfGu0Y47GC\nymk41qYDE+HqodAyqp7MaQYnrIzj6RP0+tdJid0widofgXzTnHmj2v3eGufbMO77ZQT86dHmjyJc\nb4yA2g398n+gsghxWrz/YCr1wrdDkP4Oq+JsRmXTnEuBFcIadCYC+y6YiH2PULxntE/hH18SE6q3\nUSX/CsfD9LhOsUCzUM7fwORscwTyBfh5HoGwfSxwTZRn/NniZ4XqlFIxzdIbO2b3lNIKPzqmCU7D\nbZtzXhm9O0VcCTyVc14RB8kn8Z5NCF9cznkVnKYoo4wyyvhfROmj/o3EeQivo9GDmRGSaqKCOgaV\n4L7oj16AYHYHAvOJ+CXdBJW5Zlit4WuEyblAo5z5Iyq0TVLiMlQyTw8VdHVU1p5AcPwO7QAXonq4\nVpz3eOCU2Mku4YKv7+J+dkbI7xF/vyjedyZC3VRUWWchAH2Iamax8+KLOC1/XiiXn6CK+yKCVF2g\nOdzVEt6ra9PVXAgDR2JS8gYC0wWoqBabbFybM2/Fc20dbV4DIXrDaP/hqKRvTUXhHY0gtzFaB8ah\n6lnUki7OVT1mI0xW5cwfUIUcDEyI0nWPUtmtcFtkhJujn4p61U1wseUpObMoAK12zoymUu1iQdzz\nm6jktv/xjeRsXxML5MKfvWTOTIl8/bjow9MQ3i+JBK/wMXeMNvgaeelIBMfhOXMSQufmwHxotSEc\n92Hl6rd3hnbjEHKXwlrQI1Fh7wH0y3lxElnEROSnZ7HvmuN4vRkXYy4Vzz8cE6d6cfyW8VoH7NcZ\nmAB1QTV8DI7ROfh5mR3tO5RKpZcTEYKvwbH4GsJ1c0z6WgBTUuJP0f7TMGl9NRKDaZjkdEqJwXGe\notZ4Q0yc5uBYbhjP+EHc17b4OTn6x334U8bPrVSvDYzMOY/OOVdho/54Z5s9gL/mnMcC5JzD6J8a\nAz1zzrfG6wtyzkXx7sOAi3LOC6q/p4wyyiijjDL+SSyNU9UzEQRGUVlg2DJ+jsQv5e+obM99B5Vq\nB6ciCM1ARXKfAIAVcap6ywCmuqjifY7fe/Xi3OshnNyPAPkZAsBpVHaH2xGn1tujz3bZeH0nhISN\n0Oe6EAHlSeCaqHTxMirXbVAhfhYtGlXARbH99BUIro+mxHkIL1tgLeAzgA1g+gw4oqh8AfR+FTaa\nFe22ESrgdVEpfina4/GU2AA3cukWCyILS8AsBKZ3MGFoh2pjjue+Df3nv0dlcm0EvquAI1JavPkN\noXaujSB2ZHK3xf1xEel6ADmzKJ559+jXx1H9PQm91XXQ0nBGtQofR1KpvlFUcNkZ7QiD0NaxYbVZ\nh+rRGGiSM3enRF0sB7gEJkyv5MxDyDrDEaK3iH6bEn04h8ouixPjngtVfBwmTi1sk/5/gdXDq72w\nFiz/QrzvJLRTHIXw+EaUZVwcUTf8QLR7jMJkaIWcmR/JwWwqfbYeFSvNJEwE+8R7HsKx/QV6n1fH\nftw+XhuHsycbYiLRM147G5OrEfF8s3CM9kGA/yCe5bjog/PjfQ1TYn0E9IPjGk/gQsSamCx3jza6\nBsfWO/iZmR5/Bkd771ltse5PHv8tVKeUNkgpPRf2jS9TSl+llL78F8/fHqc0ihjD32d6XYBmKaWX\nUkpvp5SK1a/LAhNTSremlN5LKd2YUqpX7T0bpZTeiPet+S/eTxlllFFGGb+xSIljEHzeQTVrGVRB\np6HquxxWa+iLX8y1UAHbFTgmZ/rlzIuo+tZGX+mzOH2/Onqt18Av7bMRxvZCy8OZcXwttBC0i9eH\nIzRfhoD4HO4IuHvOrI+A/H2c9zv0Kb+PicBMXOD4DaqSa0Zlkx1RobwWmJUzd6KyPBn4a0qsljPf\nx4KwB+J+X0CQugq9uW/CeS1gVlRLaLEAbiu+x2tgdYkxCEc94rkujNcvQpCsiaDcNdro4lDFC0V+\ncLTLi6HsP4lWmHm4mLMqjr0blcyHwtqwIULjOASsfghTx+bMS8CrKdEvJU5GOC3AbUHO3B0LHhsh\nCF4eIElKrA58kTMz4jlrx/nWpgK378d1W6fEGQHPxW6PzaKNQc/7Z2hluTJn3k6JfTDpmonAeBZa\nKSbHfbaM5++DVopRWIKwfpxzHI6RN6D2SXBVNVh+tQOs/LewxXTC5CEB4wurQ0rUioWbjWNx5puo\nSh8IbFYNMgeiQ+AwLGk3EtcazMZx2yju/aJ45l6YwO2GyVVHTGCa5MzpmJS2jDbshbaPm1HBvgo9\n7vNjg5lG+NnqTqXcZWHHOgQdDSviTpr9kBEbImRPi35ujkr0tfhZXxMBfgqy59Ro58P4maLWf38I\nN6MX5V34ux2Mfqp76IHTSQ2A11NKr1d7/Yic8zsppStwOujM+F3TnPO6KaW18D+HTv/o5KVXsowy\nyvivI/2K/17G/zUCGE5CSB1PZYOOj9HOMAmV5Lr4xVsPQaFmHH9kSpX6y/hlvjDO2SjONxah6wME\ngM8RpMchGIxGzzQI6mcifPRFW8EH6NstSpMR91UbAXYhgshdsHjzmh6oOP4NPdFXooq8czzDnCjf\nNilnzgsgvSolXkTwfznuYRECyVE5MyilIZfAlQ0rt3H2JGjZCcH7tZwZAAxI7ua4EYLhZdFW5yPo\nrovAf0TOvFLtmVrGvY5A9f949Nv+BTggZ84K9fy9aNvL4j4vjdeux+//G+PPH3Lmo2rnn4UzAc+h\nxec4flj/GQKSc+YrWDw+9o1jfxx34qJOop1SqNHLIvTegmB6MiYVYGKT0Ls9KxZCtsIE6jD0m1dF\n2b3JaL/ZEPt7PI6VneLYS1Fl/RbHaitgPmz4CmyxEjy3tJccfn5K87pA3VE5c3L09Xa42PNxnGG5\nFhgZCnpNnNHYEcfuVclNbDpFu0/AxKBO/L0hJgkno7d6JPbxBJx1WQ6tQCPj91UpLa4Bvme0S6fo\ns3dR1f5LtNPqKTEvnu9FTOyeQSB/CWcvVsHxtClaP0bE8SNxDLeLZ6qFNppL8fPWJt67dNxLRrDu\nF+3xk8e/AtXTcs5P/y/PPxYVgSKWiteqxxhgYs55LjA3pfQKZiqDgW9yzu/EccU+78V7HgbIOb+d\nUlqUUmqec570v7zPMsooo4wy/jOjLqqxC1EhLureFspZLQS3uvgFvSICzoj4uWTOHFScLKViGp7H\n0TJQlB37JGeuT4ndERi7IYgV9o2aCIWX4zbXnwNvBkR2iGvtlxLPo6q+HFpM5iJsdUR1cQtU5hbF\nPQxBKJwXxx+KoPY1Wj8GAuTM4CgddzGCTZ34uSmq3RNd/Ne/D8yPzK7LVGixNKqEnYG1UuKvCK0f\nIMycjJDePNrheyo+7T1TYkbODI02OByVxHPi+i+kxG45c19K1E9usT4rnqlLtNlIhPW66Mm9G/23\ndwNLB5DVj36YjFaa3XFB3kwU6zYOJX8rtKoslxK7ImitE8ftFsfURNA7JNp8qVB5FwDtU+KPccxk\n5JAR0f6tU+IetE3cAZwQNpNe0QcvYJnDw5O7FK6Oyv9YTKi6xN/fQm46PO7vMATkpWMsfAM0hOun\nwkrtYF5NoDucuxOc91xKdI+2bhnttA9aMXbGz0D1P7thsrQaQvTTmCRMR7/zDlRsTLOpbPhyX/x9\nMI7bZjgem0RfFf75hTjGHsBkcCSC8sMI382jvz/CxOGeeM92cY0GmFhdDGyQMzm5m+a56KMvPP7r\n41h8nYrN5484q1EX4f37OOfvgJVTola1koc/WfwrUP1SSulSbIR5xYs55/f+hfe+DSyfUuqADbYb\nDvbq8RhwdUqpJj78OsCAnPN3KaVvUkpdcs4jcGB+HO95lFhZmlLqAtT+Z0Cdc7kAqYwyyqhESukH\nyxIr/0rwq/t7GT9RLERQGI0wNw2Vs3H4ZfwWKs4DECT+giJQP+DDlDgIuDm8ul8iBPVAW8ZOCKUn\nhDJcF/2eTyA4PYhq9aOoAm4I3JoSqyGctUFgex6h5I64z4mYBFShcrcdwuYUFJ42Q1BpEPe6DMJG\nDQSoVvid/URKbEdlK/ZVEdCK0oED0aqyCzzVAt5a7F+Gy96D7U7FJKQ1gnpVHL9EXPevcR9NUQUc\ng6DTH60r94ca/GE87wk4uDco3pcSWyDY3o/cUPjOt0UF+G6Ezs1R6f80nmEznCFYCxOM76kkHy0Q\n6Foi66wW9/4sqt6bIsT1QTtDddhcFWcA+qJPeWOsPNETYX0SKts7RH8fGH04BBiWMxfGM18a/dYX\nOCdnXojyjOfE+5thEvAaQu2cnDkhJTrH8w6L5++LYPsKKsx/gE4ZdpgE921iX125Omx9Ts7rPxOV\nUY7FMf5SXDunRL14lo1xHLZANiugtyOVihvtcAy3RFjdHYH6Iqz/fC1+BmbiJkA3RJuNQ+vRcIDk\nZi0DELbvB/bMmTNS0m+OScONWCZxQUqsh0D8Po7fvYDRUZISHMe34Gf4MEw+p+Hnewx+Fo/Fz8H3\nCPsvobL+/9g773Ctiqtv30OV3kFBpdiwI1iwd7GXxK6xREWNXTF2REUFS+wm9h67kVgRG3bsDRGQ\nYqFIk6Z05vvjXvs8R5P4kkjeN9eXva7rXJzyPHvPrJmHfa/frFmzFwawCzFouZalbEuyUXEjzEu5\nBCPsK1nCahs550UYyT+HUcsDOedhKaWjU0o94zWf438YH+MH8eaccwHPJwL3pZQ+xP9ELonf3w50\nSil9gh+KQ5akPaWVVtp/p5VHkP9X224ISbvjM69tfBXVNBpgGsPGuPFpOuZIb445nxPxGfNm8mjs\nrRHa6uHD/FR8QC8bXzMQ/PZCGBqNyvM6+MB/D6pyQtvFeyYg6LTHjVYj8IHfGsF1K0xh2AI3tQ1E\nVfFVhMtmCHsrYEDwR4S2SdHO2xDaGiBM/wEB/nvMG/4IFraFY6rV8d1iBOz2XGyAHIeK9Pic2R/V\ny8b4zB6FK8mHxetWjr68j8/94nCS9agcoDIAwWw+KodTwjefoso5AVMvXidqhcf9doo+P4pq5OoI\nyy/hYSuP4grBdCyPtzDatj7mSZ+dM2/lzJPhxy1wA+ewnBmRM6PilMSZOTM+/P8Crmi0i76ugoHU\nsFDg38d5tZjKHAJB+/Fo36KceSF+/z7CaIP4/SKcA6OAxgGbi6kAbNfoX3MEyrfCjxPhttWgdqQm\nza4Hp56YEjfgXHgB528z4LGA+TMxTaM7qsxrY5D25+jfWqjAN0Nl+i4E7VVwbu6YPSZ8U5w361Op\n0DIb5962/Ng2RCi/AEH865TYICD5FfzsjAOOSNbV3hAD0UEIyS1wZWHdlGiGQdDDGGDdh/OiAQZq\njeM9M8LvRVv7YwD5Js65yVROr1yq9j8q1TnnrX/JDXLOz1I5ZrX43U0/+fkK/g6o55w/4ifHbcbv\nF/BvckhppZX2/59VjiCHUgH+r7Mf8CHaHifBFGBGzqwd+cXNsWRabYTXjIpsI9wsNxmfYUVawToI\no6ej8LMjKmvrIigPQ8D4DNMC1kfwXhaB81FU0tZAkWpvKlVIDs6ZryIndmMEhA9RUNoLIfHXCE1D\nEa5Px1zUDVHZLI5+XimuPxfhY368/1pUIG+O179nvy6fA19HumadhdDvPqBBKOqjc+avKXFG5Mr2\nQChbE+F0n1BCB4efGiEMrodAswAh+QVU0TdGuO+Oz/6rwocPha9SvO746MNRwIo5MyMlVkOFuoCr\nS2PsdkvWCF893tcON9WdGe3oyo/tYeCynLmq+i9D5V0cP9YM9fRPmLP+cdz3q5y5NlKB+qBCWwN5\npUcshtXDubZ/BCaFPYdpCfWAb6OqRT1cye+XM3elxAU4D68I380N/20VPp8I7Aj158CCs1ABBt7u\nAYMfgC3nhE/fR8X7zvBnfQTYQ3Lm60hPeQ/naSuc1x1wjl2CEFykT3WJHPGV8PNxNAZqTTE4eQHT\nMIrDYQpbOdo+BgF6ZWDtlHgfVwWGY6DaGPOvz8Q5VJTjWw/n+Wa4aXUfXJF5DT87t+Nn7LPwz8mY\nrnQupgtthKxbE0H7PYTubvwbbEmqfzRJKf0hpfRufF0ZtaVLK6200kor7T/Wkkc0X4/AORAf4I0x\nf7Y5qoNtEIb/hGmOMzDvtiHCwCIE5aMQRBsgSNwS1xyCSvZ3mJawMsLAVcDVcfLf7Qi5r6OStyPC\n32VU1SBmJEI0Uev4w2jX/JyZkTN3oqI4DJXwTTDl4UME7CcQJjphykKPuHahGj+P8Hk4gkvOmUNz\n5lo48tdw2UoVzx09Fja+PvrYH7g3JfaO9++JgcoChJoxCJbkzORoU0ME5A8R8Fui4tyFCtBsiOr7\nBnGdeQhyJ6JaelP4uyWuMjyREq2JimGYBz8O2DZOLHwPFdaijN4RqBY3xVWJ4ljuwvYEhkbKTnWr\nXskjR7/m4IrDChgIXBd50eeFr+chkH4X/b4h+n4cKu9VFhVGGuH4rYeK+zPRxi9TojbOuVVwfi4f\n18g4347BOTYTmAOzXoJlhsTVa8JxG2Lu8MHRpuVwvjQFvsiZnjlXVWVrgePXA1cDFmCufD+c57Wh\nqhzg2HjPoRggPoVBxgqYPrVcvK4mzufCUs7kyF/+DHPCF2L5xm44tgfjHL0CeC/KHGaE5F7hq1k4\nJx6NNh+F6TVXIFTfhbD/JW4EThgADcWxbhh+Lspntvo7Y/+LbUnSP27HzuwbXzMxSi6ttNJKK620\n/2Q7HB+mL6Di1hLV2fkIgrfG98MQNIchkKyPz77RCDYH4MP/GSonEP4RIbA48KIRgnM/BOqMgAVC\nV1NU0dqigjYiXn8Dqt/bUqkQQs4MQpV802r9eTr6MT7+/RNCafu4x74IkwtRDd4cIXtotP+BaMNa\nwKQAOOC2XjA9Vq7bLYJ+jalUBVkRoW5i9H8uQs6xAWe/BbqkxLkpUTPSHOqhovpG+OevqH6Oj1rZ\n+2J6yma4CrAlwlZR8WQtTBFZETg1ZwZjwPEigvjhVI6c3zUCpJuAM3Lmg+wx16/GmDyEMHdXSuwU\n5eVWRQC+PvxV3VqHb+pFXwt7F1XSlxHQ9422zUSYXxx9PQGDposRRKtU25RoF+X+1qMyH94PP89G\nJbk1wuR5CIPf5MxoZK+OCPxDMEVpHjS8HwZW24wxdBWoWRcDmGJzY1ucr4+nRK9qfWqJ8+7D8PVM\nnDsNcDWlBwaWK2Ed8tao/D4dB/0sizB+AKrBMxGUG6ZE7ag0Mq/a/S7BPPnmCOdPAc/mzHsxXt2I\nwDL6NyBnRiLsbxk+ujl8PBaD14Xx1ST62hQhP0f710VVvQaVfQB/wc/9Ul+2XBKoXinnfH7OeXR8\nXcA/KF9XWmmllfafYmUe9X+3JU8jPBgB+Hsqm+1OwaXhFzGl4k6ExBURjkajCro1PnhfxWX8rxAA\nx1J16iBDUKFriZvr6mLqwQMIWN2jOUdjTum+CO7FKcG1UGF+E2FtrZS4MiX2iEoUn+Hx28UG/8/j\nvrUQMJYBRubMCQi8u0Wb6iDoD0NIOx2h805U60ej6n1pSveehJASdsJzUL/YOPkKKoGj4j07Yp7q\nWARAIjf2PtxId3VKtEC1cz6C9ZY5cz6C1xEpcS0eqDI08rO3wQBgT4T/OQjMizBN5cSUeBPh7AtU\nLqfFuBS+fAorqgyBqhSObYBLcuaBnDkVofJEDKbuifEcByybKvWgCX9NQkV8eFyvFqYu3BI+WD5n\nLoh8aBASW2NQ8A3mMh+K8+jqlNgvJfojlN+CKusymId+K8LpD7iKcgkGFBMQLIuShJ0wwKqBgUdd\nVP2bwhY7x3XC2twHP+yP0LltjOX08PH31cD66GjH+nGtQRi43Y9K8lxMta2JaSt3A9fmzJspsU2M\n0dRQ3++hcshRUWJvXQR2knW9t8Y5cXH8vid+VkAofhY4KQKa9pZ4pDZ+Lon+749Q/DHmmj+K0N0b\ng4hNMTgdjmkxs/DzMhWV/sm4IvU9lX16S82WBKrnpJQ2K35IKW2Kk7600kor7T/WKnnUZQWg/1Kr\nj8+47xB618F0gI7x84a4dJ9x414rXHJfgAA5AyH8AYTqaQgCFyNA7I+5pAsQzoojxM+P9z2GpwE2\nA+rnzPO40W5FBNMT4nWHRxsW58y9VKCxyA+eDNRLiT0CYBsi5BQn472REh0QkO6noi5/HX1sGO38\nCKtO3Ao8nzOf5EwvOG0/qvZXrT4BTl8tXlsDQW8d3Ih2EsLZiginp1fz9aMIZueiwtoq7rVN9IWc\nmZozO4VfB0QuMQhi3yCoHxb9n4VBRgtU219H0J2BAD443rsBwmUtVCcLOxv4qFqaA3iS5BeYM3xF\n+PVMBLbropwfCMeTMee9KJpwHgJnkSLzMj+25vG39zFAezrauimqqHtgje+r48CZmQjGzeN1M+Ln\n34YvR2LazctYa/oJDOg+xvl1PgYFa+NcWhb+8ggsE2kXE5pCx+E5c23O/IBj+TLmq/+AhwU9hOD7\nPc6nvaJd66PaOxtXRNZFtb0n8G3OPJUS7TCITFgWcXkcn/445mNRjT8L+CB5+E1fnD83Y+3pT3Ds\ntg+I7oorOFPDf7OThzY9i+O7LgJ+fRz/ZzG9KeEqyjtUTvesjYHlPATwmdGXi1CF3xEDuO0jYFpq\ntiRQfSxwQ0ppbErpS1wuOWZpNqK00korrbTSlrJdh2pVOyrl1HZDpXoF4LookQfC9GeoLNdBmF2B\nSjWBmaiKfoEg8gwC0cX40N4QYXMRphsMzJlb43fnArfGsv+3qPYth8rhX1G5ax/tI/JPX82Z3yOQ\ndoi2rJsSB0X7RgVgz0cF+GB8nu9NJZ1lW1R6F2Gawd4INYuBbinRJ6UtDodJG+uChJmdNWZi0FCU\nmdsIhbRVEVZmx8mEX6TE5tHmRQhJHTFHuAOCy4fA6gFdxGvPQ3A8MCUeD3/egIB0DwLodwiYX+fM\nlsI/vVFtn46AdDGmtHREwOybEi1SoicqtNWBmkjTKA766Zgzr+fMBahAJ+C02Oi4C8LYKtHHnpiv\nvTsGSlfwtwfFNMVA4huEvp1QjX40Z07NmQOxmmffyOPdLO75CALmCxi8vIVBwwkIrY9jUHRTtHMx\nQuGVVOqofw0MgD13hEPfqjRpUq+UUqv4YQiwYc4sypm7MJVlZ4TpBsAxOfMZlZJ6q2Pe9hyommdd\ngfNjc+PZuPLSIPqwY4zZMrjq0hqV9rq4ijAtZ07PmeH4ufw1QverCNsD47UXUDkoaRbC+T0YmNxO\nHPaSM0/nzOfRvuE43q3xs1TMteVwRaQPQvl0DH5fi/HrBrRe2rWq/0eozjl/mHNeFzu5ds55vajK\nUVpppZX2H2Vlykdp1aw9gm8BUusj+LyCULFnVFnYGoHuAQTHI3Ep+mZUkTdFmFwGl8OnIdysGNd6\nHx/kT+DDegXg7JS4Ezci7o0Q8hgqhTsjOOyHatvOqMZ2/jt9qEGkEKByeBkCRq2U+F204RPcEDca\ng4I7ECIOifYdgPDTFwG5nv2Z9BYM61+51Xafwkb3IvgfjEr8Jwg24xH6ixP4wINefh0qI5hOcmD0\n4+bw6WhUBG/4Sb/uwtWCKQiP62IwshXCz3eolh+ZEm0BcmZezlUHkkzE6h0NMZ2iG0LUZ+HXZlRy\nc6vbbExl+TQljozrZqLKS/bI9JkIujsgQK+IOdRPYLDyFLBaSjSFqlSTbRHEz0DAuz9n+uVcaUPO\nPI7VNC6lEjh0Cj+dguDaHZXjabjq0AUV4NcQUpfDcXwLU0SaI/wvBurDTdsjeIJz+KL4fhCqsm1S\n4jlcEVgFg56uwBqh2N4R/dga597QaOM8PARpLM7lqzDv/XOE344xbk1j3MZhakULhO5eKfFwSlyI\nqxz1EeCvxDnTHjg7Z3pjgHQUBhdbhv8n4DzugekrxSrHGtHGmbia0AjneIcY6zcjr/vL8Mfa0c7Z\n8buasQF3qdk/hOqU0sHx76kppVPxP5ojq/1cWmmllfYfZWXKR2kAsRFtGj7s10HV9WoExLPi31sj\n1/cbKhA4M16/IsLZYfgAXgHBeToV2K6FS+kHxL2mI4A8g+D3OOYwN0TIGxPK+BiE+oOAIaGU3Qt0\nTelvNs01REhbLtrUDUFlJwS4hQiYewHLBCC2Q4ColTODojLGFagCtkRgvgX694UpoWTWnQt3LMJ0\nlNvjfm3j2ldRUQ0bAjOjlvKymDZzGkDOLEBg3QkB/CnMtf4OlfHVY2waxfuepZJe8ydUO9fEQGAQ\nptJ8CDydErsXDsmZeQiVPZFLJiDs3osgmnHz4SkpMSglLogNgg2pHPH+HDA3JX4V1xwJrBgANi1n\n+mOqRVtchfgBgb9Z5A9/hMfXr4UqaxMqm+n6xb9/Y1H7+jyEwyYIqOtjUDQw+rIJAl8HVGnfxlzo\nXXEOXoWq9SoIuy3j51GQT4cap1S7Zc+UUheoAv/Hol9H51yVs31BXOsKnL9tcPwX4arImPjdiJTY\nB4PI8biSMA0hedP4+aT4uSWV4OupnNkKgb02jv3NQMNQrreLcbsu/N8F5/z4+NssBPijoirILcDe\nsTl1Vwx2iPb+GQPI7fBz2BBB+k1cUVoVg4j5uFryNQY4S81+TqkuSo00+jtfDf/Rm0orrbTSSivt\n/9hWiq8a+AAt0i3ODPAcAaycEiuiStwMAfhQfMa9gAemZMzv7ISbDNfCjYhN42/9UInLuBTdGHOJ\nz0RwehThuj3mEV+EKSS7olpXpJ9koopISvROiZoBGIsQwPugMnkDpg1MjX+nx9dIYFRAT8e43qeF\nM0Jh/DL80AeGHQ1XrVJx129eg3ahdtIfg4geCEDbRr9qIjhuhjWbj0KV/duU2DAudFf0bVvgrlii\nPzPa++eocdwfQQlMqfga1duGCPQXoio6C1XLQ4HfpMRVKbFqVKA4E4F9OIL81wirv0fQXoRpHAdg\nYHArqu7dcU7sH/nrK6RUBcB3YLBE5Axvj5tZe+TMGQjuW0RAsUP083iEtdrAY1jwsTMAACAASURB\nVDmzOGB12cKzsXC2RkqcmjyA5SQM1O5ByDsJIXIWKq8/YGByTvhvKgYQhVJwUPw7FwOd9zHnvDkw\nCBZsAunZ4vaw/AOw+MoYv5uxmsjryZMLyZlrMC1obLynbfRnayr1nWdi6tSJGNidiqs+ozGX+S6c\nWxPwc3NzXKMXlq9cK2eexnlzCQYq81NibYTvogTeg+GX32DKSsbAdjAq9sXKwkWYVtU0Z6ZHuxfh\n/K2LudVzMNjsjp/R+TiPF8U9D8TPxNo/2aj6i+wfQnW1A1qezzlfUP0Lqk4GKq200kr7P7Uy5aO0\nv2PLY47lsqhqrggclytHHX+DD/KeeDLedQjOnyI8HYMP6BVy5lIE2tmYovBHKie9bYhwtQpCyEBU\nHtdDSDgLwWIQAkrGNJJd4+8HJI+zrhHt7Ipq4pXRhzm48WtThM27MD1gKG6mewPVuZ7x3h1x894j\nCBQApEQnTAeZBUyCNVpCbuxfa46Cq95FRXIsPt8XRTvOQtjsi5BdLJv3ir6+hcr+qSlRN5TEesD7\nRWWMnJmBAN4EFWKAe6Pudvtoc6e43kkYIGyREmdE34o0jHEI4e+hsnsRquRDYnzHAqdFADEixnBq\nzvwx7v8nXH2YBVySEq+FX09IiS1DNe2AUPYM8HjO/LHanGmIUDYfQfJxBM39EXyr5+bWSIndI4jq\ni/Ph7pw5B+fASzFegxH8d0MIbYuB20U5Mz7GrQcq0uvGvZvjCselmD7zIQYQs4HhUON+eH4CpKhM\n8s1q0Lc5wumRwLWRsnIeMDICsS44b0/Aed8ixrEpBm2nRf+ej9Wd0dGvYbjy0QxTb4bjPH8wfjce\n1fiDUmLdnJmI+f0bR9svxhWjebhi0RxTb4oTHN/BIHdK+B6AnPkO1ee2UR1kAQbRG8X4NkdF/2MM\nQhpSSblZO/r7KQYwDeN+S8WWZNfjdfztSUR/73ellVZaaf/rVp6WWFp1i4fsYQiqk1C5fRo3sr2O\nKQYNEQymIxiCEDsuft4FVc/d4m8DEQROxId5cXrhyJzpnRK/jZ97ofr8KeYff4DQ0wBV3XsQ9j9C\nFXZvhNJumDc7DFXifpjOsA6qly/ipsOtEOjnobq4JZ76d2mkVbxLpZTd8ymxY7ynPnBFzjyc0u29\nEcLDOp4DDc8Hbs+ZK1LibgShZcJPxWmMHyDoHB3t64YMcXL46qnkaYvFwSXVrTj0Zfnwz+iUOAbV\nzoypIIMR3u6P+z+O8Fwc3V5sguwXvuyEGz3vxwDiPmD5lNgUA46BMR6Xo6LcN2dmAxemxOcYHCxG\nVfSulPga58tOqLbelSxrWD3n/cDsqY4H4hx5DQOcXfFExw3jGrVwfvWpVnaPCKB2jfY9hUHTivHv\noeGLaVhPeh9MqZiBwcjOCIwvIMSDynBt5LE7cD59CNsk2P9LuD/KH1+5LZx6XyQZ9EGwbI0BzOfA\nMzkzO+bLlfi5GITzrwkGNocB1yePQd8wxqMu8FbO/CFU+GKz7YSUWARskjNfpMQ5wAXx2fwSA7jB\nCPEtcDVhBVzF2Sza9jnOu54I8K9SUdOJeTECA6M6mCIzIn6/UozT7OhHT0yLmhv9+WP4u/gs7Yif\nyV9sP5dTvXFK6TSgVZFHHV99cDmgtNJKK6200v7TbEVcVgdhcmdccp6AALUiwlRLBIPx8doUquQ4\nVLDaVrvm23GtTxB2M+Z2bhB/b4yK2qk5sy+C0O9x2bwFPsjvQJBeK752RvDqjcDaCIHrCgTBpgi2\nx2E5tWkImtPiax6qyWdESsTvEb43QMg6ClMt+qPK+EhKKcER21AVfa4yDIYfgirjlbHpsAGqvyvk\nzGU5sw1uCmwb/lqES+oFOF+FEPo8guxYzLtumzwA5DJU8T+Ltm2P8D+cSiWLhZEe8DaVjXG/iqof\nT2Le7D7R77djQ+Hw8NWk8N1fYoxPB+rGpsZPA/aGBVAX9lhc/52cORHnyzeoBs+JsbkPoXlrDIbe\nDdUdhMqFCIG/RZj8BuH9cUzl2R8V9+ri5Y44H/6CwdLDMcbrIMgWqxZ/QQX7snjfbFRtZ4QPh4Ta\nPB+Btz2q/BegAv0tXD0dmoR6PrM5bP1J9OluhPPLgeFRWrHwzRqYSpNwnGvinG2Jqz4zMRhYFVNq\n+kBV6sS3BLVH8DAblWNiL0FvDETOwLnQAqG+V0rsgUrzRFSZG+Bn7MooRTkG6JlSVb1q4v2Xhs83\nxmCrK34GiOCqJs7Vj1HtLlK0ekX7n6Zy4uJSsZ/Lqa6DDqrFj/OpZ8LS3S1ZWmmllbakVj3do0z5\nKO3v2Ln4YP4BIeMphOpBOXNA9qCUy3GpvzOwbeT6FtYYl74Hx/tB5XcCAvk4BIYxwLSUeBgB5Pqc\n+SpZPu57XALfCFXGY4BxkZvbHx/u7+Cz9HVUcjvE9T9GcCo2e/VCyB2L0NAIYWQoKr1nYFpKoewV\ny/KvoKp5AwJRW1TPI4e4FnDdC1BjPPBkBBQHIdjOA35IlWOcV0EYvgHTKA4Jn7RFVrgSQakZpjZ0\nRIi6D1XHkzAYOTXaPgSBbCgqiK8CZE9OfAlBrXlKdI4ScA3CN4Mxv3oFVJR/gxA1AAOT6Qjsu0S7\nnw2fVT/Vj9gcOj5y6sHUh4bx/q/i9efg3KkZ7e+REtdF2sgWqJA+hysR7wMf5syYnBkQwcDbqCKf\nnxIXp8R+CH73o8K7OGe+D//sEmNYA8F2Oiqn3XFlpCaWueuE+ernhn9XwvlQHEdenObZEFrvDA3O\nrPT63QPhwiE492djvn+VJQ8Y2giBfiyW1Fs22nE4zoHlo+2v5cy3AcsFRw6kUsd7RQwYVwvALnKh\nLwy/dcY9DA/i53RXDBw7xPs/wWCjsFvxM3ZhBGrtUfFeNu4/E+d+O0x9+gHTPXbF+dk0+rQIYf3x\nuFdb/Iw1Sqlqzvwi+7mc6sGRP939JznVf8g5j/xH7yuttNJK+3fajyt8lFU+SvsbK0SfyQgGHyII\nTCheUO1AjLMRjHoAW6bE8fH9Q6hCrhYbujZBCF4VgfVdhJzl4m+vUDlpuCdwU0DEbcARkQIwI5S2\nFghrj2OqSSusrvAVBgPfItjXj+9HYKrFjQgBcxEAFyAsbBp9vBTV0jOirXcgXCwPnABTDoJmt1Xc\ntNvH0KMOAs6DAT+dMbVgLgJpj6iyMD0AaiHmde8Z7VsWAbo5AvdchLxbUFluhOkirRBwauXMrrjE\n/1T0+0Sq7dMKhfn1eM2xKXE0wtDVWK95Di7pv5Uzn+ZcpZiehSB1E1b2OAPzcy8DmqZED35sdwGH\nRsWVC6lslCw2fz6HAdBfUCFugYFEI4TScRhoLI9QXu8n158NvB51ua/FlYMfcJ78GngpJY4Nn8/F\nedOIyobFPcLH9XHunonw+FaUnrsUI6PlcB4Px1WX3rhi8i0MuAVWLFJF6sNVZ4bPP6Gy8ZRI26mL\nmz674/xvhGBbpCMVJQ/bAFulxME/6e+I8BEI56Ojv2tUe806GCS0iK+bwoez4/6bY1DYFfPfT06e\n0Dkh2vZ+9G8vDMTOxiDvjfDfXPwc1cHVhpXCLwNwThW+HIr/N3TDAGph4Ytfakty+MutKaWmxQ8p\npWYppYFL4+allVZaaaWVtrQswLABwkfNnPkdpgf0AfqlRKt4XW0Ep/YIka8h+HyPD+T1sSzXX7CG\ncFeErpGoKo/FDVrj4v3zqVQTmR4HjZAzn2CebzNU5fZHGJ+GIPcdgvPHqGpOQPC4DYOC6zH94WmE\n1+OpHFddHFBzIULpY9GfOkDOmY8QBuvZr1a14bvY7NVkAfS/FwOExhidboewWtTjfjf8sF+0HYSP\n2rEk/1n49nDMIZ+EkN8HIWa/eM3zeIjcSRhYbIYbEPfBQGEhcFaRJhFjOC76vAlurjssxmBStOsx\n3Gy4Qfj5qRib0QjfzyPE758zL+XMn4AuKVUdGw9C1W9x8+Mo3BD6evigXdzj3BiXc3Aj3UhUoIu0\njGVj/F7HnOq+KXFh5EMPBTZLlt27AaHte5w7a6C6fz4GSh0wWBgFjM2ZDTClYQGmYnyZM8MwjejL\nUJX7YuD3IALy8hj0vQss1I/rnwttquXPT98LBtbFgK4FMCVZVrABzsVRGMAUQeJkDCQuy5mPo7+j\nwy+HpcSV/Pi4+hztXQNXTt7AKhuF7RnXOwDn+Vb4uVozrr05rmaMxc/KOTi/58X11o5r7oJlBM/E\n+f1SXPsTzJXuSGXPxHEI2GPj57kxvnvgXN8z2rxU0pqXBKpb5pyLkiXknL/D5YrSSiuttNJK+0+y\n5VAd6w/MSokTEDCnoIJ7fqQO7IjL353xgd0ZVb7OuPltACpvHTHPdg+sVDABl/4XosK2NqpszRFO\ne2I5sep2LaqxRXrFRgjxeyG0Lhc/D47vFyK4TQPa5sxTOXNJtHco5p22wdzh7gj1G1Gp+dyfCiC0\nAZ6Hj6+C2udXmnTYS7DKa1SOHr8cc3OfQ9CYF5C0ADd9jYk3LqBS4OA+hNyDMEd9l+jjRCqnAB6A\nS/eDw3/fI/QUR73/BVXtB4GrUqJltH1h+KQZlbSMwQhIbXPmbExBOStAthWCbhME36+jTeukqI8d\nf98zJc5OiaswtedMDATuR4A7A9MQHorf941a33NROa8F9M6ZJ6EK5D9CVbcVpu20xQDl2Oj7UzhH\nvsAVhMsQ4j5E1XZY+Lwx1TbiZQ+7uTDG97SUaBKv2wsh+/T42zAMvm6L9r2KQdchwLM5v/0YBghh\nx7eH+VsjVHcAmufMHfGeogzlvZiDfAMGTLfEm3eI6/8aVwEa4pHnpyRLQI5HYK2JwcZLGBgVgWwL\nDHZH5Fx1gEwtnMf74dw4OPx6NLJmP5ynTTCHfkdML3k+csGb4DxvhZ/JQ3EF6K6YAzdFfxZE+3KM\nR0ME91qYalVsSv5FtiRQvTilVOQdkVJqT7nmWlpppf0vWlk2r7QltPb4QK6NUPApPvRbRN3jXlhh\nYnfcJNaBypHUe1FRIOsgSMzE5eMp+GDeA6H9KVRC30C1+AUE28nVN8SF6toFFbhDEarujZ+Po1J/\n+Fh8sL+BS9qLoi+rV9uctQYCa9G+MajwfY9wsjjasBhVxFsQSj+HSw6DBbV9a73h0O8BhLyxCP3N\nECo64TL83LjP6J/4d2H4tsh/bkcll/UJXJ5fK/pRD+HluGhXTYTsFgiVRRnDJlHO7pz42gCDlIPC\nXxeiWj8WVc9r4/6fxBiNj3sciKC/J6auvIwB0pOxEe78aGsXBN9ncC7Ug6oDaZ5EpfdezPm9PXJ4\nj0GQGw8cnTyJswtC2ZoYADyDed1PosI7HOdW9/DDZ5ha9GWMWYvw2zMI9yNjTFunxCUpcUIEgG8g\nJL6IYDgzUmRA8N8PN2K+hIrzc+G7Njm7aQ+anwG1ogrJFy2g/zFEvnHO3Br7AGph4NA5xnlIfJ2K\nqy29oh8jcH60wNSL+eHnvuHLTvH+b1HFrh1AvRPOs3eoWGsqNeTXIfLSMYVj/xjPTpjKVByFviMG\nROunxFmYV79jtGNy+PcD3GBaB+tyj0Dgfil+9wywc9QUH4/BchuWgi0JVJ8DvJZSuieldC8uC5y1\nNG5eWmmllbYkVp6UWNoS2n4Io3UBAjQeAf6YErVDcbwUl/7XQUCci8D6Zs5VpcrqoFK8Dz7Y56IS\ndhfC4SWontVG0G0U17gLPDUweYx4fwTIXeI1LTG39l0Eg80RKGqian0+0CUqYYxFJfihlOiJit+j\nmBZRHJXeBpfsP0Ow/I7KoSDdgPHwyO7wYLVNX/fOgmWmRh9uzrmqxNnZCLA7A5tEQFBU+yisulJN\ntGVf3Dz3Cm5W64dpKtdgikMHhLWN4ncrxWv3QLg5PiXaRsrMaaiC7oypK4civD6HQdDdCLEA5Mwz\n+J/Cy5iCsR1C2rGosg5BuLshxq95tKcdwv9v457NcUViRwyu9kWI3gCB8bfho5uAC6NW87moiH+A\nED46xuU9hM2EgcapmLpS1D5/AOG3FYLysngCZP3w9WjkrscQjq/Def07os5ygP52WP/6BCr/Mb4c\nPlgPU2vCpm4Oq99X+fm6jWHaVsAdkbJ0d4zLVQj8k3Cuvpszo6ls/qwRbZ4MHJYzH2DaygqxOXNy\n+HVR+L0NKtsH4bi+HNcnVheOxrnyFfD77FHuYCWesdH37TEYmRr+/ADLOC7Cz9wc3Hw7Mv4+CedM\nd5wTOarjzKNyhPvceA3R544sJfsfoTrnXOyefRAnQ7ecc5lTXVpppZVW2n+arYCAsTeCEriUPxb4\nQ/Ko6n0Q1nZBAKsFdMyZv1S7TgMUj55FFfEcXObvhgrv95jS0R6BuKg93CtUzFOAgTnz+5x5DgGq\nY3w9jwD1h/j+yWjrAoSLqpVhBJPa0Z+puImtK6qFTyJs1Ee1d3rO3J4zZ1JVmmzRLnBCtTMlNvoC\nfvUywt92qIRfhvm7tRAIv8ZUhCvjXourlYVbGK8rVPijMI+3SJFpC5wUamOxvL8FwlUKv3+CgHg8\n5tTOAm5I1oRuhjC3EGFpMeZXr4yAvHZco7r9KfoyF2FrVrSrb7Tt5RibnTB94U2E020w1WA7VDub\n4srEmzlzTmwGPAyV24+w4sU3sWEThOHZVEoxgvB+Jqbm/B6Dhl2iDfMx+DkofPF7DGKuw3lQpJi0\nid9djGN7DCryB8c1FuGKQFfgpZyZX80XLyDsn4OrMaREY2AVeOYjqDnJl02uBeeuifnv+2Eqysi4\n17cYJNSKDb1gANYJc/974OdmXqTrPAfsG+A6PN4/H4O8NXEeHBbv/yB8QNzzIQyWPgca/53Nj/dh\nMPoKjl8TnB+/jb/PxjFuEf6cjnO3DY7xeFxxuByDlEUYrG2Om1nrYWA4H9g4JTrzC21JlGqiIZNw\nwq2RUtril964tNJKK+3nrEz5KO1fsGWI9ASgVUr8AeFnHp7Adxmwas58hdDVBCHk9WrXqIUg9DEC\n85RQRIs8zBeBXXLmPVSJX0L4WwHh4XvgjzkzKiWWSYnTENr6Iji1xaXtk6nUHT4QVdKmQJ2UOAWB\nfRDCXx1c1u4bffkKc8Uvxef4WkXpstgktxGwDuz8JEzsYLdqL4ZbvqQSbBRVJCaiUlpsPFwfUyja\nYtpLV1T6WxPpH6EyPovq5uWYR/40Ak1LgIC9e6LNg+PfdxEo/xq+2AkrlqyNYPlo/P0uVE+vQWCf\ngvm0XyP8VB0uE0B7MSqzz1OpkLILBjvFgSoTEeTAlYy9MXi6BKt+TMLApboyf2CM0RhUt6vbFjEO\n1a01phIVKR0bRVvax706Yh75rQh9pyI4LsCApsi9bh2+mIFzZ4+4//Pxu/Go5u+XkqcIBjzvj3D8\nZvgNDP5uhHZtYNfbK029rR28NAI/A1PxczIy/PcwVAVOYFrHBJznE+Pat+G8mYzjdR6VzZjfYGCx\nAa4arIGBwjrAR1GGcn7O9MQA4CKE8WVS4jBUlxPmeS+Dc+Gv0e85GBivj+O2TPhkBH6GJuHq1MpY\ntnAMgvdwKtU/uuGqyg4I1A1w3PfhF9r/CNUppSOpLOtcEP/2+aU3Lq200kr7OStTPkr7ZywewsWR\nxsMQzopl980wF/oeLJPXIWBsDAJrk7hGLVTiaqJ61ptKvdwRCLZ74jHUbVAR2xHBad+4byPgkJQo\nNogVKREnIjh8AswJxfMsPA57MALNy6ga/wUYkzMj8QMwFkFwJkJ/N6g6iGQ6Qky/lOiP0PwRpAzP\nHVnxUL4M1m6DgPQoMDA2l7XOmS+jPN29qFJ+G/fqjafPdcaKHechHL0Yr3kPleSx0Z7i5LyivNxq\n4Zt7sTrFxQhwgxG+B+DmyysQ1CbHeGyOy/eLkFN+iHHogMroCylxaUpclRIfIDA1QfB8BWHrPlwx\n6IGq/m0I/psiqBYpJpeHP/ahcugJKXE4QvAxCM+dU2K1ij+ryhoW/0E1Q5B8Nfx0bfitDZWUnIlE\nJZDIi+6HOcb3IXh3j/GZAjybM1fGa55EmNwXA5uGuLlyJKbtbIRguwUqw3tiHe5NEHK3AMbAo52h\nfRx2NB/YpnP4fd94fyec98vhXC8CsH2wysspOTMg/H0MzvUZCKW3xbh9D6yZM3NwdeHW+HuxEfJX\nGChunBK/Bt6JFKQ7qKT27B39bo7z5SmcG+MR7PfGVKlbMWB6BwOZ96LdE/FztlVKdMA5sU/4dghC\n/tvh74vDp6/y4/J//5ItiVJ9EkYbX+act8Zcnek//5bSSiuttNJK+1+17qjwfY+wBi6vd0D1+l7c\nqLgv5vF2R3VuOJYpOxYVsVrAC7HJqwvwbkqsiQrkxwhRHVDhvB8h8EVUYYdiSsPKCKNnoHo9JN5z\nOILC9JQ4NN77RkqciyAwhTiMgkrd3C0RdIq23o+K7S6hUtZA8OiAy+AFMJyFcAQsMw2+moUQdhEq\noo3iWi1TYuNqqiQIhGugmvg4AscuqGavhGp5D0y1WA1hduNo46V4JPw2CH9HUTncYxoq9KtRgZoO\nCKHfYN54g+hPkUe+MgLwbajcF/B9OKaXnBPX2BjTC4AqlfxGzJEuan3/HtXc81AFv43KUeyTEPxH\nxXgfiTXG38J58BLWzW4XQcPcGLOGKbEOqslTMVXjSpyDG4TPvsA5MAvV8iJlY48Yk9NRhR6PefiN\ngHOSp0HuiXOqFc6pF+MeI3COFFVqNsSgbl9MvZgcY3ETptocCDXPgi9/XW2c94J7a+FnpisGJsNj\nXN4C2sUmw7pR0u+HlOiGgcjyGOxsCrTKuapfDVFpLvjyeEzBWAlTTc6o5vc1cuaJeO2EaHvr8NeX\n4fdHMXD4FQYe+yIgP4OrJW3wc/TnaNMMDPgmYpDUG4O2bqhUD8bPSe3w6/y490pUgoh/2ZYEqufm\nnOcCpJTq5pw/hx9Fa6WVVlppS8XKlI/SfoFtgwDTFJWteQhjffAB/Qlx0AnmcvZHCFkZH/I98aE6\nAFVBENSuxQd6Z9xstRgfwg0RpBcj3NRA0WkSPuRfwof2FAS7oQhzDVA5/w0uS++MecGHopL2GRVV\nGwTS7TGndjWEgakIKnvE++fg8vjNQDd4rSVuwAubezIstyqmuVwX/W2L4HUcgsylAfetEFqOwBKE\n9RF4H0d1eUj47YTo+3iE1xoIY0cg3NyGCuBa0bZZca8tYmyKqhkbxL9NEXrWid89mzPrI7zfFve+\nLf7+DpaRGwEMCdX/MISsQRgAnY81qzujuk304VZUc/vjKZe/RVDdN8ZldLzmdzkTOcg8FO09CwFv\nh/Dl5zE2N+O8uQCrqByFgcbbCPLrxTgeg4r2d8lTPM9AqDs12jAPIXFMzvTB1KTlol1f4hxvFn3c\nCPg0Sus9G23pGj6fjXnHRb3o2sCOOfN5zvktDDjCLtoSXt052lgHPzsrYd52O1yJeSZefApwac5M\nxPn5OZU8cDAgrI9QvB6uLmyMqTDtEdo/wc/ZJcCdUVXkknj/mwjzQxCCm0df+iEsD4jrHxfXPSz8\ncWbO3ITBxYLox1QqR8/XCJ91wc9hAwwMPozXgvPvrfTjY+X/aVuSN38Th788DgxKKX2Hg1taaaWV\ntlStkvIBUIJ1af+UrYeA9wUC60LcXH8oqrOPo2o2E8GyLj7o22MOZn9c5r8U0zDATYO/Qph+BVWu\nYZgLfHC8/lvMp+6LsHc6wvbdwMU5MzQlDsQ860+TJzQOwIf/KOCJqKNNSrwc7dsMeDEllkW4+AiX\ntj9EUC82ZG2L8LwtqoCfAodD79eowMIQ2Ps+hNspCKVHRJvPQRVyADAgJRphGkC3eP8d4beJCMrD\nscJCp5x5CCuTrILK7Gz88L6OqulLuEy/DUJ7cYT1oGjH11QOXamNAcM2qCC3xXzhXyHc1USg7oSg\ntn70ox8eXX1lXH9otKMOwuq9qFLuAFwZee6HIVC9gCkzv8+ZG1NiFKqi9wD94/Ccwj7GYGM+gu5A\nDGo2RfDrSGVDXJ14fQtgcM58kBJd4/tpMf7borp+c6TckBLTUTHuDsxOHhF/PkLuRlgp49TwwVkI\n0ONS4rc4NxdFG06NMToToX69aM9TKfGd/t/7Evjr/jC/NoyoB1seAIuXR0g+JPpc5LqvHNciZ0am\nRK3kMeGLcR6vhp+3a6NPA6MPy8a/7yLYtsKVimK1oUW09/SceT98MCHGazoGNnvGz7/CoGPd6PcZ\nGLh8FL8bkBK7YopN9+jHdCqrEOfgCsnZONea4lyuh5+bDzD4ao2B6o+OcP9nbEmqf+yVc56ec+6D\nUfZt0dHSSiuttNJK+0+xov7vU1Q2HI3E5e9jUCndC9XZN1DJ64bg/FnOPBB5rp/hISH9UNn6M8Ly\ncsAtcZpgfXw4t0HIGYgQuQCV8XsRRooSXmsBi1LicoT3bggbo/GAkn6h2N2JD/nJeGLizbi5clbk\ngL8Q710Hq1YMzpkXc+YcqqpHnLwnvFT9gLaT4OGNUAUci4B8DiqqhwEXReUNopb3JATbAQithVo5\nGp//+wGfp8RxKXEhAlUTDDb6oOr+MKrtjwC358y24YMhCL0DMf92W1SgG8T9DkIQGh3j1QDTX6bi\nMv47CLUfYT78VpiCMBiBen9MWdknxqtIFWmVM6Oij3dGW8cj2N0c6QevoFI8H1ghJY6uplrWj/Ha\nJ/xeE1cIpkU7LqciUtZDwP0d0DEl1o/3D4gNqEdg2s0CnCeFzYhrNCY2u6LS/gpW4lgcbRuEqy3X\nh3/2CV9ugMC5IPw4Kcb6zZw5AhX1i4EV4eEb4dxqm1Vq94Nx32JA+kxcbzIGKpOrVTcBg8brEUS7\nxGbZRpGDXh9XTW7E6iMNEegPR5WkGSrM74Ufdwe2TYlzUqJx1B5fPa6xe/jgCpyvOfo7OX6ujfPx\ns2jLNfiZ64VgXBfTaIZhcHg8zqlrcJPoduHvQeGnWRhgFwcd/Uv2s1CdUqqZUvq8+DnnPDjn/Nec\n8/yfe19ppZVW2pJamfJR2lKynRAsv0AVtBEeqT0SVeM2CGb3I5wegg/8BAlzBQAAIABJREFUL4Et\nUuK9lDgRgXU8Km1/iQMiaiHYFIeivI/wtA5UKZx7Yw7wbXFa3HPAZZGDuhWCCsBvcuZrVNC65sx9\nUQbvLip1lldBSCxSF4qKFI2jLUV+dVHNAmABzLwcHupV+dWar0HeEPOhn0KIvhjTAhrkzLcYdJwN\nEHC5bvjqBlSnFyGQr4+w1B5h8hHg/KggMhjV0xEI07MRsGcSR3XHoTi3IMwPC983QtB/C0F5S1QY\nV4i+3h/3bodQWx8rchyFgNU12nk7pl6sDLSNnOhHMCiYDQxKiS2r+erSuNcRmLLwEoLfYlx9GBL3\nvSIltor71kSgnIWgOxWV6oaYu78GQvp5wDI58y4GGLch+P8a02AeD//NrTafiOvWQBW1K/BozozH\n+VAcKJRxZWQ5nBfrIHzeHuO0X/ShDkLnxsDXKVEnZxbmzHs5cxZwEZz2FbSJknnzG8NFO2CAuRZC\naH9Uue+v1kai6k0zYiNg/Pp9Kqs+tXKuUuobIeD3CL9+jxsTL8uZnDPf58zl0f4zUuIODGxWwk2R\nn8Ym3oaoiF8Y4/Zk+Gk5nBdPR5+XwWojb8c9vwXWinrazfBz1Q7nTod4fXtcyVg++t6KX2A/C9U5\n50XA8OonKpZWWmmlLU0rq3yUtpRsMT4ox8X3ixA6wHSKu1AZfA+VrnGo/L2OUPUD5r8W5eveRCBs\njQ/0YSlRP9TGw3B5/EMEwCsx3eSPCADgxrOd4l5947oDotIBcd+GydrZ5MzknLkRobERpkJ8HW0e\nGxsrD8T84+K49KcAkgd4fAhnHQ0TQqWuswD+cCcuhW+BMNEGgXAcsGFKXIsg1jklBiC0rIwK/QqY\nP7tOzuyB0FwDIXwzzK/dNSXq4of3LFSRt8qZh+MwkDEILjcE6BbQeDPCcw2E2WEYUFwZ3z+BQNwE\n4Xg6FQW22FB6OgYYAzHI2BXV3r8ilG6JoNQdq6nsFfnhBOA/AByeM+ch/F6BCnl/XNFoFH3cHHOW\na2PAcBAGT6MwMKoR15qBkN6lGBdMm2iBaupHoZY3QxitltcMOGebR19fwXx78GTA6idbfkvUA0fV\ntnf0vVfcty5uLL00/LMt8JeU6AiQEm3tX/1psNv1lcve0gCenh3XPYSKqrxmVImpbhfGV3Ha50io\nOmBljWS96SkIrK3CD/PwM/neT65FBK7T8XP2Fc7VogrLCuGv19Dfu+KcGR3XXoQB6ESE7BoYaLTH\nOXxQStyA86sZrizdhMr5RXGtmXG9bzDV5F+2Jdmo2AwYmlJ6IaX01+Lrl9y0tNJK+++2Up0u7d9g\nLXEJ/BsqB6mcHH9rh8reaqiCXYjgtCoqkCNzZnN8GLdGkDocN6g9jvmc3yMIPYHPzhvxYV8Ple8x\nCBd7Jetjt8ENccvig3xmzrxWrb0rx/Wu/kk/xiKAj0QQaIygc37cYwzmTndAGAA4Ao5+EO7cpnKZ\nDe6DHdZF0J+GoNWSSs7sZ6jsP5ozB6G6tx1C22rA1jl7QmTYxHh945y5CNXtaXiIze4YoHwIDE2p\nqkbyVwjJnyH8Xhz3mY/Al3GT2t7AdjnzB1RGh2L6xPsAOXMswvFpCLibI8guj+pqVwTAd3HcRmHg\nMAgV8ZejrX2KzkRVj2YpsQYGU3dHe/ZEMD0UA7HPMFWoPqrQewKH5MyFCMJFPe8XcmYBQuzklLgH\n59b7mIpRVJZoATSrFlwR1UT6YWA3IPrVKP68elyfaN9MDBhWjOu/kDPXUNk0uSoGA6vh3F0vfH11\n8qCfxzHwmwtHnwNdv/PSixPs0hkWP45pNF8jtF8DXJsSfVOid0rsHGPYAUtLFrn7i+JrNQyuig29\njTDdajmcA5tQzVKibkrciSskm1M5+vzulDgOP2c5rlvk9K+NcL15+Gc9nA9FisyZ+H/AcITn6Tg3\np1Kphd44ZxZh4LZcXD+HT/9lW5KNiuf9khuUVlpppf3Uyg2JpS1Ni3JwNRFcbkKgWgTUSon9MYfy\nclSkJxHLzQhpbxLVC3Lm/ZR4FFXiGpi/vDKC0wUIVq0x57MbAm49KsdYn4wP9aNyZnEAx7G4qXGH\nnzR7FUwNeDAlmuTMjICr8xCiOlFR+j5BULoCq1BsioB7fUrMBrrC2B7wQ9SHbjYd7r0LoWI+wlH7\nuG4thJ6O+OE7OCXGhe9WxaBk02onBxI517sg8G6ZEk/mzGfA6ymxE6rDnyIgtwROTIlnENCfyZk7\nU+IaVGDfplIB5Mbw9em5ckR8XQSnN3Hz29sp8X7OfAM8kxIDUbHsiMv4YxEA90ZVfAiC05Mxrg9g\nesoeWCLu7mjHYxj0jAh/rI/QVyPaNwOB+v1oY0cMLL4EeqbE4BiTXvqf1VNir/DzxvH+k+PeTwBd\nQtXvSjWVOlYZzgjfbY1zbC78jTpMjN2ZCJHdsQLLlhg0rIpBXicE9zk437fDoG8grhD0jXY3gfWv\ngyvege12kEfZAf7wXc69JqdEjvG+GefpHPwcLYfpN5PD542jT/NQzf8i7t8MP4O34Px4M3y5ZUps\nEa/ZCAOySeGn3tG3zzGdZp0Y42cwb3pw3O9GDHIfxhSv+yP//WP8LJ4c4/oRzttNEaofxOD6TKBJ\n7JuYEvdrjatHy/4dvy+x/UOlOqXUHaryqP/m65fctLTSSiuttNKWojVGKjgbl98PQCVtHiqAK2Oe\ndFGFoDNRZQEVzGpHeTMTISSh6rgQVeLfIWzdjA/sQxEUVkXoboYq47hqQLo2wn4foE/6cS3o5amU\nqusdf7sI4WohKpGXRnvG49J+x2hvPQS8TYCN4ZJb4bn1K5fe7NKcO7yMiuQIDDI+xyXu3yBAD8LN\ndoujL5sgvMylopIW9hsEwRcRQnqmxHIpsTaqhV/EvwuoAFBx0ExOieUQzMYhBK6JaSBHhx8mVLtX\nHWBeKMm3xs+3VttMuRhzsGvhJtIpCMQvxDhsj7A2FQF7GwTLTtGeDtHnExHSvom/rUvlmPQbUfWe\nH6/ZiUq++M0YIF2PubyPxRith/Pk8Ojb1dV8cwfC2sa4UvI8QOR5HwuclnNV2lL96EuHqLLxNSrC\nR6A6uwJwd5S1W4CnEK6C8+aVaPMR4e/B4e8HcaNe//BHsb9gGmx9GhxeLbe7//Yp3d4k2vI9wvOe\nyIv3I1i3prLxsDPmgzeKPm6Ln6s2OI8Pit+3RTV4Wdz4uh0C8905s1XOnJ8z50cfLozXv4yfsSLd\nqXWM3zX4WdiUyiFIK6Ii/RQGS/PDV1PjvsWhL7tRyZG/N2euoFLdZVlgWjHX/hX7ufSPG4tvUkpv\n/qs3KK200kqDMuWjtH+f5cwMKpu4TqeiaPWIf3dDdXMhcGy8/nR8QL+Kh7GcGWCbMI3kKwSFOxFO\nR1E5YGUygssOcc9RqGBuVLQpeWjGVajm9aACNoSC3QIBZH6079Vo6yn4gF+A4PtebGTsGb+7E0Fi\nEHAgLF4MN59L1bL1etPgkaKu8L5x3/WoVHb4MwYaF2EwsQYCY12sNPISVgSpFW1tAKweG++m4HL5\nQ6i+FhvL3gfOyZnzcuZRDECmIphei1U7vkNIujX88QaVY7nPS4mzkiUE61I5HOXWuP5fgedSonFU\nHPkcUyUuxcBgJqqToxDCHkAFuxmwYs5cnDP7V7t/dwSuZTHQODF+9wWWpFuI8Dk9fLUNpqRsG/cr\nViXahS+2j/6MQfCdnjNfhB+uzpmFmBt/fPiBlDgGYe/sahsWFyFovoVzbh8MKrbHXOR5CMbVl/lG\nxViOi/FdEzehTooAZDbOtdVy5rHw2yQMpBbq64u+hBSpRFOaw9DXom8r4dzcDFXfBzF3fn0MRr7B\nz0p7KqkTE6kclDQaofvmaOdV+HnZHgOSSdGf6tYJD96Zgasao3PmEkz7OQFV8odxbnWhcnx8p/Dt\nNAwMN4m+z8HPVl8E8fPwc1sT4R59QEIwvx0V93/Jfg6qqz/5/t4yRGmllVbaElu5IbG0f5cF+M1F\nWHsO4XYRQsgPqH4dg1B4dUpVMDsa82lHorp6Bz5o66KydTs+iDfBlILi0Jd18YE+L+7XFYFh02hP\nwnSTKZgm0goPrNghJe7C5f7lo80PISROQ2DuGm0ZhCkLwwCiosJM3Kw4E5/Rv4aLPocv1wpXLIYb\nJkKdU1PiaFRdi6PCX8D0gr4INL9B5a8d5my/jOAOimrnxvfHAvekxN4