One Sample Dual Certificates.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import trig_poly\n",
    "import dual_certificates\n",
    "import phase_transition\n",
    "import test_data\n",
    "import numpy as np\n",
    "import plt_util\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "reload(trig_poly)\n",
    "reload(dual_certificates)\n",
    "reload(test_data)\n",
    "\n",
    "fc = 50\n",
    "\n",
    "N = 50\n",
    "min_separation = 0.75 / fc\n",
    "\n",
    "gammas = [0.247, 0.339, 0.414]\n",
    "kernel = trig_poly.TrigPoly.dirichlet(fc)\n",
    "gamma_kernel = trig_poly.TrigPoly.multi_dirichlet(fc, gammas)\n",
    "\n",
    "support = test_data.uniform_supports(N, min_separation=min_separation)\n",
    "sign_pattern = test_data.uniform_sign_pattern_1d(N)\n",
    "\n",
    "# interpolator_1 = dual_certificates.interpolate(support, sign_pattern, kernel)\n",
    "interpolator_2 = dual_certificates.interpolate_with_derivative(support, sign_pattern, kernel)\n",
    "interpolator_3 = dual_certificates.interpolate_with_derivative(support, sign_pattern, gamma_kernel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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BYSXgjz2mdIjV+mWZtfy5IYcqabfb9U1tvLZzZ8HcO4srSOZFtMxC4VAlm9t2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\nvcqqkKHjmtWJHAqlV6VsKZ0mF3iqClohVh3D1mPyXrZeSlPm+y6cuY8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4GBGjwMvAa5JO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\nrIVc3M3MWsjF3cyshVzczcxa6F9cMhq2TxklzwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116548f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_util.plot_trig_poly_magnitude(interpolator_2, points=1000)\n",
    "plt_util.plot_support_magnitude_lines(support)\n",
    "plt_util.plot_magnitude_bounds()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "23.4133799771\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118141710>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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iU8N8zkO2w3ydopi50LIEJ5WqqsSwgifZojHFKhNj1lVVVbC/lsnCU54rGqk7\ny1pVPBiqWC1sZYdCOTBinSm6QSkePg3zSXO3VTY5nPc7ywbqujIVtA/zjXNjnTWmxvtay0YMljTA\nZ2/xX1CkseWQKW9MZfoBKN/UqUHh/o6NfNwD9lYL2FnqhoG/h20HOwvnxJSE8JdN7a61wnx0Hir