IhR2jT58h9LydM0OLsmsx\nFgchyK+FcFX4ezkE2V8h7PyAKuedCLu/ib+tGn1ejIrwMqiSvx/3XAOhtmeUAdwQ1ce2mGN7OqrE\nNYAdIw8YrE++etx3YwwwhsXvZkX7PsCVhRoYEK2G6QL7Y77vazEuhyOsXhh92wwDrV4xdgBto/IE\nuCLRPe53KZZxvLma3xKhVEeubx0qtZgHht+/RpAtrBGmSDTGtKcPMUCongv/DAZLd0Z5v5Wp5NN3\nAW6B5WbB6WMrb/nT6jD0u/BpT0x9OgKh+mWszPG78PE0DGIa4uehZfRjDww0Z+C8m47jtwEGANsA\nfauX60uJ9fCzNivefxqVg3u+CL9+aptZgPsFfhdpUwVU74CrGItxE+4QDOq2xs/MVRgcDwlfgQ+l\nH6IPB1EJ6v5p+7mc6hoppWY4sYrvq0A75zztX71paaWVVlpppS1Fa48pDXVQ0RuHKRMbYErGAfhA\n7o0wlXCpfgUEyENQfXsVlbWMwLIBqt71qGzeqh/3ehsfxJsjKD4e79kzrjUWQeJdBPJ+qA72w6X5\nWjnzaoDOt/ig3yvaDVasuJjKyYogUOwV12wGs6ZCn22r/f1m2HgiqsQLoq3XxDUGIJDdhUpcn7jW\netGuNxBgXoj7jouKIE1Q1XsOoWgEgu/+CHoXBBB2jt9lhK/7cSn+LAxSmiFIFSf3rYmqbAvgu5zp\nC1weKv7KKbFHjMeTCGorRhs2Qai+GtgpJVohKM5CuBuEIP4FjvPTwOmRW39p+P698MWNOTM+SglO\nQfg/AAOBUzCdaD3MVW6DsLUTKsiPAZ1z5q2UeBvn1ZMIbaekxANUNhiCc2gSgvoWUVaxuhW51Cun\nxFXEyYM580ryEJx1oOpAmrkpsTIGjweiCv51+GhDoGtK7ILztKjHvAoGG9/HvWZgQHAz8C6cPwvu\nbAuTWsIPNWH3zjBqXIz9URjI9UDwvCYlnsRyhm+hIv8Jwv0cnCN3YFD1bYzDWhg0nYDBy1xcEVmI\ngcz3GHhOwBMSc4xtUS2kuP/vcN7WDl/eg/PsS8yfrouf7SJ1qwluSvwqJT7A1YQDcLVpzZQ4IPzx\nDQZzk6vvJ/hn7eeU6ibRmXfDUe/Hz8XvSiuttNJ+1sqUj9L+l6wLPrg3xIfs8wi6DRAsOqMaeQ2w\nchzg8md8nq1H5XjshgguayMwzkTw7hbXboAP/am4zL8nLnd/gkvNE1FVfRfh9PqcGR7L+wNQfbsA\noXViSrSjktYxJto8EwHxPXxGb/qTvs5AQO0OXeoiUAJ1f8Cg4Ttctl81fn4i2nw7KtLzwz/1oz27\nohK7NS71L0BVeD6C4JU50z8U1wUIxiOjxnVzDB5eRKi8LGf65MwwhL3Poy9XoSrYPn7fC+H03Wjv\nUSlxSUpsj8BdlMybhsDYDaHrvLj/n7D83v240rAnlt7bAZiQM5tGm7YK/4zA1Yg/okL5RNz7kJSq\nDtmZHeOyAoLoIlSfm8W4fBxtWIyB0VbA9pGOslOM+2PR34zK+8Bq49YbwW9u9Ountj7OuVbhn7uw\n5OKy0ee3EaKPxzzpRxBg78XxvQxXFcZhqsq98f2Z4c8/oZJ8AwLpGVFzeg5wEdTfEi6uVu5u9C7Q\n9c+YfjQmZ6bmzJ/joKFtMAi8MfzbJNo9CefIePwsXI9QvhyVXO/mGByOyZlzw+et4lrz8DN2UAQN\nw6lU8PkBaJoz08JPNyGMb4GrCfvj5/KZGK+TEaprUylP+E345FOcB7UxRWqV+FsjLD+49HOqc84d\ncs6dcs4d/85Xp3/1hqWVVtp/j5UpH6X9L9mv8KF7MIpA61KpdTs4Zybh0vsc4MhI/zgQH8ZvI2yN\nwnzZg/Bhu3tc52UE8GMRigYDw3KmOz7A16WyQa+Ain3wIV91OEvOvIQwNA/V1E1QzZuIquiX0d4W\nCNZfRp86pUTjuExx/HY/mNARxhxfccHBgyHXppKuOR2VwWmYalIL4bMmqnhtiFJ2VI7HLpTy3THv\n9UmsZ71KXHP/8NPElLgEl+fvx2BlXs58D5ASe0Y7T0dleChCSy/MvV4cauBZMV6fxDgsRrg/H4OY\nTpi6cywGTQ9j0NMO01hOizG7Osb2HUytIcoBboBAfSCmAtSL1zwQfjg5fPRX4JOcq0517IZQelL4\nc070f4/wyTGomo+Ie7yHqTRTMEibHT//PiW2TInfxe/3xqDo+JRolxLrp8ThKfE0Bls/oCrfGzce\nNgn/fR3XHIUBwVycM+/gCslBqLzOQQgeirBbJ2dexZWD4lCe6Zhi8k2yZvVsDDi/gyNXgM0L4E/w\nwcWwuD4/sZxZlDPHISA/HL9uip+Fmgixm2BwNxgh9lhU0r/BIKRLBDTbYyrNXpH3/iIGPMehyn1c\nShyLn6kxKbEaztVLEa4vRJiejUFbHawNPx7nSlMMTraKtj+AQfYoKgf4bI+rHzWxws72P+3zktqS\n1KkurbTSSltiK9Xp0v4PbC3g+yjzdhM+7JtQOYxiV9z8tAiV0UfxIT8eQeQjhM+38Lk4GpWzrxFA\nT8CH9pR4zdpR0eIzBIBZuCy9Dpbl+hCV4H4pcUSUUgPh/EAEp82AT3Omd85Vm/FaIAB/H6+fiRBW\n1JZeBRXXLeHERZCLKh2fw94HIWgtg2AxFkGhONJ5L6y28Vpco060YTsEmYG4OXMxqpv1EIouxhJ5\n+6M6uXa8ZhLwRs68nLO1j1Niu5TYDOiQM/dgebOPoj99gXOjrwDkzByE2hURot6MtvRDoC1SGOpG\n2xvGmByMCvsiBMZbMHK/CWicEttGSse+MQcGYFCxZoztHuGDy2I8jgRmpcRuMb7rIrSti+A6BBXU\nhTnTHwF4YfhgbVTpa2Kqyd2oHH8WfXkGFfZ28fOqCIgnxHh1iX/74OrGO1EF42OcnwPid68iTB8T\nY1KUpHsg6mN3xE2m3yYP2tkPVWlyZgpC7kuYyvFxrJLcRoUDXwA+gdNvgBpF+sNmcEGRr/8jS4mT\ncAWiS7SrAa5MFKs1RYrHuhhgnY0rCc/iOC+I+98UvysCF3Lmc5wzh4YfJ6DKvUu8ZyJ+Xhpj8LEv\nBmU1wg+H4rg3wmBjEQZ+O8bKQn0MqBbheM+M9z2GKwZVc/SftRKqSyuttKVqpTpd2v+BzQNapkRv\nVO1WQYiqgQphkVP8IQLhDgjDnREATon3LMAH+HiEoB4I5w8i2G2OS98fYDWRFgijr6IyeS3CXs24\nz7kIEL2TJzGOQJWuFwLn5OThI6AyOxFV3S646W4mgu4qsSTdBvgOHl0JHm1Trf+n5Lzjd3GvVRBm\nzkMV9TmidJnvZThwUc6cmTMnIbydGPcslsozwggIIzUw3WIQ8FTO9Im2VFnO3ISwehDm3G6PwcbQ\n8GP/nJn+04HLma8QRou0hzoIShfnzL6YQrBRjMFQBPAdwrdNMHf627jHnGj3yahej46THb8IPz4S\n7euOubN/wNSPTriK0BNBrSgNd2i8vgOqreelxGmoZG8Svp5Hpczhu7jpcuu4X8bjyb9FoD4XIW4k\nqtbjMWjaN9q/AKgbOepN4rrLAqRES4TKvhgYbI8BS6Fe1I73fxT+61NtE2QRaH0Yfeka92+ICvGg\n+H4F2O0iqF3tpMVrtk8p/UitTokjow3D4lqf8f/YO+9wq6qr745Fk94RQbAgFopYsWssYNfYezTG\nFmLH3hAUey+xdxNNbFhiV+xRVBQVxQKCikjvva3vjzH3Pdc0CeZLYt49n+c+93LOLqtt9pi/Nddc\nlbzuCR2ffVHBz+jM1IOqZ2AYjp/Vo+1vAbZJiYtwF9M1EXyPQDW5L/b/HRg/3R/DfjbC8Xsuld1T\nB+IMyTsYojM9rjEgynhVzvTB2ZgmUZaFUe7t47OjWUorobq00korrbSfutXFl3YRIzkOY5Qb4NT2\nGQjBzXB90A34El2EsLkFvpw7o0I2BoGpF4JKGwSDxxAun0UVrBfG4PbEMIVC6Sy2sT45Zz6JONRH\ncKp8TWByhINcCvRKiUYI+G/gdPU0hO/BCMrzUGleBIvXg4PWrjita4+EXKxzGoBgs0+UaxSCy5fA\nxjlzVs68FsomKdEOGBMpBvsgYPwOgbI7zgBsgrCxFcJtkeCgiC8mrtUeFck5qNxukTN3Iby9guDy\n9+zCuNZ6COYXRAhDkS6xiA8+I67zVlxzAjoJy8TPDVHub4CvYxFh1/hsJQTetkQoSko8Gddqh+On\nI8Ysrx7XPgaBrhmOpZuw//5EZdHf59FHH+XMCqgOb45j6h0M43kDx+NxOI4+wTCDuwLwLsXQjxYY\njnADAvQ7ca2GqI4/gg7TDCoLF2unVLU1+s8QJEfkXLXbJqjyJ4TRPwLjYxdGcmZWQHxdHCcbwLxz\nqXKqpjWGBmcWF4oZi5moLt8fdX+1Wh8MAIaHsr4lPju/whCfa6nkqV4DZ372zZlxOXMrptebF+28\nVfTHlThb8QI6fLvhs7xitP3U+Hs0OqXdUMWeEN+tHPftSSVdZJ0IVRqJzkyj+BkV1WzLUtoSQXVK\nabOU0qHxd6uU0spLe8PSSivtf8/KkI/S/sM2Nn43xBfnA6gaDkfl8dGc2SxnTgJ+iYDUDeF7I8x8\n0R0V5iIe9iFUnWugwvdzhMoD4/foOP+XCJ/roSq+PoJxxvjtZ5K7CT6IsDwOWCEl3kAVeG7cf8X4\n2RSh6dSo0y4YhtEbWAy3d4C5G/hVzQx7nIA7K/ZG8CgWeD2EMDgjZw6JXMl/afshGBF5qDdCBW8I\nxh2PRnD8EmN5R1LZZnp4tCMp0Rxjmc/C0ISbUK0+CUG9H6qOf9MCAEeiCl0bvgeE4NT/HbHhyQAE\npt9iGM1ZcUw9hPpZCKIrp8QFCH+rYrtvFe06CCFvQwTtxaiYDsSwj3aodG9GJd/ypHCEjsJQnzVx\nvL2Bsxv1U6JF3OPtKN+amMavA46bsVHebRBij4j6z4s6F2p8Wwz5uQ/H4v44JraNcy5H5Xx+tNe+\n2I8rIRjOSok6KbF3cmvyg9BxmRr1axEzJMVsxIpxn4uBHjnnqdXaFZh/Wkp37JQSu2IO7D8goH8e\nbVQTx/uH0b5DIs1dkQZwLs5EzMNwn1dxBuIJzPjyVEoMRId1QbTFk1G/U3EcX4mhJNMQ5H8Wv5tE\nW8/GUJvnMBzoPHSOaiCsr4RO8+X4vJyEz2kzdBQn4iLnmVHepbIfhOqU0rn4sJwRH9VGr7G00kor\nDShDPkr7j1uD+H0gThsPwRfwVASZU1OiXkpsggpnTYTuZ3LmI4S2kQivdRDQrkcgfBlf9K8haC6O\nXdgOQxi7EuHzEXw3/imuvzoqdC0Q2M+jMm1/Dy4wK1KkfYNwdgm+1B/CEIHP41qfALVhZhs4fdlK\ntXvNhnMORzg4K9phNMLMRgjYU1Oi79/6QdXvNylxU0q8igpzRwTmIgdyHYTEobjJSI+UeAgVvs4p\nsScuuHwanYprMH72gbje7aiSFjsr/pVFWrP3EKbGI/gU3zVF1f3rlKoWkg7APOBzo203jnM3xD6f\njvB2DPb3OtE/18fOfX1z5ueoCLdChfVzVNVvzZmFOXMfOh3boLrcPiVWDAA+DeOJn0cnol708zXo\nxL0ffflnVGSHYGjJOjgmxqEDtHJKFCpwE1TjV8TY7dfj37WAQdkNgB5H8G8UbbI7zjCsiYv96sQY\n2CI+H4WAOTHa5WF0FCei0v6HuPfGwIKYHagbyvUdVC20XVAL7rgCHci7UuKXUc51cVzkaPMJcc+j\nUH0/Psq6bBzzND5TTyKMbx5l7kolq9zyqEy/hePtdlT4l49rFIsreyJYnxblmB33vy76/U10SmpE\nuf+MoVsDoz93QGgfheOoVvTVd1SL7/5nLeX8j1+CKaUhOBDeyzmvE599mHPu9g9P/C+wlFL+ofqV\nVlppS2fLLbdSwHRh1Tf5+nf9vXTnf//s/0S5l7CcOZfS/xJYSgxBNXA2vihnIvAOxRCP9RC2P8FF\naeeholkjZ46ObBXTUKnLCAx3IHS/lhIHA3vkzG4psRUCwX0I3CsgRO6KSltPVMXa4dT/Ynyxt0OY\nuCfOb4tqaA2cnm6FILFpHNMRAW06wtpT0GdNOD+ye9SZBt9+Ai1vwFjkh+P4dtEWC1EN3SA2E/nL\nNtsS1feFCPcPoYrZCYHjfEzrNh7B8RZ0FI7DKfza8d00BJkZGHbyBULqRghLlyM4NYt6v169GBgi\nMAdBb/vol0boHEyOvhiDKucK6HwkBMGxCLaHIcTtEN91RJBbjDD5ECrT7dCZqYPQ2yHa7cg47qvo\nhwuBB3JmcXITnUKd7o9Q9hg6T68hwDXCsfY6joluGL8+O+69GGF6bJSrATpqU6L+76DzdBcqzg9E\nfS6ikpnlZzh2u2IM8YkI7ztEXe6LOnRAGB+EMxZb4bhviSB9HTpNxwLdIvzjBuDdnLkjJQ4EhuTM\nxymlLdApCfvFIXDPruhEtKESpjEUYT3jGN4/7j8En4sF0fbTEWInQtUOnS0QmNvic9QLnbhxCMH7\nI+i2i3bugOP8tqjTq3Hv53FWpm/E8zfCMbJRlPdThOc56IR2jf7eHP+PqB3t9g1mUCk2P/qnbEnC\nP+YHmUbAe2rwA8eXVlpp/wesVKdL+y+yOqg0N0ZFcneE6544Zd4GYW84gsw8jIteN7kd9xYxtQ9C\n1nQEvJ1jSv95YFJKHB7HvYThHO/gAr+38KXdFV/i8/Dl3BzhpSmC6UKEpj3i/F6YfeIMVH43QAXy\n4Cjne7jQ7UoYtSJcVmQRAZr0gZarIVBskDPnR303xQV2ExHmGlPc8DM+AAAgAElEQVTNUqJjSpyL\n0HxvzpySM79DpbQhAth5wLM580XENJ+IIQbjEHAvjPZtFPfZJMo8AtXU5gigbyLYzMf/KGqgc5MQ\nYnoiJN+MU/jnxfWKrad7IwRujQrnLgjb76A6+z46JM9F282AqhCRt+L+ReaTX2AYRD9UaFdG52VP\nHDvT0BlaPvrjzylxLzpkKyAcFtvLv4QOSwGRDyFYbovg2wVV002iPzaIvtwGHZMVol9eQAV13bj+\nHxD6xqGDdmH8exE6Ku2A0dUWfK4W594F9MmZ7THe+CqE/tdRFO2IszD9cIy2i7rMjut0RpAHF43u\nBJBzfhU6vkmVDTgdFq2EYFss5m2O/dgWHZK9sL9fivZ4Le75NoL0Ljnzi+i3Tvi8fYvAe0aU9Rns\n4/oYUnItlfHWF9XrIzBjSZ/oh/VxseNZ6ICcis7LJ9EHtfA5rI9j7GR09Oqi8zE+jm+Nz/BS2ZJA\n9QMppZuBpimlI3AQ3Lq0NyyttNJKK620f7Eth3BSAEgHhKlJCAtz8KXbHBXoBQhQwzF84+5IwQbC\nx0gElbr4oj8ZVeUJKXEMKrKHIwDvgcDQDF/2bRAwnkJguD/OXT8WLF6LsbO/RQDZD6gXmRr+gKra\n8nH9zRAApiiUzo2Zi+YjYcxBCDaH5cz8lDgaw0tqI0wXYSO7p0StlNg9JS5DsLsJeDFn3qvWhscg\niE0DusZCMwBiYePZGGrRFMGnbrTjxvGzWlz7VYS009FxeRsBrn/UdQpCdFNgz5w5M2cG5Myb8XkL\nBKAjEdBvwVCP+ehAXJwz12U31LkqytUFgfoGhNXxuMjzYwTaZ3CMtKYSA3w4QuALwFM5s17cfwSq\nwyOIXRNRnV6MnbAMguLt6CRNjHvXQGV9NirbzyO03xft+kqU6VIcXz2iTAPjGjPj+04IjvPRCega\n5bw1/r1iSjyOjlOvKMMoYJMI6WmLqviZVBy5NRBOF0f/7hV98kYs1uyMGWoOj/bqlhKbGNozYA7U\njpmOmZ3gkhznzsAxcws6NcUCyiNxXO4SZdkz2vI4XDy6ECDGe4pj2+bMEeigrhj9dHX002PRJgfg\ns90Mn82jUSW/JNq8iMOfjePyHRwXdaNvrkbn7NW47ms4Hmvh/xf1cDzVx9mEpbIfDP8ASCkV3n4C\nns05P/8Dp/xXWBn+UVpp/1r77wj5KMM/Svu+pcRrCC8X4Mv9AowxnZozPSJe+FxUPb+msinICASO\nzfHF2genlOvmzOYpsSxC2yqoRF+GL/GxOXNaSlyOL/btMVSiEYZ49IAqSN4R4W5q3G8dVGQzAtbe\nCDwtEDSLxWNPIXxfCq/uCD9rWKnxgDdht10RFG7EGNpOCKH7IoS9jQuvHo/rPIF5pXNKHAR8mDMf\nhjOxIUJQcyqhI58g6FUfgzMQkmqiGv9g3O/rqF9rhL3GCD6DUQWsjzvoPZUSNyP0nBJ5qv+yL9+O\nvnwX42XXRDg/M2cmVTuuBYJaZ4TZXyPETsV4+p4IzhMR9B7EvvwKlezfoOo9BfggsnCQEvtgyMrz\nCFpFZoyEIHYEpuw7E8Ny1oo22xYV10UY+jATOCdn5lcrc1+gX/TBjahk98MZgpNRIR2L8NwLx8K0\naNdlEehfR8DeMtp+eM4cVe0eCRXuBahi3wSsmLM5q1NiXxx/FyHEFllHxqMq3wbHz9zot7fh1K3g\nspjxaLkIProVlivS5LWMNi02vfk22mMWwvdr6Mh8GfX5Jvorx/1HU3FwV4tjh6PT8isMIXkS1fP9\ncEy8h+PiiChjfZwxaBN9/GbOLIoFwtvgWFoz7j8UHakuUfY90RFtGtdthM//UoU41/qhA1JKvYE/\n/lRAurTSSvv/Z5WQD/j+u7a00v6jNgenexfhC3ZzjJ3dvNoxL+ML/Xx88RbKdbFt9ReobvVCZZGc\nGZ8SJyDgfoMAOxx4JqaZZyDAP4UA8QWCd0cE1R1Q7RyJsHBgXGc3BJ5NMfxhIk6XL4uA0Q3jhIfB\n3Dvh+D0q1dh0BOx2e85MTIlJqACfgOEbGyIM70dlB8lxcf2uwNYR7rIN8GIsMlyMUD4gynMxgsdB\nOXPRXzZ0SqyH7DAz6lw/7jMPYeVMdCYezZnfJnfN2x0Xi+6DyuTUvwXUYd8gABV5nCfhDpaT4v51\nEJJbopNUC52G5VGtXB/hqDOGWmyJwP0SguQmqHpugQrmgxgGtDJwRs48kBJT0El6KerXKvru5Sjj\nyXHu6pj3eEpK/Dk+a4lq6nr8jdi4Inc0guIjqOg3Qri9FpiWM4+nxJ/QKTgg6lIHnYsHc+bzyPZS\nP67xveunxCxUieui8nxJLBJdDZ2nFvhsdMRQlCsxlOY6BM9u6DC8CHSCcybAbbVgSn2YWBN6rQMD\n+qPj0hWBejY+C2DI0+e4CdA+kX96a1SCu+XM9dGX7TDs5byo6/boMKyOED0YHceGODY/Rah+A5/D\nrzBkY1kM9dkFx8YF4VxMQuV7OkL9RnGtPeK7lugg1qGyyLMDPsdLZT8I1djZz6WUJuPAfTDnPG5p\nb1haaaX9tOyv1enSSvuvs2UQwGrjy7MVAkOnlDgf33XbYRaAxzEsYwQugpqNC6Ga4Yt7OWDZlGiV\nMxPi82cRIpviNP7PEcAPjc8+wxf7KqGQzUDIvQZV6x0QWlpgvOd9qKxNQVA/G8H+XgTwR6L8a8Ft\nR8OQeFfXWQzXv4M7HC6L4PE1btfdHIG8BYLyF1Hvp1AtPxhV0HaYp7hQLreMe26Ai7++zJlvUqJ+\nSjSIfL7EsZtFe7yJ0Pl7BJ+emFv6lsjW8QfguZSokTPDUqpaJFYsCN08JT4Bnq6+iDKAuSGVHMzv\nEk5DSuyFCvrmmKHj0zhnAwwR+D2qspPRgTkt6nw7hoVcgRC1CsLXqZiN4k5UOF8D7oxUcL/DzXPO\nivK+iM7SV6hwrhZ/35AzU0PtXxznHYYg9wHwckockjPDiypSsVcQPr9CVXlHHMfTYjFssXnO0eis\nvIdhHtuGM7Rr3K+K4yK14apRln3jnE2jrmMRdDOVXTV/D1ydM9dVu0ZTXNDYiKrY5kb1oO4lGOoB\n/GkD+KAvrNUEYXQQAv6v8BkcG3UdkRLLYSjL/jh7MbS4V3ar9OWpKMbjo50vRefnHoT20/FZGYKz\nTAegen9Z9OHmOXNtSjTPbkxEStRGZ2F63H8qOlC/RzX9UXxmRmAY11AE7DvQEV0q+8GY6pxzv5xz\nF+zYNsArKaUXlvaGpZVW2k/LygWJpf0EbGUEkrtxoDZAWJqIIR3P4HR/sWiwJ0Lro3H+swi7HRF+\nPwUOSokL8QU/I77bDZXPJxFqVor7jcR43FYpsR2+pDMqb21Q/ZqHgP0NKrcH4kLB2VSyTryPiuve\nwFiYdhL0X65SzRNmw9obI1weiqBRM8q2DKq74xFudsHp+TuiPjtHPOu+RCq1gMG9EKjPQUArcvTe\nQ2V7dJJbX2+LzkAtVJNvQ0idg2pv51hE9z5C49UpsSGGzLwR9a+Jsbg740Yc56bE+pFh5QIEx+mo\noF6VMx9SydvdPmdOKoA6rANC+BeoSM9BCJ4ddaqBjsd7GKrzbBxzIjolqwPkzAs50xMdoA7Rho1w\n9uPAqGdHdKY+iPv1TonjUPn/Kq77GcLavQinV6fEZZHOscpyZkacdzUqyhOiD1eMvusTMwWTcRzf\nhs7cxCjza6i4Xp4Sj6XEJRh60xKdRrDf9400gjfmzIuoYH9GJQNG1ZbcKdEQHZQvcPFlxnj5z2D0\n8bDGRI9cmGC3xQinH1C1MRG1o986oHM3veiDnPkS1z2slRLrx/1SlGEXdHZn4diYiLB+GD6zV+EM\nyAfoxBUhRk3jnlOqt21KtI1zrsPZhi9xTM5FVfxofA5HorNcL8pdF8f1Jyyl/TM7Ko5H72MSPyKI\nu7TSSiuttNL+xdYAFdgzENbaoyq2Oiq1G+LLezKqfqsi3G2ML9VjETRaoFK9EvDbnDkTge5AfF8e\ng2rXUfhCvwkVs25xzHxU84qdBu/HmNkLEeL6IojsjWEmR6dEvyh7fwTrWXHd7nB+g4po1ng6nPUJ\nQsVTCEPNEPYaRTlHRB2eizCDvqjYTkP1vS3QrFps8v4IJ1fmzBSEirkAOfMF5lGumdwt8bCoC3GP\nteOet6CivCpwekqsC4zKmcFR74sRwj+N+OKzMBZ2CkL051HObZAv1kTl9rxon4swHd4goG1KdOD7\ndggC6boYEnARAu2mVDZ3aYxhIT/HsdEjZxbH8U8C2yW3ASdnZuTMqaiIv4qw1RqB+n4E8YU483FF\n9MV5qLCvggrt9cCFOfNnVFPHIMxumxJ7RZv2iDY4P9p8bvx7PIL77bH49HdxzW1wDO6DKu59OJbP\nRSW3iGlvgGrud0CHnJn4F+3VCMf6G+ggfpkSbZNbg78BnJcz/RCA70Dg3BlqjIL+z1QuM6o7PFKo\nxb/BZ2tK1H0wPgMp2n7LmDFqEvW8KCV2QYd1UBxfhEO1REDvic/Dc6ji/xkh/RYci53QWVoNKk5W\nzLwcD5yaM5/jM/l49Ndd6FxdjeA+Gf9fqIlj7wt8PvdhKW1JNn/5TUrpZfT8WgBH/BRyVJdWWmlL\nb+UOiaX9xOwThKt9cYHZ86j6zcawxYvi70UIgw0Q3lqjStsMAbs1Kss74q5wDyFEXYBhGi8hAE5G\nhaxXnNuNSqzqE/FdvbjvTviuPSfK93uEsQ8RHvvmzDmorE9HpXpteOtruKZaiGafT6BxQiVz7ajX\nZQhgX0fdhiLANoOqnQpvQuB9Iu77KkCEORyOIQxfxk3qUk25RCX/QATzMyNUowUCzavA8jlzP6rm\nc6PtbgaeCEg7PdrlEuCM5BbX0+Pf62Ds+pic2TlnDkH4WQNht8gWcnHO3IazEF+jOtws/nsqck03\npRIOcSFC+wAE2VUxXGV2pAd8NspE1GVwHHtaSvysWt23RwCfguC/AMMO7sMwhJoIxBsj+I1FJX5t\nDDd5JSWuzJlXUCltGPceQyUkZe1o71Ho+DSOvtsdgbk7jttnkcGGxfFHoCO2DtAkZ4aFqn1GtF2/\noj8ipAaoUnDrYPjH+Gif26Is10d7N0yJi9EZ+pBKRoxXYc9bEUzDTmwLc3dDGG+NsH47jsG3cKw+\nF31+Xc70imPmY/abLaMvbsRn6GsE9IRj80x0YJogFM+Idl+M4SJPRh3ei1mXjXA8nB4zQMS9QMer\nM6rv+0U/3hs/tRHmO0WbjmIpbUliqtsDJ+SchyztTUorrbSflpULEkv7idlLCD21MNNGRtW2NYLB\nZlRy0M5CuNwed5HrGVkZ1kLVq4CcGri4qiHGOC+Izxbhy7sGqtwbxu95CB+z8IW9KL47GlWw2QjV\neyBkvIIQcWFKnINT25dhCMFgOOgQp9kBuk2HE9dH+Psm6nwFglBtoHbO7B1ZToYBjyTT2jyA8P0s\nwkqdKBcI2w/mzFvV2nEZvr9F8/sE/OTM3ACXnlHOHhhaQ84sSG7AMziOvwkVyN6hCM9EFftnUZ45\nGGawH2YpKeyG6K/RUc6pwD0p8TAC/vYI7TfH8ZOxvx9EZfYgBKOPUEHuBOyQM7ukxKWxSPMB4KRq\nsLlstOmlwCEpsQeVEKKxCIVboVOyEZWUb59jqMiq0WYTEYS3gqpt6U9Kbof9LoYObR3ttzwC4gSE\nwHsRFoeiI9Iana/u8e9bqWxoMw94Ijam6QbskhKLgbsinn9s1OctdA7Pjn4biEr6PFRkz8PnZS90\nMJ+P/ngWAf9IqnKkMxRokTOvpvT8SrDj/rBgGfi6MXSdCsP3iDafkDOjIoxkPo71W9DZWislhkWf\nrIFjqGn097kYG71pjItV0GlbFoF6FDoRjfE5uhEd3Suirb6Jcn6VM3fwfZuPz/CH0R7fYbjYWBw7\nq8Y1G0Qf/pEfsVDx7yrVKaUiYfxlwNcppebVf5b2hqWVVtp/p5XqdGk/YfsIobc2lRjJB1CJHImA\nMwwhrRNO7a+KuX0fw9jh5RHwVkT4fAVVvLOpbBozBsH2aoSeX6LSNhZBZAaGklyMUNgSoex3GDqw\nIqplPaIcp+J0/DAEhYWet9c8GLFepXqXDYEaM3CauzaGtbRFKErA5MjusAB3w9sSAX5VhIS1MXxg\nKrBDSuwOtMqZG/6iHZchlOoA0IsQkrvE96eg07AukRqu2rmDEAw/QBhMAdTE9dbF8ItHENabRrvc\nHt/fhgD1RXZL7mEI7V/ilP2x0X4DiMwSmC2jMQLT1ah0f4TQtBMqyc1ToiPGGe8RZf4dQllCcJuA\nDlUXhK4uCHZfR/1nR9scEHV8C1X9WtF/7yJAHoGgXwdDEDojmPaLa3wb5XsR2DtntsaMIj0QbidG\n3b7DmOYHc2YslZ0u6wINqrXrLIT994ErYyFpv2iP+zF26FqcXamNszmtEfy3i7+3iPLcnjPn4nPw\nac58RGWHznnAQENWejSBHZ+qdPt3Z8IDA1D5Lmw+QM5MxmdmOI7Dh3CWYiiOgyvQ2auBrPksKtYH\nozP6RpRhAxzzO+OsSUsE5ULdPz3q/R1/bVPw/4F6+IytG/3QOeo6DJ+bmtFH2+OzslT2j8I/7ovf\ng3HADK728+7fO6m00kr7aVq5ILG0n7B9gtP/h6Dqtgm+PBth2MXPEXg3w3fY7qjEvYcv1Izg0BAh\neOs4pieqzTvmTEciBhVhqohdPRCVuP6oQD+J0NAOIflpVGavRGVsAUJMoZAV6lkXYBQsaAUfVmVj\ngN3GwbaFSr4DqqJdcPFlR4wVroHq8HNA7ZSokzPjc6Z31GMYQv7GGDN+O3BZLBSrbilSsiWElJsw\nLGW3APFv4/xTi008qtnLCEzX4qLPo1Li8JRYI7npTLc47w85VzklawBdknnGN4r2/Dau93TU93Gc\nRaiF/Xwjwu0XuOByNGY/OQPB9EUMoRiWM+8i3N6M/b5h1O1edDQWIKztg2DbF2cbrsFY6uFR32lU\nlNw7MKZ+Ao6ZbriAcy7CdoTv8E3UoWkcNzzKsBVuNlPEAY/G8JQPULXuirMsG1IJxdkAgftbzA5y\ncUq0wj6tk93E54S4906YZ/kDHA9HRl+9gsBeE/luYZR5eLTRzimxDrByzgyIv+ui03Fh9Om6wDi4\nbz1oHPnUZ9eFfQ+KchYvj0VA94iHL3b2/A4huS06vKegs7AXgu9JcY9JwHs5sziypkyJz2thLPWU\nOGdhXGfF6IvNgSZ/Y0yPwuezHobttKKSRm99Kir1UOz7jjiGlsr+bvhHznnn+L3y0l68tNJKK620\n0v4NNhZVrgYINr0QoicDs3LmppSYitB0QXYHwvkIZlvhIqjGqOY1RigooPd+YuFhpNi7KCUao/o9\nCaHprrjvlwjegxCkZ+BLfxCGNsxBFXEuKnU94u/HEBY2ggvHwxerWq26C+G8+xCwiHusj5k5DkNY\nqIXKYGdULdcDTomUYtVtJsLErqhgHgr8OpnT+HWE9EJoOxlDDIq0dXMRWmriFPus6hdObsTSL+rw\ndID53hgOcT9wTM7fi9Um2mYaQuXmqFouqvb9h+iwjEHVfRfszytRdW6ESu1W6CRcHp/vg5k7To+U\ngO+mxFdRp4HAVjkzMCWmxbGf44zBDFRLH0XHbB6GI5wUZemMcHs1wuDh0Q8HYr+vENeYinC7Ks4s\nDMdQhl2jb3YCdkqJj2Ih3UBUuGfkzD2xEHPLOOfuZJ706td+Bp23oxHAx0NVfupaUdacEifHNfpH\nKNB6CIyjcLyD46YDOkNro/p/aEpV6fFWQ+CvF3V/AchQvxacOwhO2jmu82t48WHYpmWAdAPMhtIH\n4bkZOlHLRHscEu3QESH39+ioNEGA3wAYlJLx0zkzOyWuRwX7LVSTZ8YYeCDGRDG70C8mW4sQsJqo\nyH+Fz/azOKvwUhxzLI67etEX20cbLpUtyULFvyL2v/VZaaWV9tOzMuSjtP8Fi2wW44FaOTMO323t\ncfq+Z6hXKyBEfBoq33aoTLdGiDoTVeYGqKoVi8/mAPunRP+UOC+ZL7kuhorUpZJur3hBT8RY59EI\n6Z0wBOBVBOxZqGzuh9PS4xAohsHoN+HKakLW3LNzXrM3FRX8CkwT9rHHMxnVyx3iXp2j/HUwtCHF\nMZMQGFLU60VUHYfglPxKGLd7cEq8i4rx9inRNxatbR91mAc0SokdU2LDlFg1Uuadi4D5Fm4wcx7O\nFqyNMFy1eU1K1E6J32A2lPsQdoYjHF8ALI4Y4AMQap+N+q+NavTt0S9bo2r8GKrN0xF2x6DieDnQ\nO257HQLXLODnKXEBgtvHCI5nIExPRMjbA6H18Og30Ak6LOozH0H4WATS9VGBfRHBbxQ6bI1Rrd4A\nAXgcAvxkzDW+PCqk60XbgYA3O2f2x7R5RfaPlVHpfRtYL/IxvwvsHRkvwHE0HMG0adR71SjLCrio\n9Rl0xlrE96cjfE5FB+9CDLGpg2ElgzBEo0Gcu5Zl7PUbaFbEw9eEk38Gi9/CcKkRCNJX4fi6lMpW\n8sR9ZmEf74azAR8iKLfF8Uy0y2CAcPA+x4w1U3HcLwu8ljNzYlbivZzpk90ds8hgUj/afysqERiL\ncIyvgc9RTXTwXo56LvUL8R/FVNeN2OmWKaVm1eKpV0IvrLTSSvuJWxnyUdr/goVSWge+p85mhJv6\nOH28NgLTkbig7RtUGCejotgZp8En4lT5SAw96AE8mTNno9I9HF/sB6OC3QLBpBuqv/XjvqfHsU0Q\nHmYjaOwW5euMIPE6Qvx+cMaGMD1mkFtORVUUIqwDWDtnBiAIjkY4GoCwMgahd0DkJT4XweI+hP4O\n6CAUu+19heEtZyG8vBnlKBYKNqWSQvdRBKrBCEyTMBfzr6hkQ7kUgevm6IvG0c5/BG5IiVtjQeZd\n0S7XRHuPwNjnexHu94tzRiCgtcdFhydhiEQB6idHuWuiytgcQf4mdJjOALZIiSujzbsikO+IztAQ\nBN46mJFik4Cxlhj3/GrU7yF0kvZB2HsVZw6a4xg5D8fBRHTOxiOInoIhIxujU/IGQvo0hLy1ENRb\nomP3bPT1+sCwcATnodLfHh3AvTCsqHZ8/w6CdauUuBMdhyJ7TRGGMyva94MoZ8+iryNE6Juo2wk4\n0/BmtMv20Yf741h9HZ3UXv6u1wsurZrFgSGtoU8LfB7a4pg7pZoav3K0y4XR78egYn00OhSTid1K\ngR6hum+FinJhMxCET49+WIzP519ZtfCRu3A8v4zhQ7/F0JFNEeL3id/Lx7U+5fszJv+U/SOl+ih8\ngNbg+/HUj+EAK6200n6CVqrTpf0PWg0Eli0CNhYgAKyA8HMnwsIY4OWcuQqqdj38LI67DF+6D6Ky\n1xxh5kygV0qsHi/qIQinLwHHISTtjqBbbL19B0LTKfH9MzjdPTrKOg7Boh7C/2vwQTO4v9pGL1dN\ngbwmQKSym4fqMgigG+M7eZu47ihUSndNiT1SqlooOAVh74Ko/81Rlk9Rqd0RVeM1EKAfQIVvBIZd\nbEwlq8bFCIHr4qKxxagGz0G43RMX152eM31DTT0Jlex9MG76jwh+f0Cg3TXa6hhUnIutoy9BeD0y\n2mpuXP8IVKmfjDIsjHJ0jToeF9f/OPp9syjvIgTUp3F8fIjQ/BGwTIRPdEWVciKGKrTCcTIjZy6I\neh6NsHowwno/KnG4TVCdLbKHPISq9iPRjv1xPA2jsqPjR3GfNVJiIxyDDXE8F2NxAjoyn6Pj0A34\nBSq266NzsRaOtTej3qtFf70Q/VlsT98oZ24kLCUOQ2CuG220RbTz4VGfT6NN9ov7f4VpDs/M+fCr\n0YkJu3Z3mNk/2ulVhPFia/ZFcY1Ho38G4ngbguOxHWbjGYTj+3eYLnB6zG6cg89k4bDUiLJtldxw\n6e/ZDOzLtqjyz417vRX9Nh6dtmVw7LWBv1ovsMT2d6E653xNxFOfnHPukHNeOX7WyjmXUF1aaT9R\nK9Xp0v7XLGKdL0ZIew1jdNfEd9zHqEQ9FL9Xj9O2xTzJRfz0NajOJgTt9rgo7peYceDwlOicEtvi\nS/crBM2Xcuaaakr2y/jyPwTVwkJl7IRQ0hnB9lBUn6+HRZ/AUbkikG00HQ74Gng0JW5MibUQnNeJ\nA/ZB5XMGlZzRqyFA34ahEFelRGcEzZcQIK7FmOJiY5j6CL3F9u4DENC6Rh2fA67Nmc4IsHOjfaqr\n9JdFm47HMIFOKXF9hMqcG+2+ApXNbbZCWOuPU/jHRL89hSEkxXbge8f1V0KFeHmEvcVRn5EIgvug\nwv4Kwu78uO54hKex6MScEPduSiU/8tD4mRjZSY7CuOwxCK33RhutEiEja6Iy/R1uST8OofU7VMef\nQFjvgg5Jf3ScDkXH6nfxs0Z89geE4oXRb3fH36vhYsNX47N1EdqL1H6Po1J/CcL72QjNl8d9BqKj\ndwKqv21w/MwEvkuJU4DxKbE5wmT/aNsir/eX+Dw1j3Z8CcfURwjM26TEnslc532g5nQAmLEsHFxs\n2DI+2pmU2DHOm4pj/0gcQ7OiH/tEv3QOp/iOuN8WEWN+ZbRVU1Tcr0OlOUdZ14/n8q+sWoaa1fE5\nuQifk9ro7DRBB7JutNddULU50j9tS7JN+XUppa4ppX1SSgcXP0t7w9JKK+3fb6U6Xdr/ssVU8YkI\nXLuj8rZs/LtQqA6uOtyFho2pbEX9Cb4PJyHwfAU0zpmPMd6zKU459wZ2q5YLdwdUG4EqRXkkwsIs\nKrmW6yAsbYAw+xyqdu0tW69OMKhJFC/DZW9DjQOpwPLdUa4NU2JrhN7nqGw00wBVylWAOTnzAqp5\nRa7h24DuOTMQIarYJvtyjC09AxXXmaHIPouw2jPasthI5s8IaE9G+xaKbz3g2Ag5OYzIUoGgd34c\n/y0qrnsivPwKF/ldFf00Bx2YbTBM5qH4vA3C7GcIU6dg2MNdCHuHAS/kzGlx7ZYI0btHt9yN4LQv\nKsRtMRRhJYTUveMeDyOA90ZnZYu4xhE4VvrmzPk58ybC5dxhx4AAACAASURBVPiUuAYV3XsR5veM\nPrgKFe1tgV4BdsOB1XNmiyj7KjgrcET0cw0MT+mEEN0uJQ7EcftQ9HlddPTeQodw02i3P+E4nhzt\nuhfC/pXR5vWopOw7IvqtBzpBN8ZY2JJKpo0eCJw7RF0aR19+gcDeG2eCToN8MpxabB4EPLUjPDgq\n+q5ZSuyLDtGfcUwUGTaKGZsaUccL4v5XYf83w3HzII6h4TjmZkV89Zyo1xXRlp3gr3bbLKxm3KcP\nQnkzdMK+i88XxjGNo33+clHtEtuSLFQ8FwfydTgAL8XpmtJKK+0nYqU6Xdr/uNVCdfGDUK37o4LV\nHtW2T/GF+x1CaF+Er5n4HnwZ1eThCL6dELBABfs4BOs5wIxQjsEtvydD1QK8PVElb4OAsB++oJ9C\n+PwdKr4PIhzWhTnz4ZlTKlU5aAJsdhCGCVyLwPQiKu5Do247IrT1QiBoiBB1AJXNWzrG3w8iWI6P\nBYDDUyKyi1TVsUVx94hPPwyn5XsA66XE5SlxEAJXXYwx3zdnjsWY7Nm4ccqFqDTvBTycM+fkzOCc\neQnDPq6LYxfiYsB3ELYWUAldyDjFPwIBcXj07VoIug+jgzEx+vNlzDfeDOG5BQL0wTlzac48jPC+\nDEJ4reiXb6u1V7u4R1NUan+N4wMqGTLOTol+yW3lt0aw3Sb6oCGmZ1wrrvXbOO923Klxmbjv0JTo\nljNPYsjDfej4rBTla4IKbwF7HXCW5OfRn0Mwi8zPEEhb4RhuHfU5CJ24mjnzNDqCxazN9GjbiVG3\nMeg8PZYSD8S9e0TfHB/OVQtU5s/G52YiqP7mzDsY878MnDMYlp9ic82rAwcdEG23Jm5MdCvOcNwV\n5zwXffg2jsFdo//fR5W6d7RlS4zt7httXT2d8/Ro04+ALjlzDbCsubT/ytogMI+J876Oz3fBEKot\nor8GACPDOV4q+0GoxodjG2BszvlQrGiTpb1haaWVVlpppf2LbR6qhO3BRUpUUurNwOn4tnFcJ3yJ\n/gljU4uNLG5DoB6I6uPouNZkhJzrES7OQBV3Rdx0pV1KnIHwUcTg3hrX2h8XqzXF1GCnIEy1wvCQ\nY2GTp+GbZSxCk0Vw8VAEtZMRDjui+j0NqjbkuBLfzQUo7Ylxx2siWCyLYDgSQeHNqNfVUZcdY+q+\nf5RxJEJ8DVQMM25LPg+BfGIcOw4dlPbV2n5dDDl4FRXz16Osd6TECylxU2QDuQhDCoagiv84qs9/\nzpl+OXMdhgbMR+V3VVRy70bVc30qmRqmoNPUhorD82HcY1SU676UODglekb/N8PQlrMRqo9HB6CY\nUXgC4W5VBMujcuZCBPELqi3+vAgYld1a/iYEtcIp+ZLYOhyBeLlok9dQ9V8ZuDHCYo5CEH4v7vlh\n9OMmcc5CjEF/EdX0j6INNo361sKx1Bqh/OCc2Qsdsb0ia0uP+O7puHeduPa+cf12qAy3ib7viOLp\nGsnNhPog1O+PsD8xfhPx3+cCF0C9N6Dj8VTZ/F/A64chMI+MD6eh8t0AY9uXR6jvFN+1jHbaBh23\n0fgMzcRn7iJ0wgpbCcfLGcDnEf7xFrBmdbBOqWoHzJnoeDZDR6xGXOMPOAvQGB2sv0xF+U/ZkmxT\nPifnvDiltDB2WRzP9x+o0kor7b/QlltupVCoSyvtf9tikdkhwNMpcVmk2GuK0LIqQvJQKhkbnkIF\n7EuE3k74PqyHL9ZaQK2UaIDKavv4fHrc61KEw2YIZL+Pe8xGuO4f312AL/45QP2UaBTXesjyfXMn\nfLpapSZnToO2GUMyrsRwlNUQpO5E+DgMofNABL7X4pjOCAmXRPmfpJL1ol/OTEyJwXHefnF8v5yZ\nmhLHY4z2YmIzkJyZkxJbodr5GW6i81b8+9yAqhFRnhrR1h8juN0YbXodgtSOCHhXIthfhZA3Dlg+\nJQ7PmdtQrf0iynIhquwD4763R/m2RjDeJ+5XL8r3CjApZ7NopMRx6BwsE9d6F1XbjDA6Ltqt2Lr+\njei33qgG75QSK8Qxj1X6iF3ifmCs+Jc4A3EiAuPg6IfFuAHNHyPv8wsIt6NQof0WYXa7+Huz6LeP\ncZxuhqD3UVx/ZXQoaqIyvlt8VhchdSRAzkzFePoV0LlrGn0yDp+F96ONj4uxfEH8e3sMe1obnYGz\ncTalVpTnyzimTzJ39hzchj4bTvXyPZCeiPYBDl8GPn4Val6QEs9HO36Gztv+qBZvjyB/EoaAvIFj\n81h0NtbF8I7bo/16U5VthEboiLyE8emnAG/kzFUp0TuZm/vr6NN5wPs5MygcmiPjng2jfYpQptY4\nO7LUtiRQ/W5KqSl2zmCk/Td/zE1LK620//9WCfmAH5F2s7TSfir2ZfxcGkC1MsLC6ggudRBGD8Dp\n9JGoir6N77Xu+CLfIj5bA8FwA4ShWhji0DS+G4+AsgiB6lJUrw+N68yKc9tgXOunCJN/zplzXZC1\nz9swN97Dqy+E47+OMs9AFf1YhOIi//F3CDPXxnGLEaqbIIDeh2ri4Qg36yCQn59Slcr4GkJGRkXz\nptgM5z6EzwNwYd550YbvRXkORyjrSAWej0TnYYucq0JJAEhuAtIyytA0ytExyjkZFfTdcXHi5ICd\nhKryBFSpj0eIvyW+2yqcgw8xM8g2CNM358yslLgiJd7Mmek5c21K3EwsZsyZGeHUXIaA2ZmK4/E8\nwuuv4vge0dbzcYbjjlD2v0TgHJbMV/5F1GUXVDgfRvX2bMz2cUZKfJ0zb6bEc9EW83ER5J0xbtZF\n5+RpKluGt0dnoohlvgZDPjaJ696C6wDqRD1WA55LiWGo4tdDZXxclHd1DAupG9evC1ydEkPj3G6o\n1F8f/bw9cFVsunIKzkKMQsfqF8CtkQWnsMaOkU36wDu7yKeftYJaGfIbCNNboEMwH2dUhlLJtFKX\nSkz3c1HHP0b7LoehTpMQnF9OiTXRWRqRM+NSYgjOMtQEyJkrU+ISfH6LNRWLYhFkI3QCN6bihBZ9\nMztn3udHWMp5yWMsI0d145zzUu828++0lFL+Z+pXWmk/dftrdbo6VP8v/r1053//7P90Hf5BOXMu\nvaEltIgXvhBfmCuiirUOqpNX4xR9F5yWH4sv1Jdz5pBY6Hh2XGoHjImdidD4e1Rvd0Uw/BVC4pkI\nyqsgjHRHkL4FY0BrxU+TOGYCkHPmQMubuuPLPuyRL2D35nG/Fgiz2yOkn49wXQOnxbsguXyLkDQB\nQ0p6Y4jE5ag4tkDY74GAUYPKboGL0bHoHNfZNI5fhKpuCwTbFxH6zsyZcwK2v8P43f4ILcXeFbfn\nzLfJzXXuRYBfhAsJ3w3lvw+C8nqocv8MwbhhlGUYhnysg+EtG0dZu2F4xC4YttAdFc/aCN+vo6J9\nTJRz/yhX+2iD7giljVGZ/DbKvhjHwiYoHv4Jx8zJObMgJfpVnCB2iDrPRoD7OH63w9DYdxH2mke9\nP0cH7Myox10YTtETobpj1L0XQmc/hL6N0CG5EGc6Nsfwh29QqR+EzsnG0YZr45g+AsfMKnGvoQjT\nV2B408noBHwWfX8UjtF3oi6Lo43vwpCTYvOjqbjA73R0ZD7OmdnR56RE3yjfnfDLDeDuVeKr0TDp\nFWj+Pjouq0Z970e4nhn3XB6h+Y84NnfOmcOizYtn+kF0LBcihO8AdCiye4TT0iBnNk1usX50tP2X\nVGYsvsbxcxOGT22Mz1sHfN4OBzbMmaEspf1dpTqltO4/+i7n/N7S3rS00kr7/2OlOl3a/1XLmcXJ\n7bRnIiR1QDgpwAcEz1oYfnEYbqJxLkJ3TWI3OwSxFzCGdQTCch98+e+F6l5zVJ6XQfi8JWfuAogk\nO0MxXdy5qMaeDKysWppmUtnYBdhmGuz+EoYlfIJhBAciYB5PJc1ZF4TI7xAgWyIg7YnK7SwMSTgI\nw1WeQbXytfj9y7h2I3Q85qMCuS+V3ReLhY6751wVP5vi9w4IhEdGO24HnJ4zc0PBPypimD9BAPsN\n8GzsdgeCzvUBQu8C76bE0VHH99BZ6YaAvS86MxNwqv5ejMM+OGeGREhBrZwZjduybx/3/CYl7sDs\nFQMQxIoUdKdRySwyr1o7HoQq6Oo4LoZG2a8peijCHFZEZXMRwmWnaPMXo18+iXtcikB6PKq8NyEI\nbghVm6EcE23eIfpm+yjPGATaa3GsbY1QPCv6bCrOfrRG1XhO1OezOHc+Au46VHbybBh9NgRnH96l\nEkP/PDoEw6Msb0XbDMdMHU1xxqUIkbgZmJTS92KPV0YgnQ9X14HH58OUOkA7uHA7uLwxgv7K6NTV\njWuvgM/U/KhX7yjvzwLUQYdiXtRzBj4X30U/3pHcgh50DE5OidvRgZqI/xdsEnVYiM/QeJwhaIFO\n25b4jG8Z/fEdP8L+rlKdUnrpH5yXc85b/5gb/zusVKpL+79g//fU6VKpLu1vW7yIP8KNNQahKvUk\nvrwbIwyNwJfpgajOzsIUb6vHuTvhCzghhEzLmVPj+i0Q1uoiILZHeLkIQzXezZmBkSHiTlQ9P0PI\nvxrVvq6mzavaMnkBDHkf1poZZWuAsa3XoIpWxPy2RJV6BEL2AgSz0xFwU9RzEcLbvLj3BATWIl78\nj+hAHIPgdDoCzf0YjlEPHYU34r7DERh3wRCB1RDiGiJA9o/7b0Ylddpq0Z6tMY66JpWFgq8hzNVA\nZbpNlLlLlLdQE2sjRA2t1iaN0Zl5DmFzASqfhTVCIG2I8Dox+rQOwtVz0Wcdomx1UQHdPepaFxeu\nEfX5KPr35fisByrcK6AyXuS6BtPnTcPx1iHq1ynKNDJ+PxvlWoywvwrC4CwEvmboyHXEvi5mW5oj\nVL6HMDgTAXuFaIMh0YaTMXvGuLhHrzh2v/js2zhvZrTv3RjvPiva5Q3s283x+Tk9rj8QYbgj8ErO\nnFk0eGRdeTba4hjL0WwcTL3BI2rMhyHPwppPY8aXwQi9y0W/PIgO1LQocz0cy8dFeXsBn+fspoMp\ncWK09cpR/g9ydrFxSozFMfMGwvGGOLN0U7TbFzjOWmHc/wnobLTGsTwa2Kxabut/2v6uUp1z3mpp\nL1paaaX9+6xUp0srrcq2xCntUfHveqimNkSIuBNfyEVYRpG7eiFOFW+Hqtno+FkDN8v4HQJAGwzZ\nOBRDRL5ESDotrnNaSvwSAWULfJEvG78PA16GadtCky4yBMDO78Bay6NyVyOOnYfq6nsYorB6lL8u\nguhkBKprETS7IdishOr2VPxP4YY4f3ME3s+jzqMQ6HqiMvhbBJ4GCHnd457nIJSsEOcsG+02Nj77\nLP69HjobxVbYbaKNWkbZno/7H4LQk1A5fgQhrn+169ekkje8Fc4YNIxzVo+23g/V4fkYTz0xJfZA\ntfl+DMs5EuOCXwSIONzdMA5+IcLnAbjQbRiGXjyJSvrEatlRXs6ZvpGG8FscO13inPYYgnIlhv1M\niHqPj859EB2up6iovx+jGrxDHDMYwxZ6RzmvwXG7Cyrev0fY7oqQvhghuntcd+No23rRdmOiH1KU\nd38E0/UxfntZhPSXcMy0iWveher7cXG/taLdX0Ol/IDozy1TonPOfJISy+EYGRixzdlrff0hrD8d\nPm8Mi+vAYavk/PaNcfyIuO4UhOUzU6pyBPeJsfJVjJXG6ASsEyFFoJOxQvThbpjJ5gBUoxvhczoc\nx/UnOTMqJR7DBcQrooNzBzplU+Je2+C4vOPHADUswULFv7fRS875nh9z49JKK23prczsUVppf9Oa\nIHANQkgajApeT4y1vT0Wq7VGpeweVKxr4XT4MQgvz1OZCn4UQa1fzjyeErsgYFydM/f/ZQFCSVsJ\nlcXb4/5bA68KZ4duAdMax+Hj4cMdUUEdguEk3aMcVyJYjEFVrlhkuCMVpa0jgu1ABIrlEEjrIaS3\njPLXjfOaYLz3Tgit9TGzxCYYKvJdAGTnuOZdqKh/iTC7AAF8HQwlqYEhCofkbO7faN8zcSq/Q9Sn\nMVTtyvgSwu81OfN5SvSK+hc5qzsgFF6G6d1a5cxJETN/Y9yvHYL8L4CbUqJOtHfPnJkZ5UjABskt\nrK/KmY9Soi1mJNmcyg6QO+CsQGNUZvulxImR/eQFKo7XXqh4/jbavIhbvjHau0200eToy70w1rk3\njqc9MH48I3i3QqV1Gm6SciGO2dXjs1+jCr45OnLLR9m3ibouQujeH53B0+L62yJYLkJHbBkc0/tF\nfy3Gsb0AHZNp6JwNiz7vhuO9Ps5MLIzQl9UwbGQg0DslpqITdhJwahEi5HmNdoNeN8GJp/rRO51T\nWmMH+LQhQvuhGJoyL2Z/LgI+jUw0E9ChHIPqepH7vUGMk2EYavJhtMuv4ntwDHdBB6IH8FqsAdiT\nykzVYnQYuqCDc2zUeQaGC/0oW5I81d2r/WyOD2S5+Utppf0HrdzMpbTS/qY9iS/OYpHYPFS15iPU\ngepcdwTNXXEb7rPxRb4WQkOx/fMBmAf3QKBbSvwGgeD3wEYpVcVqAxAL8dojWC1AJexVVP5IqeXK\n8OgmlTP2+iN8dRZCeEeEhbYYArE7wsCjqMp9g7B0Bi7q2gCqtpmuiXDTANW+PqjG7YlK4qUIMych\nrF6O7/97URGtjyCyZUpcibB5Ei7cq4OgdhEu5myGgDcmzvkc1cLzIz3bo3Hd+TkzDNXVAqhrI6SP\nAsZGjPacnKu2GO9EJeXchzg9v0KAUQ2E2MHorKT498YIhn0KoA67E0H3Utxivle00zRgnVAkB6Ez\n0g8BbmUEyl8DxAYqK0a/NsmZKQjzDTF0aG8MpfgljpthUbZfRNuNjXIMjD7tiqEOm+BMyC2YieZF\njFX+bbTt6gh/gzAmfyqq3jtE226ODt9Jcc1ZOfNAzhyNkLl69OuWON7rY3aRBgjG92EWt0E4xpdF\nNfopdBLGoKK7A3B0StxIZeFrDRwTjRBE94i+WJHKFut3wQnvQssiBzww/XZYuDE+o+vhOoS7gENj\n0eO8lNiMSorLTeLalyH4FtlCjsOxX4y9+6LvRkSZXsYxWD/atBkq9otw5qZWlHsCjq914vvJVNsE\naWltSbYpP7bazxE4fdDwx964tNJK++es3Gq8tNJ+0K5FQO2LSuKmCNUfARunxNUIYU1QpZqQc1Uc\nRuTX5XOEv9kYe70SKsBbI5B9ijGo96CSDEDkBb40fopjlkWVvDmwAazxHOTY6KXVSLj7HgSYIs/y\n6TlzCYJxHVzotjjuOw9V3Hb47h6Mcb3dEYxWQnBqiu/o+6INlsMMCk/EhiU1EKCOQFC6MTaleY7K\nDnXDEYSLbBmD0TFZF+O5V4i22Q6zSsyOa8+Pe60KnJcS56NiOAIBcG7ObIJAdRGquO9HyMMDca0T\nUUU+Dh2MBxFWr7cNOSP69XIEocsxVnbjlLgwJfqkxCZRz6uAI3LmfIT04vf6yV0xp0Zdu6NqfFrO\nDAKWSYm1o2vfwlmDaSnxbLTHk6iszwRODUBfjDsZLkble08EubViLFyK4SSrYqx3d3R45sUYOTna\nczo6YxfnzGPhcLwZbf8AQvhqGC7RKPp4Yow/cua1uP8ChM19o786R5ucE/X+NbBHpJA7D3NxP41O\nQJHx4xEc5+3j/jXj/pvGtefibMJh6Gjujs7DHkAbuOvxuBbwXRu4sDY6r51z5pOc+Q5oETMN7+Hm\nQE9G/Vugw7gAx/2R+Oz+GZ+XJ9D5PQfXUOyEMzOtcMZhAD4DsywL30Z7zcJnq9jsZiSqUx9Xyrr0\ntiRK9V/aLPTmSiuttH+jlep0aaX9oHVHEJuC8FObigq7BirTrREe5+PW0wemxDGYfWE+guRRGMJw\nNCrap6N62gNVrpwzgzGf8+px/s1x36NRSWyJL/NtgI/gmqHwRsdKUZv9Ouf670aZhyGQLQQzTSAA\nNkGIfBuBaiECWD1UOvsiWHyJUHwQqo+HoUI5BFXtBHyd3C778bj2EXFcz+RmNqsDD+XMnTlzdc6c\nhWA4J9pmM4T7BnG9QxG8dkQ181bgo5x5MWfuDcjuj4rqocgNq6bEyQh4tRFMr0KF/oSoxzsIuoMw\npGE2OheTo63eQdDaBmNqG6Gj8WAsoLsMgaxfXLd9cqOaXaM+9aNPj0Lno0bUZygCXlt0zn4Vyuk6\nVHYmXIhK9JsxTs4LiAYBukb034gYJ68gYDajMiZHI3g+jgp3T3Q4ik1cNou2ObwIqchu8z4JQXpS\n3O/AKOc4HCf9U6JGAOrhGCq0XNR5MTokxbqArsBbEdbRDB2TYbGDZLNo16fQAWiLTsBVCNN7YMjQ\nCznTJ2cOQ4BtiYr7y1RlkNlpbThuIlV27brwXS9gtZQ4OSUOxJmJExB6i7jpu6hsDHMWjrMB6FgR\nbdUCx+Z66LyeizMD38R5M+K8zdDJnYPrHI5C52AOOgjfRPsUOcR/lP0gVKeUnkgpPR4/xUrmHx13\nUlpppZVWWmn/YhuIgPUwMS1OZcOyo1H97IYv1Kb4DpyFCtgIBK5WqBaejopfsYV0O1TDegO/TImB\nCDnPIBjdhFA0AtWz13PmYKA2zB8K1xxaKeZyz7o5BiDsP/KXFQkFMVMBiI4Iza1R3T6aSnaKgQiu\nLRButkXl7Tqclr8d1bxnUAnsiOrk/ggafVH5q1LqAug2x6n4O6IND8WFg50xNnovhNHnENg6hlp8\ndEq0R+VxAi5k6xWg/SBC3BoIbOvE9esj5KyJYLZ31Oc3qCIPIPIIY3jFb2KWoX/0Y+9otzk580SE\n9PRBBfVuVDsPQ0X2KuzjPdBBeQXHxkfY72dEM/RGpfqdaIe3EKzPRwekAFwQzKoz1c3ozK2AMxWN\nMYzhSQzL+AKV3Vq4WK7Ib30GVG2kc0E4QsTx0zA2+lMcc0+hwzUp7n81gmeR+/l9DLtZHsfDtxhi\n0gWYnxIb41i9IGfeCLV7arRrE3TK9keHYkOE1KH4DF2dEkelRBcE2wejXTZCgB/jeV03REcCmFQD\njuyKMyu3RLt+imOwCz6TL+Di1ZboXCyMtp+MsxjN8FlcHtgtZ6ZG6MvpGIu/adTzimjPt6Ltl8dd\nFT9DCJ+LKnU7dBqmxu8fZUuyo+Ll1f5eCHyVcx79Y29cWmml/WMrFyOWVto/bYsxjGMXzHhwAk5d\nL0Zg6hG/F6Fa9Sm+44rttochxLZBhetNhIu2OJU8Hd+b3RF+9kSlcAACaReEkBcx1+65QFO4dGsY\n2dwiLrMYHhsGHJESjfGl3hholxJr4Mt9as7MReW22CSjPaqt3yAg34nx2g/FNX6DUNCQCjAcFnU8\nCiG2AcJVg7hGAWBFZpG5ACmxOQLzw1HvzgimRyE8n4ZK6HHoaBR1+ApDRb5AoO+CQL9CSjREmPpV\nXCdj3PHdqNpuZFtxG7LG9ejQ9EcYXQMB/XKE9a2AxyI/+THAG8ndIScUgyFnFqXE5+gADI+yd0Uo\nnBD9uTvCXQuE3QnAJbGJzQ5UYo1HowO2GgLa+XzfFlPJh17c+87os2PRWesb9a2FwN4o2qktOhTL\nxmc7RrmeAm5OibPisjOirzKq1Kdgn6+J6vckHJMt0XlYGR2jSQj838U1J0e7bo15vyfH9Y8ELo4c\n1LWo7MLYGsfB7VHe8RjWsgc+Z2OAejkzLcr6LD57H+Z8xHcpHVlkZQGe6g6pfc75s5SYGWWdiWA+\nBB3EgRgC1Q1nYoqFxcWMSV18NvpGNGTGMJgir3yRx3o5BPZO2NdfpETXqNvn0R/vRRlOqjbrsNS2\nJDHVr+ScX0GPZxgwO6XU/MfeuLTSSvvH9v1wjzLko7TSfshyZh6+0Ofi9H8DDBVogUpoawTExxGO\nNkCQ+4rKFuAroXpaxGTegwrhCwgnJyD0XRTXPAHYNGeeQ6B8NGcuxXy+/WD8EOi3QqWUtS7OeYMT\nERy+RFD6GpXKtRCujo+c20Wc8joYotAHY0qvQZBphnB2cNRtEsL1GFSrb8L/PA5BxXQCxu2+mzNn\nRUzrM/FZXQx/uBydihNy5lVU+26MdluEcdhvxaLAmxEkh6IDMiDucV3cb0CUZflom1/g1H7zqMPr\nGK+8DjovRV7mIzGGd3PM9T0cIf+LnHkw+qpRShyTEikckGOAP0b4A1Cltp+OTsBChP8+ESbyCYJu\nbVRzP44+eA1VcuKc5XCBW5EqsDvmRp7B920RUCMlWqTEoZHNYzsqaugzsTnQBjgzcnL00WIcjx9H\n39bBsTYu+u8jdG56YMjO+/HTLdprPVRj18GZhMLZWj+O+SLK1iru0yH6sKjzeSlxTyzknBj9ugPC\n98Po3HyL+doX4TqEvujc1I1rtwc2SYnLcEyMRqenoQtf574HHUKMXVwDWt4WDmd/BNpeyKNFCMd5\ncZ1GADnzDY6ftaLfxubMuTnTJ46dF+W9D2dh6iJcv4xhTfPw+dgb48YbR7tvG/2zOv8iW5KUekdG\noedSScWSsWNKK620f6GV6nRppf1ouwpfml1RkVsF33UPo9JYG6f7T8QX+T0IGzuhCvZ1zmwVKvLP\nEO5aISA+gbDYCJXCZxFqF6XEjgg4xS58C1X8ft0eFoYQ1XYhDCniNh/BxWtDcmZQSuyYM38sKhF5\nebfEkMvtEFTuR2A4EdXaTxAEeyLwFfmjv8R39GVRx1pUdq5bAdgnUs1NjZ/9UGGfh/G9E6rn682Z\n91JiV1SRTwfapMQsdFyOC4VyZ8xMMRhV8O4INgdh3GyxQG8HBL6pCJv7AffkzNiU6BuA/Gb8kBJH\nARfEda+JBYbLIFh/A5wf572ZEsMxtvi0KP++wNNRvusxVOKIlFgZwfIGZJoPUOFtivHbL4XCvS4C\nbBFWsSfGeC+gmqVEa4yxXjX66bGcuTO+a4wgfWdKnICq8sk581aEW+yDsws7YhjMA+ik1Ed4vCIy\nsnyIYPgSzj5shELnPITC9XA8to16DI+/14h+6YKx0lOBA3JmVrRXX4zPPgl4KyWOQ4W7N4J/g7ju\nurhxUFHftTHs53F0aDZEUB+FY3ELHIcXwjJHw53TlfiOEwAAIABJREFUYMt24uPEzWDZy3Ie/3hc\nrw06tBNwlinhc/o8cExK3IBO6DM4lleO89rheCzA/9245/4I+oWDsUyU54so5zvo2G2BUA+OxUH8\nSFuS8I9TgK455x8da1JaaaX9Yys3cimttB9t7VC1m4GLwz7Cqd4uqATug9PYRUjI+gig9RG2u6dE\nvZyZDjyREoPinIMRXvbH6e99gbdz5ozINnEDKsDToxzfwPGbw+NFFgng+Nfh/7F3nmFWVFm4fldn\nusk5i2RFgiIYUDDjiDkLYsbIGDCAAoIgggpiRB3FNGCOCAqIiqigBEFFQAQBkSBNbGjopsO+P75V\nnJarc70zYMBaz3Oe7j7nVNVO1fWub6+9dpXKZlyKAGo/BPW/ZHcjmLsRqYErEETnISU4HSl8dyFI\naAEsCoHHzJiBFlp+hRZ6TUdK8OdInTwPPduX+znqIsgvjZTy8q74JgPtXDVPRxD1E1qotsn/7mjG\nBqS+rkJg/4S39fcIqlshmJzvf69HALUawVotM2ah+OYdZsaZCBCP9TJHW6PPR9krvsV3WPQFkI8j\nOL3FjOeQun6vGV1R/+cj0OyDVM3JwPGef7yct8GTaBbjfi9/AQLRKxDwVgNyPWb8VD/fT96uT7n6\nH5W/MVK61yIgPQHNLswECIG7XSHOcMj9DCn7N3h/7YfGaHMUGhJB9Czvp94IeusjZ7KT/52FwHYt\niXjyLASQU0Mg14v4MYmMGlHu9P2Qc/Ahir+ujWZSCk2bt5RCMyY3+PWjeOWJCFobIoX/ChTf3AbY\nCu1nwLl14AW/TvbdZvZuCKHAj5+HZjIqoNCVi9AMyVMI+vui+68VkOehOYehcVzK+ysLuMHzXR/g\nfTUSrSto668iNEMyx6/RGIWuvMYusN8C1YuRZxZbbLHtBovV6dhi26X2CYKFKWiWdT56yC9GMb1b\nEBSeiGDhFASMI/3nT2ia+TOAEFhjRlXk7aYicLnarzHcjC8QoM8G6pm2KB8OLIG3hkGRh1nuuxZu\nnIAAYj1aaFgIpDrA7lA/PWxhPwQ11ZHKfgFS6n5EoRAPobjeVBTeMtmv/yxSGFuhGNQuSEWt7T+3\nIqi8AzkS9yOAaoCA68MS5dgf+CIEJScwowkCzWQEfc8iqOyBIOVjBLvLvfxRSsEIJqOwmnpoGn4T\ngrL6KPa4rWnjmc/9/WmeYhAz9kJOwqkI1LJRCrzvPf3dUARmbZHS+yEKCbgWQdqb3u4BKatzkTqa\n4/38bzN6oRjbvfE4YTRu6no/XOD9VxfB7eshsMLL140SIbVmZCLwbODfXYLnFI+yvLitBpp5hpIn\nUKjKi96OD5vRx/u7GM2UfITU/TneTk+iMX8Wmolo7/07EKm4H3ub5US/mzHIwzwmIUBOA/qFQJ4Z\nPZGDNgupvQciWL0dhZccARztTsAKNNbSvS+Cw+wryJH90vvkPPX1lTfCW4/B1mSkoF+NZnaO9jqU\nQ+A/z+vbFI3jASHwji+s3ILGe7kQ6O2q+SAfL5OBrb54sj1S9Muh+2CZn28jAvTXkUP2PTDGw4j+\n5zjL3wLVtwJTzexzNDAACCFc+79ePLbYYovV6dhi25UWAvlmXIlgcTVSzjYi9a00UpnvRVP5GQiu\n8tADF/RQ7+uxxZ8iUDoBTT+n4OnRPNzgJQQP01GscBFSx96CxzfBstY6pQFXDIXk74BjQuCfZtyJ\noLIxerhHi8VAEDIdxdQ+i8A0HynRTwK4MjsFgUu0w95YBKjzvaxvhcArZkxDkDUDxSl3QpD5il/7\neKSGztqpOfdHcIoZGQhqT0Hq+vcI7vZGQHsWApflXt6qiB86I0j6CoFlJoplTUcqdAX/WR7B+lIU\nUx2Ac91J+cLfPxhB/Er/ea9pp8XxKB63D5qhOMC/Uw05Ef9A8eYLEWh/jkIiGiNIjWwyCj9IJrG7\n43EISN9C46AIKc3HAdPMWFkiT3WSt5UhlbU6yj7SGTlRz6CFpfj3Si6+7OPf2YCcvcXehkPRON7g\n761G6uw8L//zaGwsRmO6HIpV/g6N685e/mloVmIcCm85MWhr8aooK0ae9/GZfsxW/36O91Ev5Pg8\nCwQPvWjj7bEKuN7P9T1yAkejDB/jkPNYDdqfAX0K4DZf0Jlxt9mQ96FXCzTTs9zPf7C3/ytodqCO\nN1lZPPVdCLzoZejvZViEgPsc5ER8gMbalchpWO9ttg79H/gSjc85wNxdAdTw2/JUP+6F+wzdcNEr\ntthi+y8t3sgltth2q7VCD2fQNHhlNI0OAoALEcT1RVCzHpHvZgRoXyIovQuBdRZ6uL+BwGWDn+s5\nBMAtkOp3ts717xOhd9tEcU7/Ca5NRZCVYUaKn/NLBPOV4Gfp2a70vyv7KxuFgTQ27e4Hen4XIuAY\n7/U8Byne2QiossxID4EfEUQej2BzCMr80A2YEQKRSHalGed7+UDAvNR/jxbdRfmEy5DY7vxIBHLF\nCExf8/Pn+9+pCHqOQJuaFIZAbgisCIG5IfBJCIz1vkkCWobAXn79a7xvjkHKcYa3TX9vw3FIjR/p\n/VjsbTLF27uKt283pAJHYSbX+nF1zDjKlDP5PASVGUiVbY7GwcMkdoM0759ZCN7vNG1ys6/3bToC\n5w3IufkXQAh8h5TkKJUiKNzhS9/gZQZyfF4kkTO9FBp/0SLRTH8NQuN5Der3BxFIfu7t96P3z+kI\nNPcFFjo4jvd2eNOMC/CFuqbt5Z9G8e3fuQLf1/s/HcUiP4sU4JHIiYkWltYEng+BW0PgCb/mXDQb\ncZT3+8sh8A+4fjZU9vsnLx2mvebtnIsc4Gw02zAEzfgsALLNuBXNfnwAmPfXS+hez0GzMPX9Wich\nSH/JzxeQA5uLHIbyyMlO9jaO0hb+z/ZboDo1hNAjhPB0COHZ6LWrChBbbH9HizdyiS223WoLSaSR\n+wyFPhyPpr8bIoUvUiIXIEWzN3po10IAE4F2exQSchxSPC9F6e9SHVIeRvHPL3t+3+/goX6wrpqK\nUqoQ7hqHHv7nINXsEb/2RwhSr8Wh2kMsGnp5J6Jp92pe3ofRwq0KJBa1fYoAsDIChHx/7w30jH/b\njOEINM9GUFYfpWw7AHjRtN36QqQuzgfuMuNyFKoQ/ZM6GoXFvIwA9yQErmn+szcKj3gRKcs1UZjH\nRgTdS5HTcoMWcP7czDjd+6VH0HbghEBRCHwcAheGwGHeJgu9L4aheOBz/LUPCuup4m1Vw8uZgxT/\nCbBjG+zWCLKqI1X9n8hp2RuB41qk+NZG46Cqt+s13n5jkZJ7GlKtJyNQuw85SobU5ie9/ba6irsU\npRfc27TJzBYvBwgi85F6ug3Baj/kEGQgoO9KInRhM5qN2YoWsL7g7bIKjftbQ+AcEqkSO5hxsbdf\nClKhT0UzFef49ZcjYI4sym/9A1K+a3s7N0Bjci9vq3dC4KcSx6338+JtMR04QAs1S62DfXomvjq2\nMcyq6te93a91KHKCRiDVujNyZFahmZbI6fkWja0vvP9qAwM9ReCpaDbmR6RwB6AoBNYg2L7IPzsb\n9ecusd8C1e+a2eVmVsPMKkavXVWA2GL7u1isTscW2+9m21DYwlcIADLQFHYyguI2CGab4g/dEJiD\nAKwJgseOKF7UEIjM8lRsr/pxfUxp045CYFlLl646FuZ2TxTljEnQ+FYEcBv8+q0QhJ2IoKoVyshx\nDXrAf+yvaBOQ/BAoDoEf/Fr/QsC9HwLBxxDEpKB4338i8EpDoJoKfOOK6BcIWpoiyAwoNOAH4NAQ\nmBUCt6AY1/ZmXO9ZKg5G0NoTTfFv9WPykcKaB5wdtGlNMQK1xSh+uQkCm07eF0PNOBrAjGSPZTa0\nYU7RL3WoKb/wjd5uN3n/Pe/Xeh+FZ1yPoP4R5Ay9i2DxJgTDB5FYqPchGg8BQfNLyAGbjhyLNf75\nqhDoH7TD5DwEc5kIiF9B/R7FCEehEOu93o+a8Y73yVA0FhsgAH4CMVg9M45AsPqKV/dINOMwCS32\nm4Icuq1opqEPmhk4GPX/eWhjnGIv9wKgpxm1/PNRyGGahhyRW5FjVYQcsCOR8xNC+Nkaunb+WbQA\nsTEK8VmPZnF6en+eZsYJHoqDl6EK6tNKwLyg3RrHqb0m74ecGy/yxcVQPB85Etcg5fghBNn7onE2\nHSny36P7Owu4zlMb7o8gejwJJ6UuchL28r83AphRikQ2uzSgvafi3CX2W2Kqz/Oft5Z4L06pF1ts\n/58Wx07HFtvvYw5mL5jSsT2PFkRloNCD6R5CsRmpqQYUexzsKvQwroJPlzv8vYRAewKCir2A/v55\nHwQmz5sxBsoeANk+nVyvEC681Bc7TvLjuvk1nkJAPwYB3iEI9quhUIAI+s9EIIwrytXR9PhSFFKx\nHsHZWgR4axBgReeZ63Vv54vhPkfgfjv6h3QCUvTOAVaXWLCVjxbBfYTgbjtSDsciByUNLRbrbsYp\nwMUhsNKM85CqnYsW6mWgGOkbfEOUHJSZ5DQzHkJwdF8IzDWjecl+NKMBCrep6PV4AEgNgX+Z0Qip\n85GyegAKI2iCYPN75ExE9T3Gy/yOh2t0RJBZFzi85MYfZtzt59iEssGMQOp3hRCYasZRCNi/RpDc\nFIFyW6SA3gC0DYG1Xs77kGq/wa+5CTlUM73M+OeVETwvRwsERyEorYfigMujsfk1itmu4+cY6J/P\nQLMmI9BMxZtoZmEJyjCyAOjn9S/rry7IgSoNVPOsGp+i0JFBSLlf6q8xaNamK2LAMxHoT0WgOsSM\nxQiCq6LxmO5tQwh8Z8Z7kNQGPsuCQwMUG3xdA0a3h66LkQNxOAqpykJO7MnoHrkKOZKF3o5bPMNK\nHa9zdSDZlI4yGy3GnUlii/lsFPZRDs0MdUGO5S6z37L5y96/8IqBOrbYfoPF6nRssf2hVgmFDIxD\nD/83zDgWxWV28O8YArbT0PRxiv9+gxnlESh9iIAGBJRvA8c7iJdzFbMH/DsJFp+SuPywXDgmes7O\nJZEHuhhBVUf/ew1a6BfQdPv+SGE8EkF4kYdMPIsAYRZSNfdB8DzR67EKAch3Qdt0B6T4rURK41cI\nIk5FMdbtEbSehNTXZOARV6ZboUVcA73O0e6OhwLjQuAilAqvrL/3nhl9UY7qD/24w1AIw50lFOgv\nvH4L/HrLgBNcQcSMWmZcZ7Yj7ntkCPQKgVGuSkb/TAcgYO+CYrhbA8+GwKVI7RzjffaR17cJCgk6\nASnZWxBkzUAwhl8/zcu9Bqn947x+M1GqwTsRrE1GoJ7pxx/s368FrAlhx5bX+Qhus5G6u8zbqAJy\npL4KgckI/Jshh2Se92ULBKvDUIjQcj/+ev891+t9hH/vX2jHyiQ/T1WUd/s84GQz+pvSIx6GALUQ\nLUBMResMyiD1+R00q/AaAvI6JNYOfAA0DIHnkXNUyev+g89wfEBiR9NWyAm40YwBDvPNVbeDzoQO\nU9lht1aHZzt620zyfi5EIU1rUQhIe/97NgmHZCDKRf4xiZ1ST0HKdnvkeC7zMs5EztdZyGG4jl2c\n3e63bP5ywS+9H0L4tdyascUWm1usTscW2x9jprzDddBD9CYU2rEUKbJZSKWOUmpNRVPLryKFsMjf\nGwRsDtoKO7JyKNRgGFIeP/MrfgqNR7FDrGr+A5y6FbjK4TsZKdXHezmiaek3ECg85GUcjaBgMFIS\ns7yc35FIZ9cXqcjTEXjcjp7nS/29az3dGSGw1Beh3eGv+1DowTSkThYh2HwCKZCzUGx0R/+8Gopd\nvSEEFptxGnCMGW29vYaiUJVCL9drJGa23wEGeRxrZO+iBAjfAP909bqVt2kdpCC+EgIr2cl8EeB2\nr9dmM2Z7e96HnJN2rrR+hKB4pbfXROQ8fI5AvS1Slyd43W434ypX6AeT2EQl29s/HYHYVyHQx2cv\nzkWKbg0UolAJwd6RaLxFVgGNkyreN7NRCFB3NFtR08M/mqHZj2VmDEYqcBk0DrcicP4Bqb7vIefp\nAzR2olCc51CYw0ykmK9CIThlgN4hMM/b8Q0/5makjCeRmO1Yj4C8Lhp/b6Fx1Q8B/BC0+U9Pb998\n5ESNMmM7cpry/Nh6fs7xIezYzOcq9FAsCw88B4cdBDkpsCIV+t0CF2aie6sachwPQA5ReW+LWrBj\nluJmNHsQ8WgE1Q3QzNJ0BN7fIGX9K2/3ct7e1dD9t8vst8RUtynxOhytuD15VxYittj2JIvV6dhi\n+1NYDoqFPhk9mEcjSGyNFL0spKgVoNjRbDQtPwepdnm4euhhF8FjRs1DBd5D6uEYv95psDAC5SJ4\neBYkfQss8FjsgSQ2oyiHoG+Sl/EU5HXnIJgbhgB4Pz+mIQopeMCPH4QgugUC4EIEsy95HSog6Mvw\nBXKL/L1bkDp3A4ksF8HLcCwCrPOR47EvApjhQPcQWOx124Rg5y4Ep8ch5bM7iZjgZKRSboAdii3e\nflcjdfdhoIsr0scgsJ/uda3AL1tdpDpG9i8vT3u1ORsQ0D6EwmfOQP06H4UHfEhCed2CgKu8H/ua\nh3kcj5TbSFX9Ac0W3IjCDe5EAH15CFyDHJ2PELCdhqB6kBk3m/IqVyWRLtGQ4trP2z/aHbEAhSl1\n9Dj9S0hs214JqcSlkTrdGeUFn45gMR+B9HZvu5YItr9DMHwkiRztmHb+PAA5L2chh2gyUvzLoHF/\nCXJAPkbwmYnCTW5GfbscgXc776vSSDUfi8ZNM693npfhBjOmmvGKl6ct8AA07wU3LEh055oe8MoE\n76N+aG3AAjQzFNDMTLGXa4X31UozzvKZjiLvzwbIWZqEZny+9/7ujzh2GXJG1uyUM/x/tt8S/vHP\nEq9uqDNK78pCxBbbnmRxZo/YYvvjzVXHa5FaWh8pZ9GuiYMRPKcj1fA59JCOMjJURoB2KHoQ38HP\n1WUQdNQFCs0sAym2bqfMh/afIjjuasaBCNJWIiX4TQRMR6AwhhUIRlJIpFGrjMIDFpGICz4FAclN\naLFWXQR94xDYdkQAkYlApCKCqVeBM32B3o0IoNahBY63ed0Mqe4FCCrzUTjMP4DD3bEA37DGz/UT\nApfTkZMyCkH4QAT7lyBIj2YOHoiO9zad6aEdQ0NgCYKpm1Cmiv4eflPS9vbvRJaCwLcAKffLEKAv\ngR2x9fO9DYZ5OyQj0J6AnJND0OzEXkhN/giFClyNHINsBMDrETQ/EwIvezx9utcbFJcMck6KkTNR\nwdugG+KmzkCrEPgUxXdvQk7fzBB4KQSGeHvugyC5Hurnk5BTeDSCxYF+rnZ+3UIEvX38mLO8L59H\navWpaBfC2Wg24Xng8xC4IwSmIydjHApjaYzU/G8QnI9DzttU77/D0Nidje6bySFwE5r5uC8EjkOh\nH9EMx0shcHYIHIrukXyk7lcEcuD6f8I+Hhq0LQmeeohE/PSBaH3AyX49vL0vRLMTP6JsK2X83N1Q\naMxqr8tc/+x4BP2N/BzPedkeYhfbb1Gqd7ZcfN/12GKLLbbYYvuzWgh8RkLBvNJ/NkLw3A4peEsR\nOJZHMANSnzNQ7OgsBBYtkXIcecvno+n7I5Dy689FWw+P5yGg2ojA9wwEi3OioiEYzkJgOxUtnKyH\nAG46iR3pOiEFeDB6Zq9CMcMbEXx87+X9AE3VT/LPXvLvdkZZL8r5IsQCFEe7FanDn6K44rpep4DA\ncyZSCich0LzftNthAZBiRmmvU7QZyiNe/qtx8AqBbWhL71tQho5ctBDtApRVY94v9FlBCIzw891s\nxiUlgH5vIMeMyz1E4mmUym8bAq9zvY0GoRji5gieqyDl9zrkAKxAAmFqCHQNgYP8vWO8P+d6387x\nMkchEkXA454ODwSx9yBg74ScjO0h0AuBfUe0qHA62nCoI1DaY4vLeVs9Dhzpk5vdkNq80vtwsH9v\nNQphqY3A/hIEzqO9vIv89Toaw8kItq/wdq+CnMdP/by3AdX9msd73aKFtOvQeoP9kUM6IAQ6ktiQ\nZbm3XQs0O5HtbfEJckLxukfq+3VmnO5j73M0rguRkr0JyveC/jMSI2B8XTh8iJ9/JbpHXkCwvMJ/\n34ju3RQUslSMxuhSpES3RVA+GzmYeyOnMcV/1gQ6hcBCdrH9P6HazN42szH+GovofpfGoMQW21/d\n4pCP2GL785ln+bgb2BjlC0axptuRWloNTVVvQmDaDIHhNPQgzgLweNBPEAxGYQy1gKdh7rkI7Nwu\n/hCqDUGA2g4BcSZ6mJdGAAhSz4tRGrBmCLwqIBC6189ZB4Hxk0htW4F25WuOQPZRBB5HeN1SQ+AL\nBHjRDosLEEweghYhHuSfGwL4Gghgf0IwGimuRX79qggMb0Aq7DkI9N7x79ZCi/9qozCCxQjurjdj\nPAodPRM4xFXpmZ5H+NdCPPA2z/YFoF8B/zLtcHm+l2ESchrGh8BL3gbNUTjIbd7XtyPg6oEcmAFo\nEV4Bmo24HXjQjNZmnIvCQ97zcxkC2lYIQId5O0ZpF//tcckNEWCmoDE13a+HLz68GTk0p6N+rgd0\nC4G+JDYjqo3G4Tf++xz/uwA5clFmj2jDode97EejMIhUNE7zEVBuQVA9GI2x3ojb5qN+L4VgtwOa\nLbga9fNGNPZeRmOtJlp8WFSiP25Fjkx1pFo3RvmnB6HxcrSXcX8vzweIF9cDw814Cjkppbyea4Bi\nODtArWjcAUsfg+3PozFZw9tjjp+zq/dzQLH7wfuhDQr7WOWv93RuvkAOa7R2Aq//RHaD/Raleiga\nUMNQJ7UPIfTaHYWJLba/qsUhH7HF9uczD1FIQQ/VyAYj0F6M1OhXUFzwvuihvT+Cy6ySx4XAqwhg\nmqLp8fcFb2c1ZkcIQPpCeLQagpRvkTIYUBz0pSjGNNqkpSkC5Iv9mkkI7GchON2KoLmFn8/8FW0S\nsigEpqLY00v8++le1iiH8hBgWQicgBTLDggs+yIYfB0BTxQDGymG60hs2vISyokcQuABBCnDEES1\nBk5yiL0PAdc/vI49EXBnIGeg1E7ds9Ts12e9zahnxvUISOcgMDYERD96ez7qX78N6BkC3wAzzbjQ\n494Ho74qDaz2fMT7ICfqS6Qcj0YwugDFIW9FTsY65ACt8Xar4u273cuTiiB/CVrk+hOaFahhRkfv\nh+1ILf3Kz4mHjZyFxsKH3jYbkNI6GYFuUxJ5nrt6WcojNTr45y39/Sj85A00lsagRacjEBjP8HKX\nRop3WT/PQm+ful6WLmhGphUaX++jTYCiWQK8/O94/Y9H8d4foxCpFOBYM/p5HWagMVQehS8FdD+d\nhRyqQuQYzgTeg7ufhmQPA/lxL7jrAhS2Ms3rOxA5ut8itbyWl7cfckY6IMcxC0H2g37uc0nAeWVv\niwthx+LGXWq/mv3DzBoC1UIIH+30fjszSw8hLP6VQ2OL7W9h1avXc5iOLbbY/sT2OHCbGScixfgt\n9IDPRYDUFD2c15DYBTADhTAUWiJvMwiODkLw0tXMDkIqsduzayGtu3+vIsrPvCEEvjLtZrcKAUVj\nBFStEdBG6tpItCjtYKSYdkWhCGkojKEdUjDLAo3MuNnfz0WAE6mZINiYAxxkxoMIGIvRc//cEPje\ntKHKWKRi1kBA0gupfEsQ0J/l5brHjH8hEF2OAOdJoLWHEFRGYH4biucdgMIDTkUhH6+Y8RraBjvP\n++FctCtgZJW8ThXRVP4LocROfWbUQDDdFrglyi0dAkvMyDSjfAi8a8bVZrRHoLXC65xrxl4IsrP9\nVYig8BAv92YUi/4MUt9vQM5AaxJOWDqC5xlIdHwRxWov8/a9BOhtRgfkeOyPlPVtQJIZrwPTQ2CI\nL2S8ycsU0OLPKHTCvFxzSWxRnoaU5VsRON7m1zRv485o/LRBDt0iNJvQAsXx74XGem/kxH2FNsO5\nqEQb56CxP9n7YIAZfUrcA5DYQfJLFOc/xdu9nJe/C7qfLkf30zA/pg1yyhqjsXIkCqHpBF2egVcu\nhrc8b/R9B0OjqtBlO3IGNnhdk5EzMw2N1epoliINqfRvez9Fzmclv9ZMdI/V9DKX2NVx19l/Uqrv\nR9McO1sOP78JYovtb2mxOh1bbH9+C4F30YO3PALIlgiMFiMoaI/UvdPRQ3sFUmafRXDzlRn3mDaZ\nKEI5hCtD7n6Q/HDiSnt9BudMCYEvEaCuRMptMw9DWYEUtRoIZg5EoLsNLWr7CgHJNUg1r4HUwEw0\nbZ+DpsHbA0d4RpGRSHkth2CqtRllTRuO3IyUwsYISOohZXIJcJgD3aVItX8TwU4UqpCDwmTWonRm\nnZBy+QKaRm/k7VPL22oaArujEVANRttFf+TH1PH6TUWbj1yHAKiqGc3NuNVjpOsCT4XArSHwePj5\n1tcgJ+g9FGZxhcN8ZGNIgNKjKOTkbAS8vbztu6OxUIwckd4I/k/0Vydvn6Ek4oOnICfibaROt/C6\nz0FQ/iQKszgO3y0SgeyPSMEt7X2wn//cBmSZ8RhyqIYDewdtcZ/l39nLyzkJAeW53ket0Nh9AGV7\naYRg/iGk5M9AqvD9aA3BMjQ+1iFHMMPb7hEEotW8jCXtTaTkzvDNYt5GY6mkRbM7H6BxXdqMe9EY\nutSvMdE/P97rcoO31/VoDD3kdT3b++MuGHQvlPW80ZvLwItPIIcmE/XfMDTOWnj/dEb9uA3dNxNJ\nhMP8iEJqHkaOUabXeSWadSlgN9h/gupqIYSvd37T36u3OwoTW2x/dotjp2OL7S9pvdEDfSlSrUoj\nqLsOTX2PRtP/wb9zC3pA34zv3IamtA9CC+L6wsgXoOhAP/92GFOMIBqkIi7y+OYiBNAVEQgUo2dv\ntIAsyjbyAVKvc/3zUQgk1iFoq4xCCWYBH5hRNQTWe0zxW0iBbI4g6AG/7iSv07EhcCMC3G0o3KE7\niv/9HMHJhwhajvNzrUbAVw6pqcPRNHpPpEQ/EAJXoXCPyxDMHIPCSZaEwDoAzy6Ri6CvMVJXv/dy\nnomU70e8j2ZHx+1spk1mtnlZB3nZU80YbkaIh215AAAgAElEQVRDb6/9/XuVEHjNQ+D5jdfhMK8P\nJPJW/+jlz0GO1v4ILI9BALscZZAo5/WejGY3ot0vv0LOzWwU730GckTaIZhM8j4chEIX3kZOU2M0\nTuoDF5pyiW9GsxSl/fcTSUB0PaTS9vfrzkYq9rfIaTiSRNaXJ5HDeIZ/L9qFcX8UZvJPNObXAa+6\ngo/31zygXon++wyYa8ZlJbpjDRrPK9D4nYick3PRzMQdaDblfATaGWjGaC0K4zgU3W/voVmSrkB5\naHYCgm63sYfBnKVe307evs2QAl+ORB7u+cihm4pmgp5G47AhcuhmI4espR9/H7vJ/hNU75zKpqTt\nHBsVW2x/C4vV6dhi++tZCLyMQgZWoIf9vkiJ+wGBVx0UIlAJQcxhCKYn+HejXfQKgDKwYTD0q5e4\nQtoD0GI9CWBrhFRoUGxrPwQcryIwrYemq/dBKnJFBIVjEfzMQlB8AQLQS1Ac8DakBF8NjDPjMs9w\n0RJBZBICj/5ep3QEx83NdixKPNTL8SIC5AvRhiyZIfAMgo/DECx9i+BnPXJGmiNI2g/obtq05UgE\nR2u9nGNQmEPJnZef9va/DcFlGgLGaJe865FKnc+v295IqR0aAsFfb6NQiJORErsMAeMApCRfjeA4\nhEAOytRxHILMffw7w9ECt7FogWhVpN7f723V1tuwlffdAuQQ9UcAnI36eCvwhs8gXO1t/Sbq63oo\nnGQg6r/hCCQ/Qo5aVwSGlyMHZCNSW5cj8L8Mja1FSAkGOSlVvNxZSD3+DDmKk1BISeQUZaKx9LTX\nr7rXf7OXcawZzUq09TYzKkV/eBx1nhmn+98BjcUmyBk7w3e7HIT68DE//zYE8leEwDMhMMwzo+Sj\neyoJhX88h8bERlibCjbLL50Ovdp7m6STUJzf8LoOQfflYjTul/g1j0L37zMIspuhvs5EIP4Uu8n+\nE1TPNLNuO79pZpehGz622P4WFqvTscW2R9j7JOB5P3bshMgnCAi7ItWxKXrol/eFbcvQA7s1AvJN\ncFkqbMzU4ZUKYFVrP9/5fs46wI9mVEAw1dSvPxzFdrZE6l20HfhKv858EhtVNELA0s5/rgfyQiAb\nLTJ7GeWcHo4AeSVyEN5BKmj3ELgZqdMfoen3V/3Yy/x6hyJQfNrLAVJ1qyEF9VWk8t2EwiAq+LmG\nIRX9eBQHfIUfG4VXlEfp8I7y9HEDEbytQxk7XguB3BCYidTWh7z9j9oJxkvaCcA3IbC85JshkBcC\n9yEw2xflKp4DvOhq60wS2VkaIFX1TATDl6BMGhnAGM/YMRPBWS+kXnfwNmqB1NZ/IZgdhEIsVqKF\nn4OBc8wo62Er53qfpfp1D0aw2xCp+yehcXaet1tlv952FPe7Fc1qrEdbyt/in32FnIZ0NENxtn+3\nLlp8ehECzUfQ7Ew1BNafovEZjYeKyIFrimZnxptxqRlVEJCetlM7jwLqmO1YQ7AV3Udzvd0h4QSu\n9Dqcg3bH3NFnPpOwEY3DfOSwnO8/x0HqZHj+28SVJ5SHMWXR+JuMnImv0Bh7AjlxM9E9d4XXKQfd\nP+1QzHw+crZSUC7tPHaT/Seovh642Mwmm9kwf32EvKTrdleBYovtz2axOh1bbHuEvYtUs1yk1m30\n98ejB3quf14bwcqZZjty296J1LCVMGcuvN42cdrKt0DFcmjavaanDdsPgdINJLaZ3oRCBt7y65/t\n193u116HFLjSKCSlNlJZ55BYKPeTaUe/G5FCeSxSTluiMIryCO7fjVKhkYhprg5cGQKXIbVuMIKp\nJgiS63pcbLQY8i2k7AUSaeN6eZm6IA7oiuC8E1L/jkWq8VFIib4a5TnuHQKvobjXwTv1ywbEIo8j\nh6CTGUNKKqeeE7sjio/9NduMlN33EOTm+eYsq4BpZlyCnIJ0r9MRyCGIFhR+DODhNGmoP6simN4P\n5dUOIbARhWEEBJD5COJ6I0B90oxJSEGvimD5NQTq+6J44yLktFRAzsBdaAysQGPlbOToTUOhOqXQ\n7EEZEuE7VVHYSRZy9toj5yoJhRt9jvprX+Q0jPY2fh0p55uQI1WMHMuBKKRmPALxDjtn/kAZNTqY\n0dL/zve2+MEzufRFKvWhXs9BaOv4s/1eAs1srENjdiSC+yuR8l9ebXHufnBWCfDtUgoKktBMSeT4\nRjM6hV6u59FYvsDrXh+FqXRE99M2b9tR7Eb7VagOIfwUQjiUxE5SS4E7QgiHhBBW785CxRbbH22x\nOh1bbHuWeaaILxBURdsxgx7MVUksvEtFgNMBhQAsQwCbDmyE7tFCR6DCt/DNP5Aq2Nlf5dHDvTEC\n2XNR3O5QBOcnIphORrBUGcHndgTdMxBoVEIQ1BrBwb0IEAf6TnjzvQ55SMWd7+VahQtfvkDyJgQx\nd6JcwUkImp5Dqu0qb4+KXm5DoFUWqdanImfjqxB4CKnXRQgSPyIRnnK5t99jCAA7eRt84pB8vF9r\njqfKi2wMUm3TgM1+jX7AIWYMNaMNClOZFcLPspvsMFc/70KOTFnkyByKYpFXhMBE5CCc7m3+LQrx\nuMuvPXmn7BYPIudiIYLWVDyvtsNhZeSUPe6/P4NU+yUIjLsgZ6G+1/lktK35RqR6L/P2bu1tHaVv\nrOzvNfZydPR6HBYCfRCoZqHx2g5B6RIUGhNtflIThazMQLHD872/aobAaM+5/jnq2wu9HschxXwh\nGncpyLG614w7zTjJjFLeRgNRfyehuO3DkQP2AgL1q7ycw71PJyEHYbgZDRD8H4hCZi7yY5v4cZd5\nO6yAHndDujuGWxrC/e2Q85Lp7dQWOXUF3qY/ovstip3u6OfPQTM/ecCPvzaGdpVZCHuu+mZmYU+u\nX2y7zwTT0dj5M/z+ZynHn+33/+74nx/9R9fhP5QzhNir24VmRmukBhcgCFoeAnlmTEHQehla8LQG\nAedgBGmtga5w7xdwy02JM5Y5HHLOQKEEjRAMfYYe/P1QvGg2mgbfhGDoAhLxuHkI8I5EU+Bt/bP3\nEQykITXwSrTN+B1ej9IIQkohOElBU+CjkBJ5j9ezEVILj0Tp2coiIClCivjtKKVasWejaI3A5N/e\nPqkIuoqAx0LgRU+btgDBYi2UxzoJeDsEJuzU3jXQVvHJJGYGyqEFdP3QFtaFZtyFALFdCIn8wWak\noFCHFsgxuGgn+I3a4m7g9hBYZ8ZUFAZwuLdvGwS6h6EwjLNQ+Mc6BJejgf08p3nJ86YgUHsdORX7\nIKW8GlJ+tyJYuwtl6zgLqd0p/p0DELAvR6EZb3qf7of6twkKneiMQjxqeX9Gm6U0QFD4BHCd57ce\n5X2yEMF2NRRn3YLELoPzSSzE3Q85PWW8zE+i8dkfhYMkIwCNtjjPRI5AoZdnLerfTWgslfJrr0fj\n6g0vQxGC2AIUZvGDl68OkBQC/X3WoDeKff/S+6YncsIaIIX8aTQTMj4EZpt1ngwvdFCPVAzw7XdQ\neRsKL1keAleY0Rk5qhmwQw0/AI31LciBKfA+fD8EzmA32n+zTXlsse2RFqvTscW2x9sCpPSlIOjq\nYcYdSJ3riSAkGcHsBgQ184GGUJgGw7qUONdoyKmHYKA0UgzXIrW4EYLGISgUYjV68M9E8cNtEKBM\nQYvoipBi1xLBfJKX8zaUFeQA4HUz0sy4CoUWvBgCA0JgbQishh07Kc5H8NQdgVY+gpyTSaQV647U\nxKlRrmcEIHj95yK1Np/EAslLzfgEQVkxcgbaIniaBtT3xZA7LARWIagZjWKzKyL19HmkMg70cJbm\nXsedFypmeV+c7D+HuWqaBD/bMfMOB+pDUOaSegh090J9Xtnbtoe/fkQOThtvhx5mNDHjTDP6mjEA\nzVJEce+XkMgFvg2Ni94I1i7xLC/lEGC+53VrT2JMvERiN8NSaLyMRs5WJorRnoBmFT4hkSd7BXKI\nXjHbEbdcD4F6DQS4U9H4uhqBfiXkNLTzax2EFPsfkGPVE4XZvIscyAyPPe+BQo3qo3CVp/z4jeh+\nSUPw3AA5SiuR89LKv1cepUN8LwS+RfdAMlDs/VXD23KG93VDBNSGHLKr0f03JwRmq6qPTPNyA+sN\nTljkbXUIWnybhZyjyJHJQs5TDnJEKyAVv52368/G5+6wGKpji80tjp2OLbY921yNjHbDq4Mewlno\nIZyFgGgoAp1jEXj3Bc6AgaXgpxo6U1ohvD0RwcVBwJAQGIAWd+2FoKEIwetsBN4gEJ2HAGUbAvAG\nnq7sUS/TSqTkjfK/QUpkS6QOTvYY5Z8t2EPw+gNa1JiH4L0hig2O4rdXIJi7GUFGOwDPa324X7MA\nqeZZKDSjNYpfne3tlooU0Y1I3TwWhTs0QfmKL96pXE+gGYAJJDaEWYXgPAOp5fej0IwzzBhkxkVm\n1EYxwUPQP+WFKJZ8CwpLuAAp8gNDYI1f63R/7yCkGl9AYpHna6hfy3l5jMRMQn0vx3d+/BD//GsE\n1FcipfloBOOpIbAWgXZ1M0ohdf8Mb+/ySOn9EHg8BHr4+4d5OY5ATksGiS21ixDsHoU2J1nt7X+K\nfzbcr5+G1N6VCKhrImW5KQpTOgPNsKxD4Pw1Whh5BIL5s4Harvg/i8ZWlNFjotfjKjQ2v0NjsAya\nCeiL1PoNKMwiza97mr/XNHJ40PhOQU7ZgeheSfc6fIPGzxw0rlZ6ZpEkzyuPGalQIQ85Gm6zjodZ\nK5CTUtv75A50/1ZGTtJWNP7PReN0iZfhnZ1nOXaHxVAd29/aYnU6ttj+djYFwdB8/3sVAr/qSBWs\nTGJL7LXAq5C9CQbslTjFFd/DiZejKfQCEop3PzTNnI/gpRwCnyVoWrstgtS1CCqmIXg9HIUXpCGw\nqRkCwxCotkKQvjAEbvZY6l+y4N+dgRTuXASTHRDI1fdyPejXzAA6eszypQh6L0aQsw3BTHUELN8i\nWHkXQUwhitte5ef70ut1BpBmxnXRwjRX4Z8FLg6BHAez+Qj0PkSw9QGCtKcR6H7qdajvn1+I4q1D\nCHyIVOJO3kcnmpFu2h0yyjV+EEqjthnFerdCC/aaeduvQ0ryVqBHCFyMHIpDvBz9vCybHNhHeV+k\noFj0+zxLxuNIjb0HgfqB3ue3k8gbHszogiC4EIV+BAS49ZCTsAml4wsIpm9A8JoaAt8jWL4TORYV\n0XiY4+Wd6P3UBUHrl8gJWBICDwLZPpaGI0fqA+AsM17CnUBPjQgany8j8D3Ty9kYLQ682+Oqow15\nCr1Or3s/LPZ2/9CMf6Ox1hCpxcO9rMchp66j9/1ABMKNgdNCYCQJa4bg+1Vo8qPeKk6CrmWRQ5aN\nxm1lNO7qeHnT/dzN0f2Vg2KpR/A72K9uUx5bbH8HS6jTkAjHii222PZgewhBSx8Uw7vZ1bVe6CH+\nGolNRurqdV1F9PAGqm6FgZ8B61yBBMCMdgjG5qFFX68hoG2KIK4DifjkagjGixDolEb/gB7xsv1o\nxjASU/hHhsD6X6qMGXX9usciIBtJIh/0Cwg89kVwei2CxlVIuayCAGcEgsCaCNIO99dYBGGXI/XT\nQuANMw5DQNQHKflPI6X9YRSGsBFoacaVIbA9BGaacbJvWLMmBCZ7GMvt3jZHeVsEjx1eD+SEwNWe\ngaIr0MRDRQqRunpzCCz2PN0Pohj16SgkYS0KU8hGMDzcz/eJGd3QzMEzSNEcasZ1Qdtsn44crNEI\n9JZ5M2/y8i1CIHqbf2+19+9aBI+fIbA/FsUyL0ex+jeFwGgzXvD2zUKLCh8jofSmmrEKAWIEg6l+\n/VFeh4Zex32QKPomCn+pgOD+AzQLUVyi7JFNRGE33UPgB2+HTX6dR8143/v8QbSmoB1S1xujrCIP\neFtt8Pa/nkSKwZZ+ngu9vVejWYLT/LUUhSdtAO7xGH4LgRwzvkDqfyMzWoXAHC/vAcCHIYRg9nE2\ntK8FGMxvApU2wLraXr4k5LSWQSCfixycIhRO8u0vtMVus1ipju1vZ7E6HVtsf19zOJ2IpugL/L1i\nBLXr0YP/MZRmbh18sw+81CBxhgGLoVx1BDR4LO5QFAP7MvCZx6h2QrDzMAKn0ij8YgpSaqcgZRyk\n2kYbomxCISR1EdzsBXTxBYL4NauacbUZ9yAQn4piYOcDaZ7h4FY0BX4hgusPEHy8TWIavg2Cl7sQ\naM/2z95Fcczfk8gGcUgIvOFFWIVgaiiKkb4JKaIn+/tRWMJkMwabcTmast/hhHgc8iIU/303DuL+\ncRT2ESnd270/HkWq82ZgpBkf+/vbECDXRc7Mpd63hSj8IQJukCOR7f0x1M833IymaIYiAzlQ+3r7\ngyB2JVKKD/L2fMjP8whSeDcjaJ2E+jsXOVfXAMe441YRjYngZVuAQPzf3g5vkkivmAak+IJJvH6l\nEFj/G6njbb3OIxDAD0axzBOBMmZ0KtHeW4AqQRseEQJPoHCY9d72j6CQmaUIiPshEC5EY7gVGged\nvY4dvU0OQv2dj9Too1D4SATaV/k19kLj7TEzrkZbtZdDITGX+TkPMqOfaXfJesBSM2rB4dlw3Dx2\nWJkXIT/F2/JCNBPysn9YHzkjq9GswEkkdjrd7RZDdWx/O4tjp2OL7W9vfRG8DCzxXgqCjO0olrQc\nMB5uKqtpZ4AGy6Db6+jBfaZnDRmIwCgvBJ4scb6WCLoeQ3C2HIF8KwTU0eK2mv5ZAVK530ObXHTz\nn9kIBMeYsdCMBUhJbYlCLl4lkXViGYIqQmATAsrNSC1cg8IdBvqx0cYbjVAWhySvf18UfnErCiO4\nDsWvZpVswBBYjGB8EILd2/39R1C4wPsoJKA2SvfWHqnNI83ooJhZxiFoPxo5FqeZcbZ/v4EZF/ui\nwUvR4sBRSDXtEQJHhMDhXoYTUDjEDC9eT5SN4zkEui1CYLt/FjkU8xwsFyJn5xQEytcgWGuKdhZs\nRyLG+m3/7nyUxu1ur/9aFMYR7WiZ6e36PgLOZxHwvowALw9BfQe0gO8FBKM/eTnWe/uX9Vdfv/4G\n78MJ3t4L0GzC+QjEW6Dxcg9yfG4G/mHGIR7iMd9nNqI+fMbLUoxmMQpCYFYI3BcCvdFMRA/v+1dR\nCNNbJHaSzEP3wlKv+5Uoa8w8r/PHKAxqKImwpEtQuMppaGYow/uqCDlE//L67uPF7AKUhxFfQGlf\nVLssAwas93IfiiC6PIkc1EXIgZmC8otHDtVutxiqY/tbWKxOxxZbbJF5doJs4EjTroegB3FZBNXJ\nwP7w3KEw3p+TBtw7HpKWoYd5CgKgwQgU0jw84TAzHkDhBRMROEQ75T2KHv7N/Rrp6DlcGwHKfShc\noIrnNI7U0rIk1OMuCJhaIPV3GVIAD0EhD1eacYcZzyJQ+wiFT7yAALYsis+NsiRURLDUHMFPyQwR\n61A4R3fgCDPa79SOPyH4uwL4KlqkGAIvILCOdoh8DAHP6UhVziKxyPEWFPKwEIHo/V7uOgiK+iPI\nTwUuC0E7JZqRYcZtKI75mRC4wnM5P+/9U4jSu/VHOwGW3MikBwI8EAieh7JEXIhU8kYodOBMb4/P\ngD6eMnAWiZRyY/389yNn6Vgvz3xv21Ih7Mi+0sXboieKe66LIDkLjYnrgAuCdpq8B80alEczDOvQ\nOClGCnZnpFqPRGr/WuScRRsHrffUhEch9agRchjygJ5mZJTow+e9T5qTSHsYfVaEHLMM74vFCODH\no7CQA1Gc9IVej8eQ4nwEckDKIeAugxy5F0NgJVLBVyNHaj4C4w7IubvW2ynTz3UJUEcO7YlvJUp3\nX11YWUhiy/mvkeOWhhyct7yPvuB3tBiqY/tbWKxOxxZbbDtZZ6ToPWlGEwTZ0aLBeyF3EfRsmPj6\nGSvgtJoIMqej9Hjb0dT1+Sh2swICk0ZICW6K4PkdBIlHIKD7CoFctFhtCQLXS9A0eaYZ9yNwngx8\nHQJDkIJ+DIL1dkipPBpBxXIEkRtQSrx6KHVcPgLIdihcIBvFSL+KoG0ccg7SEPg1RgD1jLfPNKQg\nvgs8qOn4hIVADgr/OBBlf2jt709AqnsaCtGY6m2+EcXjJiF1fjmCIUNwNwWFFdRDDoN5nR9zdRwz\nDkYq8fN+/idKFsnPM9rrOAXB6DwzHvE+yfR0f4RAIQKvtihcBgSo3yGVv63/vtY/m4NA8QAU8vK8\nA+xP3n7dvN3vQxvYlPE+nICU6tO9f5IR9E5EoR+377QxyVveF/1RH3ZCoLnR67cCzVREm/FNQY5E\nPoqRTvawpvcRtE5FwFoW6GXakKezGeWRo7AaKcY7zIyTUEjKfagPayInrzYau6nIKRvrdepOYoOW\nO7xeaciB2B4Cm/3UPYAFIfA1MD8ErkJ9vNTPfS26hyr5sbnATHi6KlRZp1PkpcFVhmK4a6B7ZYm3\nwWY/fh26p343i6E6tj3WYnU6tthi+zULgR+ROpeJ1NbVJGKZe0C32rDaVeysIni4EkqT1hepfv9A\nytw2pDJ+jeA5CSmX7yHlrTuChG1Iaa6Npsi/RxCQ5cd28fPfgyAsBcWyTkKLuKr5eceFwKgQKA6B\nKZ5NYyACntcRPF8LdAqBHp754U2kCK5G0+vVESgdjWA/k4S62wsp3l2QUtsETdVHOaYfhUR8t7dl\nPlKc84FbzTjSjAtRjHgUvvAmAsRvEeg9FQL9UFjHan/18es1Qir9u0jh/iIEvjMj04zbkRNxPVKM\n00MgG3Zs2NILKfHbEJSVQXG/7yLwOwrY4qn7hpsxFkHZJhK5wRf7eYoR2DYOYccOnJWRuj0AbUt/\noBm3IEdprbfPEk95mIcWoi4OgUs9POhyfy/X274Xys08KWpP04Y2p3qZNqIQi4VoZmM1UtUjxXof\npBy3RjA5wPt3hBmHI8j9DI3rYhSaMQyN+a+9Lvt7e083Y4Q/NgejcdQGjav+KOSkNlLkg5fvET9v\nOgL32Wg87YvycJdCMxEveN0ixX6hKc80ZjRGCn595My9hGZ4qiDFewMwHDKyoN9Udtjb9WHGQcjB\nqIGcrIDGYSOU//p3VdLi7B+x7bEWZ/aILbbY/h92J4KtExAULQCSwapARqfE1w55Gqqdg4BvGoLN\njmh6+cEQ2OZg0ANl7+gGrAlBC6RMu8nNRYB3K1LQFqAUdnlIPT0ELUKbgMD3Ff99MwLTPsCtvuDM\n8/hyJOwIyViDwjAWIuW2jxk5CHTOQirscH/NQOpkQ/RPcru/BiNlNgnFMQ8isYPeCuSEVAX2d4At\nRuCTjiA2B6nf9yDgGxUCRWbURGnwOqA451nAdWbcEAIFZuQipbs/gqGyCOCGIIA8yIyRCHpviRbb\nmXEJWqAZ2c3I4YkWKa4F6nu2iTfQTEKRv38sUqi3o3CMpv4agB4Y5b0+Z6Ot1aPMIwXAhhB4wowZ\nyOk5Gs08zMM3XDFjNgLeFAS8mJHpbX8DClFYiVLHlcwiUxGNy8EoXvxo5OD0Q07foyRyWEehDzf4\ntU9AoUHPIXW6DQrzWYRnIUHK+HEh8BqC6q+9f0Yh2L3Wzz8RhXZUR87dXmhW5kXv933Q2GyGZm7q\nonHdFTkxNyNIXolmQhp4qr1tyHGphpzRo9BsxYPeN6eSWHwZvL3f8+9cD1eVhdHrYFolfXxjZZh8\nMiR19r5bhJypb1F2kt/VYqU6tj3KYnU6tthi+63mCutI9OAuw44459ojIC/dv7YQllyDlN4MNIVf\nG0H4eAfqo1EIyKcIvPZHYBQBdUBwMwGBSzEKHyjwY0Yi+PoCTalfi+CoKlKJV6Cwg0LTjoKDkPpb\nAPT3WOJFCLyXoJzHvRCM3IoWt0WbsqxBIH8LAtclKOY3F8VUP4VCLy5EIHWzX/8TBFJf+PGt/VwP\n+DUe97q8j4DxDeB2X2h4LtoS/AGkzFZBMbYXm/JZ10RAlY+cgHe9rUYgYPzeyzId6GbGXR6/vXcI\nSpdmRkdgmcfLN0Bq83SgqtmODXkGe/90R2E+dRGszUJOwCrv238gOF+LVPkXUdjGkd42H5hxHlJg\nr0DKb7rXvSoKTXkZOQEnopAhSGSq+BbNSmT4Mdeacm3XQLMOt3mfrEPZMz70339EYzQPqc9bEOie\ng+C+GDlAZbwN0/xncwS/Udz6Afzctvixn/rvc5BzMBOFvuQhqH8RhQI9hByU0giSD/Uy1vQ6F3k5\nb/fPtiMVeQlSsl/0eh3sbTEBKfhV0H0119thEwoBGhYCjwEvQVJXeNwSmvDHBsO+RPDf1OtXDNz1\ne6vUEEN1bHuYxbHTscUW2/+nTUbPwsZAa5h+Dqw4I/Hxs5tg0YcIgiJg7oBAY4QZryIg+AlBwiMI\nXk4xoxfKgFCIQONSBHE/ktgCeiHKCPEEgppkBMABzw3tx1yGgHQd0DcEbg+BDz0mGKQwj0Pg0sKM\nQ5FCeAIC6IokUvQtQlkuZiF4i3aZXI3U0YBArRipfuOQqr0oaDvpFUhRLI1iZReGwMchMDoEBofA\nkQiUqiEYG4lgajQCzmi3vSEItpO8fY9DEHUrCjW5EqnXI/yzHATeA/37eQ7Yg5FS/KK3xb4odvxq\n5AicgKAuF23Nvg4p591RGMlW5FBs87ZZgKB8IoLtrt5WNZFz1QVoHwJ9XfGNYotzENSO97aejZyP\nUj6Tsbe32RwS/HWnHzPE632zL1I9AsUJGwr7icIcaiJH534UFvERGk/RItArgBoh8L7XfX80nhYh\nVbglClspuXDzQNix5fudaIy09DrVQmOzCXLaqiDH4R0S27hHbTkVjeWnkfrfDI0hUBrAdG/Xjl6m\nd5HT8hxyVnJRaNSJ3qbXAIUlcrQH1bX5ROgaxZIDw9pD7t0kNlUaEAIf8QeYhbDnwoeZhT25frHJ\nqlev5zAdWcmQjz3l9z9LOf5sv/93x//86D+6Dv+hnCHEUy6/g/lisqVQXAZabYCvq+qTtqvh8y5I\nEW6HwjoqIWB8AUHGUAQHVZCKNwZBzvEIkJuiUIIfEEj+gMCqLALVNxEMVUDK4r4IuOoiGF+IQLIa\nUlKX+Su/RBWaIAh6GYU1pCGofN+/d/mb9XUAACAASURBVCyCnHkICNv5uSr5NTYi4Jvq170AKYh5\nCLau9O+fgQDqPD9vfwTN74TA57/Qrs/4uXv4ojkc5gagxW3nojjzpxG8FaDY2PpIMU1Hzsjn3m4/\neJlOAbJCoLOHoTzidY12Uqzr/VMZOTsPISfmbeSUPAdsCYGxO5X3YNSHc9GNON7PUR4B3ywEsxNQ\n2M1kpCrfgrKFFHo9aqAQoaORonwIcrh6o5mHKHPGw2gsZPnf9yMHpgcKmzgJjYcxaExURlB9lvdR\nGlqI976X7wsU4pHq5aqJQL25h8CkIOi+Erg7BEZ5ruhxSKH/yc8zBjlNPb0Mt/vxn/h7g72NsxFY\nZ6Mx1ho5IFH8+eFo/G9Fzl57zygSLYLsA7zm2U6ikKZ53h6TEYA3Aa4OgbWmXUtfU7uuHwgNM2CD\nOwd9NsPAKIVjs5DYuv53tRiqY/vLm0I9/ngA+jPC457/+393fAzVsZU0h41P4IV9oXMZvZtUDHed\nBz1LIcXwSzSd/SVS1QylO1uOQh+GIvhqh6BsPJo6PxGpnfURrJTRtfgewVM3BE6TEBCdjoD2bQTA\nExC8VkJK49cIVsqgafU1SDlMDoF+ZrzpZTsbQelApHBmIJjrhKbVJ/h1KyD4Wu/XGI1gbYEfn+bX\n/cS/eywC3cUoW0O2lyeCXkgM4mQEZ1u8fkUInPP9mHrIofjJy1KMYKoZUp0/RSrpjSTydVdDDkv9\nEtco9J+rvN06eT+dhEB4hbdXVQSNZUPgUn7BPPf4bK9zaT/HE2hRag3/eZfXYRpyEFYgR+c8FDOd\ni2YoCIG7TLs+voIU97YIsJ/2Mq/38n7n7VMGhcl8g8bI68gZW4QWdd7nMDwQOQ4jvA1noWwb56FQ\no0dRiNByYErQluVRHZugcI1HvS1bIgW+J3I6zkUgHC1qPQ85BC8hB2aAf+8LNBuwGo3L3uheeZxE\n2r3WfkxZpCQ/hlTteWjG55kQmGLa9r0/mpGIwnHMvz8fjc3D/BwV1Y43fQ7DjlStMoEFeVAnL4Qd\naTJ/d4sXKsb2l7T/W52OLbbYYvvvLAQKzXKWQM82iXczxkCbNvBNJ1g9Fip3g0UPQoPToFQ9yFsA\n+XWhqApkfQTJZXXc+gnQfqh+n3ITVDkZ1r4OZ9SA9yuDpcKcuVD3ACi7HLgDkstAdh2o0gZsFWz8\nEk56EaacAz9tg7RBkP0tVGkK7d9Hah3QvSZc1AtyFkClw8ysEySVgaIc2DgMyreFzXPhuzWQVQYa\nVILsB6G4CMrUhrKp8Px1cPHLsHUppBXD2gAV28C3X8NN78KyArhtKhzaBk58GqYYpFWA4gJIrQNt\nhkPqKHjnUlj+PVzy6c9b98oJcMEVwF5wyzBYvh3qpEG/ylBqLWxdDdWOhdRSgEHhgTBnBDTtBIsL\nofE6SB4EKyaAJUFKGlRvBQVrIKMhJFeE3FmqZ2oWpJwCpfeHosaQXB6KDoW0vSEpC4pzVaai9WYb\nnoTCrYlyFheCJUO1ekA9yF8K+fOg/KcQ8mH1AfDddMg7BjI+hYN7wLzvoN4cWPYxtOgNSQGK6sO2\nryGjG6x9x+yYhvDkgZA1AprdBoWrIW8urNgONQ+FzYth8wdQrSVk1Ia8lXBMHvz7emi8DdamQEom\nlLsENs6A7KpmpzeEjypA8eWQuhhKN4Hc2nBcKoyrARWqwjnfw0sBZrwFB15ltrEh/PNx+DofjsuE\nBwySe0PRZtg0FsaMhGNPATPo9BC0Kw29+0KH+6HfZDj2cQjrodIz8Hk/aHk+FB4AW1+BzSth7wuA\ndyFvKRR+DEkVoXR9sBwoOBrWTYHMRpD2HFx+LczYBjPPhgllzMqfDS2Ph1AIpVdA0t7wXXcoXRlq\nNIcN29RHFUtD2n7qy7AdLm4GLxfB8mT5ADcGeLn///4f4b+3WKmO7S9pfw91OlaqY6U6Vqp/LzNL\n6QtFA/7ocsQWW2z/iyW3C6Fw6v/7e7vH4oWKsf1lLM7sEVtsse0OM7NaUNTrjy5HbLHF9r9a0QNm\n9oexbRz+EdtfxuK807HFFttusqtQPC5QswYUFkJKCqSlQ8F2SEuD4gBrfoIKFSA5Rf+DklNge75e\nlqTj1m+AMqWhbFl9ToCCAli7FqpWhfx8yMiA1auhenV9tmkTZGZCufKQtw22b4ekJL23aSNklYYV\nK1W+ypUS187JgdJZkLMZ0tNhUw5Ur6ZrhABpqbBho8qcvVZT+6UyoHx5/Z6UBMnJsHkzbNyk8teu\nBXl5sHYdVKmsckf/d6tUgm15ULmyrr3FwykyMyAvH8qU0bnS0lTvnC0/b+YqlaGoCFJTVcfMTNV9\nSy5Uq6rjonbaulWfFxYm6l6lsv4GfZ6//f/uykoV1XfFRZC9TuesWgWKi9Uu6zyTRJnSOte2PMjK\nVJsUFak/ypZV+2Vn67tFxZBZSuUsLFS7VqgApTKhsEDtWFgEoVj9l56h62VmaWxs2ggVKsKGDVCq\nlPqqsFDfi/o7L0+vmjVVhrQ0v3aR+q6gAGrVgtwtar/CQvVtkkGdurBsGVQsr7IUBx2fnu512q7j\nU9NUxq3b9KpRXeOouAhyczUui4p0bH5e4jxpaYBpzBQX6ZjcLT7+SqscZhqXFStCRinvjKA2T01V\n3UqVUrlTUyHJFxjmbNJ1t29XvyUnq+2Skvz+QXXMz9d5iwpVxhDUfiGoDbdshs25KO7/eJSd5He3\nOPwjtj+1/T0ye8ThH3H4Rxz+8WcxMw5AWS6uQQvnfkBpy9oiIWoqWtj1LMq8UB0tMDO0NXMHlIVi\nKlpYNQ8turoJZUVohxbrHYYWeG0nsZV0ml/jCN805W2UXWMYcFEILDNjNMo28jFKVTcLLVhrgfIR\nT0OZKI5Bi74Go0wPO1KQmXEOyqudhjKQFCAIWYYWKI5Ai+JWAmeUyM5wqZ//MbSA72S0qLA1yoDx\nJcrF3BBleygOIbE5i6f5G4qyeRyCMj/c61kfnkKLEGujBYqZ3l4/oEVuA9FCuL2B/8PeWYdrVaZ9\n+7zpkgYJkRJsQBAlFHsU7BoDxzHGHLtbrLFzjBnbGbvbURELEwMDRUBQwQCUkM77++O8Hp49fk68\nvvq6gXUdxz72s/fzrLXuWBvO67d+93U/nzPX/Iv5OzHG5BCshtIrxnYIlv87Mz5XFTepGUd5QWYH\noBtW1jggrlUFq7k8F2M6CBdNjsA6zqUa2y2wbN+lWCv55jj3zrhJyte48PFVrGhRN+ZtA1ycWmrn\nNjF+78dn5uTsBj8pcS3eZ2sBA0rbfqfE5znTNiVqUC5l2DSG5GKslvJJtKsRVvsoVVGpjYtDN8C5\nPw8XoR5Lue7zjJiHtlh2b1/cDXJzXEz7SM58nRLdsILJzDj2C6xXvjVwON4rZ8f8fIcLIF/C+R2B\nlVHewrmvjwtqJ+EC4TOxFN+waG/JqnUuLog8tsKul79aFEp1EZUu/j1IF1FEEUX8cpEz70SJvYFE\npQgsn/Y2gtYxWB2hJVZpOD0OXZNyPeBnEYiaxXGXIqx9i/DyJFa3yMCCnDkrJV7AChtNgLNS4nSs\nQrEvAvxZKXFDnH8VrD+8Ndb5vRBBay8s5dYeweNo4LaKQB2xII7fASF4K4TFWlgfeRpC4SPA/JRY\nI2c+Qmg8FatdrJ4zfwdK20xfimD0Je7OtyfQKCVq5cy1AXyDsEpEe4Sh36TEfQhzi3DTletiXOZi\nmbnnEBSvwkoZXwGdU6JKqUzfD6IuJhcHYwLzewS6BVjirhTVEMY+jvY0QdjdM7ZE/x7hvh6CYmes\nUvIUQvhUrI5xGoLzY1gJ4zVMeIZjgjAF//P6HmHzs+jrWMplAwcj9DdCYO+Eczw/xvAUTFjmxpzN\nBo4LJ+QKQN2UuDvmtC5C6Y2Y7GyHScJRWOv8WyyzNxorkqybMwdHBZwhMf6lWur1sCTgRExSNopz\n3Yp/HxdgwtkmJX6L99+OeA8dgNVWasW1+sd4fIjQPjX6vhlCfkes6tEQwbol3tOH432werSrMyYf\nj8U87wlsVhmAGgpPdRGVMIoNXIoooohfOV6Kr/moLLZAWFwV4etZhIdj8D//sfHZtVEx3gnB+wNU\nI2djiTuwPvL+WCt5DaBU0q+kGkxGyDgW/xG8HmGjCULbEFQIj48dIUtw8hrC7BgExbWAj3Jm+I/0\n7whUpd9GgJ4JbJ4zk3LmXiyB9iwywmLgttime29UNr+ONgCQM6MQfG9DZXJLrJU8FdgmkoHnsIzc\nNIStgdHPx6Itn0UN40sRujpH+46IdnyJickEhLolW3v/SDTNmcmUazh3RmBdJca7OW4ucyRC5xoI\nbYflzOgK57kRAXF6zryJavl4nI8HUQWuF+e5MsZsv+hDc7wfhsdn5uKTiRYImnchHE6Oc22OTzha\nIkBPw4QuI5CeiQnTSpggZMp1nInz7o0K8hxU3eei4n08cG5s0jMlxnM9rJGeUqINJmDvUlayN8Sk\n6mZU0WvHeTNuitMKFeRDY1z6AJvmzITo99AY+4Px/v8jPuGogeC/SXyfjDs8jgb+njP9Y276YeJz\nNG5E1AlrgKcYx49iXp/LmR/YjH69KKC6iF89Ki5ALBYhFlFEEb92xPbGRyJc3IePzg9EpbY9qtIL\nEBomIqBkrJf8Kiptn6OK+BuEikGoWo6IyyxAYJ2G0PAkAtU8hJuRQLec+QDV6LYIPN0QhpqE+nsR\nKqorx3k6opq5ELfp/qeILbs7I5y3Rkh8BiG+FPejsjoRgfuG6M9T8X0HoH9K7JcS7eOY64EDcmZC\nzlwR26T/DdX+ndAy84do1yYIhCNz5m8IzH1TIsU241Vi/DfHzW8uQRX2SATXfYDZKbHVD/pWYpqF\nKbF9nOf9sHx8CKwWx5yCNZm74Vx+ignI2xXPFzsbLgKahV3kNgS6x2MMNo1+d0P47o5PJzpGH+vE\n7+fFe/NjvDsCl6MNpnWM04V4vwzHzV36RjOeirb3Q9j8IsZkE7T2rIfqfRV8cnFLXHcDBNhVo82z\nY4wOxYRxBirWK6PSfmvOHIn2itIW4lMwWZiOgP0gJnALEbJPxb+PNXEXwxkB6F/FZ46Ozx2A9/qB\n0Y62mJh9itD/CCZZc2MOT8InE8MRpntikrYS2kpSzOFITDYqTRRQXcSvHv+sTBfqdBFFFPHrR85M\nRW/qcQjSzRACrsZNMK5GdfZhVB6HIHwcgP/xX4r1pA9A//Gr8fsP4xJNEFJWRSXyRoSGD3AHvMeB\nxSmxU1wbBLLZqAbvikrpGwhQl+fMWAT/WvH5CtutL/ERP4rWi4ygNxwVyG/D80zOfB+H1ETfdn2E\nvEWxiciXcZ3RwGahYpe8ynuFPjIAYXEuWggeRfV8nejvhcAJYQ8pwfq50cYrcWe+sTEHKyMgzs2Z\ndxHmVgb2Sol2FbrYFjdU+SLGZ0SMMTFOXyGMjUYP+KbxfgtU+EvjVA0tFWujXeJqfBLQGdXubgil\nN+OTiW4xbyNx90YQJudhcjIdk6d3EJIfwycdCxGkuyPgbovAvX4cNzn6+RqC5s6YYK2Dm7esiVA/\nLM7VBmH7H9GWlpjM9QAOS4mn0Ud9LFo5NsdkbhFQIyV6xhgeidaObqhYt4i2NEGgfzX69yx6t58C\nDk2JFTGxm4PJwkv4NzMPbR3t8Z4dF9d8Dbcvb4xPV3ZHmB4ffdwT579xnHMBbk7UIl7vmjMLqERR\nQHURv0oU5fGKKKKIpSCORCvDY5TtH7PRM/t9vLcuZSvFdwh/tXHB2XbAyznTC+GiA7BOStRFQCmp\nsnVy5juE4beBHimR0AZwEELF3XFMW1R/90MFsl689314wY9HhX1/YJOUOCMl6kV/zkQ4uQnhaGPK\nkH8aMCiuCyzZWfDQnLkEoefKeO+jaPfaOXNjzpwWxw/GxZpjUEG/OcbtGVR3ByDYDkTVdTFwU4D0\nBASsSxD4n0ZwLVlZrgX2SYnuOTMzlPDBwF0V+rdGjNH6qLKTMyOiT2fFeI3DBXJbIty3QStDz5Q4\nK7bCPiXOtWqM19oxV5sizB2ZMwMQpO8DvooFmaPQY9wCIXdSzE01VI8HRP+a58y8nLk82nVvjHfz\nGLfGMVcfY1JyMCYJHRDQt4ixmY3AOgGtNh9jwtcc4TwhZD8Wff4OLRib58yGCN9VUZU+ChOdWahU\nD8Ak4tBoz98Qdk/CJOm7uB/eiTm9CxXnPdCm0hHv3yGoSn+FUF1S3S+OtveOca6O9/Ke6INfDxOR\nN3B9QJ3oe9+Y25Oi35UqCqgu4leJwjddRBFFVPbImdkIXZcgjL2JUDIeQWt9VEOnoT90JcoLvDqi\n0lslJfrG+y8gXJ+E4JDjXI1Toj7aA75CyCttjz4VAepRVB7vQ0iaC3yQMzfGZ+ejAj0IFeUZ0bYb\nEZZPQUX05fBivw20iz4SNpMpqKCCINwLbRZtcuZCYHJsj/01wv1KKbFKShyPW3evidaXu2N85iAE\nbRLvtUcLxVhUO2fEeDyIgN8IFf5LEdyaIEzejwnHp8DWKbFRStRC+83NwDspcSzC4NYIit2ALilx\nHtpj2sR8dMVkaRJaD15BuByTM2fG19nRj8fiPG8jQJ8PDMmZ12KMLkAbyVcpUSd+dzGq2WNQ5X4d\ngfM5vE+eAn6XEi/EU4iN8N5aEP2eGJaYVVBhbo7qdHUE+y9y5nN8erFujMmWCNPN4l54BROfBylX\nsqmBiyQbAS1Sona0cVL8biIuGnwA2XBNvN87xjz9BUF6VMxFJ7wf/4oJ3EZ4f7fEhOR09KifGcc/\ng6r8azEPZ2Ky1AH/Zlam/CSmASatT2NCsl60cT4mY4Nz5pZ/sVD1V40Cqov4P4tCnS6iiCKWtgiP\n70xUyY5H+LkC/6N/EWFtEULGKAS6+fj4+zCErhYIndUQdq5DSNsaK2/UpVyGbuW49M4IJ6ehUrkv\nqoUPRRuujWuAkLM/cH0s0KvY/q8Q1jZF6Hov3hqF0FoxhuDCwpo5szCuc2tcn5yXeG17IuT0R6C7\nFZMB0LaxGBODPYAbc2YHhKhPERRXQH/tyGj7fAS8TvG5BghUTREG+2CCsQmqnCej7WFLhMHr4nUr\ntCR8jir2ydHOfRHknkT7wIbArJzZEW0U2wJzoopJKaoiMC5CD3d7oGfOXFxhbBdj4lIH1eP1MQl4\nKa4/GOf4E0yKVkErydXRxjPQjlFa5PousGdKDItx/hJBdgzabZoBrUPZvxfBtS/C7EMx3u+iXWdt\nnOsPEbgHopL9IuUqK2shBHdE6O8ebRwe6wqeiHNOQijeH+e6LyZ1Z+JTmzqY0Owd118YY3ZnSgyJ\nsdsjzrdafG8YY7w+KuJz8Z5vgxDeNsZgz/hs6f1v4vhKGQVUF/F/FoU6XUQRRSylMQchpgdly0cX\nVC7bxNd8BIbx8VUD6BoVLR5HNXQB+lgPjvcfQCvGTFSUv8TH4SsiwF+dM2PiHOehD7gKwkxPWLJI\ncBNgWM5LFkGWYlZKNEAP8kgEyM4pcQCC7Q83T7kHlfGD4ufH4txfpcQGKXE4JgXrIky9H+05A3gh\nZy7Omfnoi30aK0AMTYneCK7rUq74MCz62B2h7ndoGxiK4DsBIfkTBKmROTMQQfJthMM5OfNo2Cje\nRwivFV+rYYm3OxH4BkebJkX/fh99HBPzMx24LiWqh+o8AP+zegyhcQ1YolBXjITWiYsQNr8NWO8K\nSxZhNo3+jEXP9XxU+7/A+Z+Bc7kD3l/z0IYxFhXirphsjaxwvX5om/hjtO9lyqX7TkTFdyNU0+tG\nO7oCn+fMXxF+n8d7+7H4uhSTkpXCBjMQFz52jnYdEu2aEtdpEmN0ByYJteMaz6MC/RDaoO6LPm8V\nxx+BSWktymUHR2LyeSImoDXxvqgV13gH/3ZaRF8rZRRQXcQvGoU6XUQRRSztkTOzEPYOQlh4AkHm\nfFTQ6iEcDEVlcT4qwfumRGuEiaG4KPAUhKZNEHgeRUj4Bu0Bp6B6+WcEIcIr/SAC2CRUQwdjVYod\nEJoq7iC3ONTM9+MaI9HvuihnzkBAuRGrLSz5xzlnpiP4N0mJZpgc7I+q4SAEr4tQ/eyPEHk0gvgu\nFTzJ96Ba2jA+0yDO9RRwSVgsjkBw/RgXWl6FycTvEcRKZdmGx5gfmxJHIojejiprTolDUqIx2iOq\nICT3j2t/jpBXqkLRGm0mI8ICAyYnr4dv/BVUYu9EQB2ECcA50ed5YTuhwrzMjLksJVZHxULHOqgs\nj0BLyKaoUG8eY1LagGWTGJ9FmLCMibm6Cq0fF8Y1msc8jMf7sLShzAMI44PRGvEuQmgT4G8582HM\n2fFoy9ktmr8ZlnccFPM1Mz63LSY3/RCqu8b78/A+G4SwvAI+kVgd1fhhWDZyKFpHPkPl+vIY4yr4\ndOFwXCjZIPr0Jtqh3sUnCIfivV8X78Xqca3WeJ/8LVT0ShkFVBfxi0ahThdRRBHLQoSP9WGE0aPR\nJ3sgwkFDBLKxCHJfIVBdjOXoeiEATUAozKjmfY7+3i4Iy63juBPi3H1SYiV8vH9pzvwJAWQ1BJcV\nUPV+B/5p84spaHtojIpfB4S2F6MvbyP8zEWAWTF8yrtStnW8jQsHayNgzkIw2xphpzsqv/OBQSU/\nMtpaFqONoHrO/C1n/pEz70S5vRLMkjPjUYG/KM55MNoQelCucvIVqsgrIbzvgeD9FYLqJExMbkSA\n3T/GtVn0/9qAsFURYKcDH1aA4z7o7wYtEWsg7E1HMO0TfXoClee9K4zzhvH5U1Htno8J1q6YDOwC\n3B/XPweV4ykIogdjEvEtqsV358zGWJlkS5zjJ9GTPQrvsTXRLvFNXPNzhPm/IXzehwncJXHemTHO\n36MC3RbonhJ/xEoqd6bEepjcfIRJ2woIugfFMW3QxtQGgfddvG+Gorr+MIJ9PbTiNEPAXyGO6YL3\n/Pdof+oWc3hb9H8KqtMHILBPwqcTGROahTEXzYELKssmL/8qCqgu4mePQp0uoogilsXImTsQCC5F\nT3MdBOGZaOeojjDQHB+J90G46RqfmxBQUBP9w3dE5Yy70fZxEKrB9yFITURgfo7yI+/nEYC2jmuW\nvuYDRGWRhGBXslxkBJYNKqjJO0bbmqEf+GCsqf0NAuEFqCgORHjbGcG3IQL6gPj9VGLL6KgBfQDu\nSjgfeCElfvMfxvSbaNvmqG52jrFLCJHP5cy6CFv7xZgvjDFO6G8fi3DeAZObdRBMXwQuSomulDeO\nuQmhr7S7Yr2or9wo+jEfE5rhOMezEHCfypmPgU5hEamJSVNLVJPn4pOFTjFWHwBVSgtBMTlpj/DZ\nLM55bM7sjPdPqWziRWh5KC0sbRvnrgtLSh2OxDndCgF0TXwq8R16mS+MeVniEc+Zp/FeqIcJz+sB\n19fgvfQlquON0HYzOI6fhE8YHkLbUUbluR/QLsZ062jrVnhPn5Izu1LeHn4nWLLBTJeYn13wPto6\n3p+I99QO0efRCOEzoy9/qrBAtNJGsU15ET97lNVpKLYWL6KIIpalyJmxUQHjPXwUXwUBrw6qeHUQ\nom/DyhRPoLe3G8JzKVairJA2p7wz3774mHw1hI8eCFznRem4txDQV0TP6RyEkZKOMSvO1wuW1I8e\nBJwQ1g8AUuICBL+DEWZfR5i6GtXe+xHsjo62dkPIeh3926NTYh76XwelRHVU7f+SM5PiMo8Bl6fE\nkFj4+K/G9NtY0Faqubwx2kKOwkoZ2yNsvQjcm932vB4qqE3Rn9sW/8P5KMZ5g5x5KiW+QyX3A6BV\nznwQ1pizUuIZ3CimKUI5aGH4AyZIo9H20AHndRZaQw5DGJwabeqCqmo7yhvDdEePdjv0i28Uc/UU\nQnf1nHkrrCLDgTVTYoNow9AYg3Zx3i3i+0Wo0q+P4F3yiP8eE5wjMMGYjEp+D7SSEDafqqiSN4/P\nt435nIb323bRlqeB3jmzZUpcj/fmHXh/34D2lfcoPzlYIfq2DfBmJG0N8H5aF59clD7TFBX4DeLn\nt9Hqc0WMZWntQVPKO2n+JWeuYSmIAqqL+FmiRYt2AdNFFFFEEct8rIyPvTvi4//xuHHFDLRntEUw\nfQ6rFxyCUHJFwE3jOM8GKbE3KpjV4ntNhKa2qEieTlmtnoVwthI+mv8U4WvNsF4AkBLXoXWjN4LK\nBsCQKKPWP87fA+HzBfRaXxmLGo/Fx+07xzW2Q/V1ACrflwLToh/XoGe2FgLgCjnzUKkdOZNT4mZU\nmK//L8Z1YoztFExMqufMbaEiH4WKbauUOBWTloaoFg9EcP0A1dEmwK4pcS96u/sgBI5IiSo5syja\n3zPG8BxUgs7Ima8DdLujd7szJhbnpsRjMT9HoJ9+75i3p+Ka3XG+L8TkZBaqsV0wcTkGE4DmwG9S\nYguE9yejb1shwI/DGtCjYlxuiPMsRGV8PMLompR396yLTx8Ojmu3xgWH92CCdSDC9mxMyEqbtsyN\n612CCd0l8ZXCq94bIf8YTPLmR1uIdrRDsK+GKvc6+OSktJX6cFzku0HMaRdUrZth0tcrrn803pN9\n43zzsUb1YzlzJ0tJFPaPIn5yVLR5FN7pIoooYnmJnHkTIfFNVPmqoArYE6G1E6pvqyE8HIvw9Awq\nx5vho/z9ESRfQYD+E6qjK6AiegKCbank2DMIZycigLdBmKuXEusDpMSOqGY3RXvHR7g47DdxvvFx\n7utyZvgP+jU91OxXo20roMp9NoL3IgSxDmhtWIiwWlpMdldK/OEH53wfWDklGv6r8QzluB9WEXma\ncum/0+IcUyNpOBd9vZNQgR2HKu1EBMYXMUl4D+0v+yDkvRxt/AKV82YIbH/AJGURcH4AdWk77Okx\nxuPCT39cfP4S9F7vG2PxcZzj7mjHJqhkf4me61q4Bfgfwtu8GyY812Nljf7oBe+JMLo+5YogtfCJ\nQXVMNHpignU9JnM3oa2kKTA5yideDku2V++EfufzUHH/BsG3Gt5vgzAJfAETgkZxznUR/t/Ce2x6\ntOFE9LHfHWNTB++nqviU4P6YD1ZVGQAAIABJREFUj1dwceNkXHi5HVo8OsW5PkYl/XtMCsdFf4/G\ne+/FuPbKaIVaaqKA6iJ+chQgXUQRRSyvEYv9WqLqNwGhoyFW7ngKoasJ2j9GI2RUQ/D4EtXq0pbi\nFyGUXIuPyr9AIOmcM/chlM9HwFgXfapPoZr5Z3zUfl1KrIZVMe5D5bwVKo11gFNz5qycGYZWjhJQ\nfxHHV4yStWVvVMg3RHCvgmDfAaie3Na8OUJSm5z5O24Qc/APzncVqrv/Kg4F3smZKQilxyK0fZoS\ne1X43PUIYEfGeB+PdoEbY9xGYBLxIVbx2A0B7bXo764Ij4MR8rZGz+6VAc4g2N+IkNcbd3xshmM9\nAxXbjRA2G6BdZSYCZw+c47aoFj8ANMmZuwDiPM3Q/3xaXO936KV/DyH7xmjfPdH2zjHevdDXPAWB\n8x28j1ZAL/VxKfERWm62i/c+QpX5WUwUtkAFezoC62X4FGE1vFcWRdsnx3GLMXnpjffD+phs1cJE\nrTbaSG5HBb8NPjU4N37/YMxX9xiXsxG4uyDkn4wWkn4I8RNjTFeJ9r+QK9k25P8pCqgu4n8UxSLE\nIoooooglcQBWAZmLoFsVH+FPDUDMCHQjKAPJ3QiiHyGAn4YQ1BrB+VAExW7E4rWoHvElwuL1qGjX\nBXbPmXvj2g0QhPpgbePJce4ngU9/sPtcR4QdEM5alt5IiY1Q2Tye8g6Se6NtYMNoy3AEos0QAkcB\ntVNinZx5BJiQEoeVzhke6+kp0emHA5gSPRDOxqREL1SQV8JEYy3cFbFrnGcxQtiKmAwMRri7AOF/\nrWj7tphY7ILJymLgrZzZKebnJlRcG0Xff58SB6XEyQiy3+IGLi3wicPJcY6rEC5fiub3xvmvjlBZ\nC33H4xFQJwEPRlUVUMH+HK0YpyMMv4QWjrfxKUap2kvbGNstEagPx3ugJirms3Fzmnl438yPY2rF\ne50R8jdH1jsLE41+ce0bUMXfOdpTHZOA2qggd46xaQDsmjPH5czpUXrwS1wgeSXlpy6tgQ9j581a\naNc5MN5/HmF/cIzB6DhvE/xbaES5okhHBOyvKSceS00Unuoi/kdRLEIsoogiijByZmFKnIDq7WRU\nDaegajwzft8FgWwSLhJrhHC8DgLeQISmGWhBmBU+2D0QMEmJJujLPjosGG8ld/+7JSXaokLePK7x\nF1xgOAOhpTdR77pCpAqQ/SHQPGoun4Cq8zHhh66G8LpNnHfLlNgWQa5Up/oCBLYVEQp3yJnHU6J/\nShyZM1fGdf6CycCxSxqhh/t36EHeAQHvZFzY+RKC8nnACVGpoleM4WTcVvyo5Bbwz6HqOjnacyjC\n2UaoRr8KS7YRb4Uq+NMIoe0QblvF/NVFmOyMSdKGCJyXxfhejE8ZvkGGahHneQAV5cXx+fqxyQop\ncXpK3BCfm4EWiVnRpt5oxTghzncK/ic7Dv3rzaJNNyFwt41rzMUE47n4/E14v7VFwG6EFouSqr4R\nKtYXoD1kIiYPExGQeyFwN0KbxlsIx+NR2a4YDeJ3B1BeyDke6JkSxyBQj8Pkax28p7ZFNb9bfL4q\nLpLsjknAePS/vxxzcUllrkf9r6JQqov4j1Go00UUUUQRPx45MztnNkCwfBR9sdfhQsbVENr6IORd\nhY+/uyFcHUF5S+aK246PjN93Ton6+Nj8tNICu5ToidA9BaG3EVZ9eAlB7FRUoA/ABWKlhZGlKhBL\nYCXqRjdFf+01OXNnBZh5HNgmlOaXEI4uR/XxBLQ4PB5e4WuAjimxapz3KeCjgKzSdYamZCm7aMcZ\nuEiwOiYAo8Kn3QYYHwnEKQiHj6M9Yl9MNmZEVZBZ6NvdGZ8EPJAzn+XMczEXwxFKN0xpSdnC0oK9\nw9BSUSrR9xKC7ZyYi8moEC/CpwmDEYTb4JOGxei1vhNV1a/RVtEIbSMDosrKfHxScSDwQc7MRNgc\njnDaAyF5FbTznIxK+yaUyzROQQgdgU8G2qGVqHG83j3mYyEmB1+i6vwQ+sC74SLGlsQOldH/lsAp\nFXar/DaO+y7GbTb60JumxDopsR0mgy/hE4z38R5rhQslj8JE7R/RrgvwiUfV6HMLBPnRcZ1aMU9P\nUS47ud4PnqwsNVFAdRH/MQrvdBFFFFHEf4yRCCJTUQl8ChXeQQhOtRG228dneyNElBYxdgb2SIl1\nsITZLAS8qxGKOqTE6aj2tkF7xECElK9R8e2O0HcEwtUIBKXGKXFN2Cva4mJHUqJhSvwprnNc1Iyu\nGG8gDBJtb4lq4hAE9u6Ut+4eho/vrysdnDPPAsNT4viA6IeBbWNh4h+AB3PmO7Q0rIcL+ACqlby0\nAVcLsHLEsznzDAJjXVRWD0FLxWS0UOwXVo4VEVT/hOA5Fe0PX0W/ZuTMKEwoqsW1m6KXeVMEw9Zx\n7hroR56Ldoz6aNF4HRXeEahUD4jxrR/XrYfqcVNUgx8FtkmJazFBOASV91aoQpe2AC8t3Hsnrj0N\n57wu3icLMTnbgbKXuWVcvx7eT+3wXlgdN75pgonX4vjqFH1ZCLySErcg/DZHKN8+5qIPJhTvYfJw\nWYzLo5hkNUI1fSEmGgvRErMuJlp9MQGsEf17F+/P5tHvYfh30wsrp/w7732ljwKqi/jRKNTpIooo\nooj/PmJTlycR+Opjeber0EvaAkFpHco7y72JINkPVb/zUM1rh4pmG1S6+2P5uIPimKuBh3NmDiqo\nGwKvRJWNaWgHqI+K7s5x7qtxwWSbaFP9lNgGVeCrUOld4quu0KcMfJMSLRHC5iNYjkDQHQrckRLV\nA36noIK8WYVzDKG8FTUItmcgIL6R3NlwNVzs1yC5rXuDlOiUEl1T4hX0BR+LJeKuo1zvGATJNSj7\nkxvE599E+Nudsg2mOqqz/VC5Pgt911UQPtfDhXn1Yq4WxdceqMauhAry1BjfXpQ3ejkuxqghznfv\nOG4PVJzHozrbAWGyaYz7oQjwE2Pe6qJyfXKcczQC+fRo93y0rgzGyhmPRLv6xRx+iHaXidHOF+Ia\nNVDJb0TZu5nx/myJScv76Es/H4H53jhvp2jHA2hd+Sz6VQL9TzGpq4v3Rx+8DzfDJykT0dZRAxcv\nVqVcUm9GtLkjsNrSqlCXIuW87KqPKaW8LPfvlwxhuqJ3+v/q9f/19ZaW15WlHZXt9U87/p+P/rX7\n8G/amXOR1S5lETWU+yOEvIRl3erHV20Eln0RjqbiYq/eOXNmSpyNG5XshCD0HgJPX1S4O6NFoBWC\n+YaUt9O+H5XL2xG2mqJq+hZCWWsE6z3inDUQjj9E3/FYhKOq/PMfWD2ERxCU9kF4/4Tyzo4JFcgV\n4vjuqGouqnCelTFheB3B7O+oXC5EJfQTBOEFqPAPRQB+AS0Ij8Z7F6C1oAX61Us7EW6LCcsCVDvb\nxLH9KNcV3xIV7RTna4Wwu2K8HhnjsyHCZpsYl01RGV4R7QotKC9ObYl+5ecQyu/EDWQWxLnnYaL1\nePTv8vjc6dGWjVG13RNV9KdRLd8IIfbp+FwjtG10iutuHP0ueatXxkWsVdGTXgOTD+JaT2LicD6x\nw2bODEmJ9jE2tYHf5cwbUZ7xBnzqUBXvo7ujjePie1V8GvMZVhCZjclJH7S1nE7Zz/4QJm/bxDw9\nG18r4317NnBWBf/9UhvFQsUilkSxgUsRRRRRxP86LkN42AlVzIcRshsgYK2NgFvaje8W4IuwZqyG\n3tdvEXxqIxzdjirigvj6AmsWP48wegLaEz5AZbYOQvi7CIZTEYyroaq5Hyq7HePz3yP4nRc+5iUR\nCyI3BPqEp3sc+sdPy5lRsQBvL1QjV432TQNmRiWIiufqhVaWLYCdcubcKDO3MqrvT4dyvRWWw9sW\nIf7Yks87uevgP1AVr42Q1xH4KGcWh82kNiqiGyHY9kAA3wnV0f6YLLyC6uoZ8bnNMHGZjMptxkTh\nVGC/nNk0JY5CWCxt2b5ijF9dVF0zwvnsaOMOCJ4JFfQe8Xo3XLx5HiZNe6PqvDb6uNcG/ojWlbox\npl3idReE/fMxMTkeK4V8HW3ZFaH7UVTnm8W1G2LSUA03IrowznsjlgqsGlNVulf6ISAPQrvOSvFV\nHbgrZy6L+bgRn66sgsnI9vgU5DRMJIgxG4qJ3dF4r5TG+8FlAaihUKqLqBC/njpdKLLFuBRK9Y+2\ns1Cql8qIxYUnwZI6zqtQViyrotK4Miq9bSnvNncYWjVORgW6CsJZS+DICmDZDdg0Zy6Ln98Frojd\nBy/AxX+jUAUfjhC5FSrT6yGgv49q+SyE0m4IqzfnzBdx3o6omL9K2Yt8RZxvz6h5TXi9S6rmw6hC\nNsGFjx9VGJd9EchaI8w9hgD4cfR3KFoOWsWYXA6cnDMzfjC+7eOzX2PS8QLwdvR/B7SS1EQgb45g\n+gpaOkbEWNTBRGAeQu8ITIYeQ6j+ECG8OSru9TGB6RE/vxzv/QYXmR4V7x+DIF0NAXcwwuX6qBzX\niPbNjGtOwycXMxF6pyKc341w2hHV3Nfi2CuiL5tGf3ZB7/VoBNnhCPqfogVlHUww3kUL0W+ibSfG\n57aIdtTCpwYnoUWnLoLwtXHsV9GW2gj1A/AfrLsR2segV3syWlzqYcm/tWPMVo9j/xbH/BmTyEeA\nfZfGSh8/FoVSvZxHoU4XUUQRRfy8EdUwTonNWIYitC1AKAFB6C18lP9bVPM2Q8A6DwHteISW9xDO\ntgEeC2DfF9W+UhWNWpTL5k1EWBqDauVUVBdHxDG7oBWgVHv6Q7QWTEJouyEl6kab2yCYj0OFsyv6\nu+vhBiyljVmuAw7NmbNT4u8IyEdj7eo/hILcBWicM5emRHeE6SOiz3OiDYMRDi9CP/G1PwTqiM6o\nAreMtswF9o9r9EagbICAOQth7oiYg+NiDKYi4I9DgFwbrRanIViujXDYEmH3a8ol8y6Ldp6AkDsK\nFzRWR1W7N+WtugcQu03i04NOaK1YnzJ8pzjnHphIvYcq+7iY1+mYyIzHZKgzwnCfuN428XokJjbT\nY+5exhrYtWOcxuPiQfDpx28RkO/Fe6EfAvzDqJ5fEr+vB4zImWvj3hiNKnrNONcUvH9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P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\np1Q4b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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_length_distr_and_chords(lengths, R, solution_A_pct,\n", " triangle_edge_length, sol_A_coord_a, sol_A_coord_b, N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution B - The \"random radius\" method\n", "\n", "The second method proceeds differently.\n", "> \"Choose a radius of the circle, choose a point on the radius and construct the chord through this point and perpendicular to the radius.\"\n", "\n", "Selecting a radius of the circle is equivalent to selecting a random point $\\phi \\in [0, 2\\pi)$. Moreover, selecting a random point on the radius is equivalent to selecting a random point $p \\in [0, R)$. Given $\\phi$ and $p$, it is straighforward to obtain the cartesian coordinates for the two endpoints $a$ and $b$ of the constructed chord.\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "phi = 2 * np.pi * np.random.rand(N) # choose random radius\n", "point = R * np.random.rand(N) # choose random point on radius\n", "\n", "# for the radius at \\phi = 0, the two endpoints are positioned at\n", "# angles +/- arccos(p/R)\n", "absolute_angles = np.array([(np.arccos(p/R)) for p in point])\n", "\n", "# selecting a radius at \\phi, simply rotates the angles of\n", "# endpoints by \\phi, i.e. the two endpoints are\n", "# positioned at phi +/- arccos(p/R)\n", "sol_B_coord_a = [(R*np.cos(theta), R*np.sin(theta)) for theta in phi + absolute_angles]\n", "sol_B_coord_b = [(R*np.cos(theta), R*np.sin(theta)) for theta in phi - absolute_angles]\n", "\n", "# calculate the length of the constructed chord\n", "lengths = l2dist(sol_B_coord_a, sol_B_coord_b)\n", "\n", "solution_B_pct = 100*sum(lengths > triangle_edge_length)/N" ] }, { "cell_type": "markdown", "metadata": { "variables": { "\"{0:.1f}%\".format(solution_B_pct)": "50.3%" } }, "source": [ "From simulation we find that $1/2$ of constructed chords are longer than the side of the triangle. The plots below show: (i) the distribution of lengths of the randomly drawn chords, (ii) some of the drawn chords." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1aMOPU5GrvN3H90Tvd61d4g1N0aRiLYpAfIjc+UOB60NgOYL6oxD0T0UOdzv/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\nI3xP7RvjNyjGaSi+LxehqlwbY/RDVNT/aVYBcmWVVVZZZf9SlhLHoeJ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fbd8egXPPUM1b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cdd4IIbAeLt3XRgWzOBJuKi4jn4gwfB1CzEMIwK0RgO/LmVPCh9fgxr2rUGEcHf77NQYQR4fv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_length_distr_and_chords(lengths, R, solution_B_pct,\n", " triangle_edge_length, sol_B_coord_a, sol_B_coord_b, N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solution C - The \"random midpoint\" method\n", "We saw that the first method constructed chords by selecting random pairs of points from the circumference of the circle, while the second method selected random points from a radius of the circle. By contrast, this method proceeds by selecting random points from the *surface* within the circle (i.e., the chances that an area will incude one selected random point are proportional to its surface). Specifically, to follow this method,\n", "> \"Choose a point anywhere within the circle and construct a chord with the chosen point as its midpoint.\"\n", "\n", "Suppose we have selected a midpoint with the aforementioned method; let $r$ be its distance from the centre $c = (0,0)$ of the circle, and $s=s(r)$ be the surface enclosed in the 'small' circle with center $c$ and radius $r$. \n", "\n", "Consider a newly drawn midpoint with distance $r'$ from center $c$. Observe that the probability that $r' < r$ is equal to $\\pi r^2 / \\pi R^2 = (r/R)^2$.\n", "\n", "From the above observation, it is easy to see that selecting the midpoint is equivavalent to following these steps:\n", "\n", "1. select a random point $p \\in [0,1)$,\n", "2. select the circle with center $c = (0,0)$ and radius $r = R * \\sqrt{p}$,\n", "3. select a random point $m$ from its circumference (equivalently, select random $\\phi \\in [0, 2\\pi)$,\n", "* use $m$ as the method's midpoint.\n", "\n", "Given $r$ and $\\phi$ associated with the selected midpoint, it easy to calculate the cartesian coordinate of the two endpoints $a$ and $b$ of the constructed chord." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "R_sq = np.square(R)\n", "\n", "# pick midpoint so that\n", "# midpoints are picked uniformly at random\n", "# across the area inside the circle\n", "mid_radius = R * np.sqrt(np.random.rand(N))\n", "mid_phi = 2 * np.pi * np.random.rand(N)\n", "\n", "# the cartesian coordinates of midpoint\n", "mid_x = [mid_radius[i] * np.cos(mid_phi[i]) for i in range(N)]\n", "mid_y = [mid_radius[i] * np.sin(mid_phi[i]) for i in range(N)]\n", "\n", "mid_y_square = np.square(mid_radius)\n", "\n", "lengths = 2 * np.sqrt(R_sq - mid_y_square)\n", "\n", "angle_a = mid_phi + np.arccos(mid_radius/R) # angle of first endpoint\n", "angle_b = mid_phi - np.arccos(mid_radius/R) # angle of second endpoit\n", "\n", "x_of_a = R*np.cos(angle_a) \n", "y_of_a = R*np.sin(angle_a) \n", "sol_C_coord_a = list(zip(x_of_a, y_of_a))\n", "\n", "x_of_b = R*np.cos(angle_b)\n", "y_of_b = R*np.sin(angle_b)\n", "sol_C_coord_b = list(zip(x_of_b, y_of_b))\n", "\n", "solution_C_pct = 100*sum(lengths > triangle_edge_length)/N" ] }, { "cell_type": "markdown", "metadata": { "variables": { "\"{0:.1f}%\".format(solution_C_pct)": "24.9%" } }, "source": [ "Simulation shows that $1/4$ of generated chords are longer than the side of the inscribed triangle. The plots below show (i) the distribution of the lengths of constructed chords, and (ii) a sample of the constructed chords." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/T0FublHkRE5HcFYNObY5yJFtgFzP4qQ2CAEBWaZ/nmwkAoLLoWjN4xL+d0Cg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N4fE935uPLMpTkXq5swIM7bsqj6uO4iTLReRRvVe1F3I/Dz1A4ThsLGtRyVkZu5QKeUuIcfIf6N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s+nDjKHNPDE25Fed/LYaTdMZ51DiedwiqwwdG/0zFbDE5JVbBeX0urtrUY4jK8wjf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_length_distr_and_chords(lengths, R, solution_C_pct,\n", " triangle_edge_length, sol_C_coord_a, sol_C_coord_b, N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What solution to adopt?\n", "\n", "It should now be obvious that different ways to produce the 'random' chords lead to different answers to the problem.\n", "Moreover, it's up to our imagination to come up with other ways, simple or elaborate ones, to construct the chords.\n", "As an example, for the following method to construct a chord (let's call it **method D**), the answer to the problem is $100\\%$.\n", "> Choose the chord that coincides with the diamemeter that forms a random angle $\\phi \\in [0, \\pi)$ with the x-axis.\n", "\n", "\n", "\n", "One might argue then that, unless the method that generates the random chords is specified, the problem is not well-posed. On the other hand, in real life we don't always get to choose how the problems are posed. Suppose that we have to make a decision that depends on the problem in *abscence of such specification*. For example, consider the following decision problem:\n", "> You play a game with one opponent:\n", "* You draw a circle anywhere on the plane.\n", "* Your opponent draws a chord on the circle. You are **not** told anything about how the chord is drawn. The chord is **not revealed** to you yet.\n", "* You place a bet of $100$ dollars on one of the two outcomes: (A) the chord is longer that the side of the triangle, or (B) the chord is shorter than the side of the triangle.\n", "* The chord is now revealed.\n", "* If you lose your bet, you receive no money back. If you win the bet, you receive $300$ dollars in the event of (A), or $150$ dollars in the event of (B). \n", "\n", "Also if you choose not to place a bet or complain about the rules of the game, you die. In absence of any specification of how your opponent draws the chord, and assuming you want to make the decision that maximizes your gain of dollars (and stay alive), do you place your bet on (A) or (B)?\n", "\n", "If you do the calculations, you'll see that having method A, B, or C specified as the method used for generating a chord would lead to different decisions. Do you have any reason to assume any one of the three methods to decide how you place your bet? Would you perform your calculations under the assumption of method $D$, that we just specified above?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a strong argument to place our bets while assuming method B is used to generate the random chord. Specifically, method B differs from the other methods in that it is location and scale invariant. The argument for method B is then that, unless we have reason to believe that the chord that the distribution over the drawn chords depends on the location and size of the circle, then assuming method B is the only of the aforementioned methods that is consistent with that state of knowledge." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To demonstrate the argument above, we perform more simulations." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# small circle\n", "r = 0.35 # radius\n", "c_small = (0.6, 0.0) # center" ] }, { "cell_type": "markdown", "metadata": { "variables": { "r": "0.35", "str(c_small)": "(0.6, 0.0)" } }, "source": [ "Consider a small circle that is entirely contained in the original one -- e.g., here we choose as our small circle the one that is centered at $c' = (0.6, 0)$ and has radius $r = 0.35$. Take then a random chord of the original circle that intersects with the small circle, and consider the chord that it forms on the smaller circle. What are the chances that this smaller chord is longer than the side of an equilateral triangle inscribed on the small circle?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "sol_A_small_lengths = get_small_lengths(c_small, r, sol_A_coord_a, sol_A_coord_b)\n", "sol_B_small_lengths = get_small_lengths(c_small, r, sol_B_coord_a, sol_B_coord_b)\n", "sol_C_small_lengths = get_small_lengths(c_small, r, sol_C_coord_a, sol_C_coord_b)\n", "\n", "small_triangle_edge_length = get_triangle_side_length(r)\n", "\n", "sol_A_small_pct = 100 * sum(sol_A_small_lengths > small_triangle_edge_length) / len(sol_A_small_lengths)\n", "sol_B_small_pct = 100 * sum(sol_B_small_lengths > small_triangle_edge_length) / len(sol_B_small_lengths)\n", "sol_C_small_pct = 100 * sum(sol_C_small_lengths > small_triangle_edge_length) / len(sol_C_small_lengths)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our simulations show that only for method B does the answer remain the same as the answer for the original circle." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "plot_chords_and_small_circle(c_small, r, R, N, sol_A_coord_a, sol_A_coord_b,\n", " sol_B_coord_a, sol_B_coord_b,\n", " sol_C_coord_a, sol_C_coord_b)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "plot_solution_for_small_vs_large(solution_A_pct, sol_A_small_pct,\n", " solution_B_pct, sol_B_small_pct, solution_C_pct, sol_C_small_pct)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can experiment with more small circles by changing the parameters *c_small* and *r* above." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Setup\n", "\n", "Run the following before the main part." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.patches as patches" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%run bertrand_helpers.py" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }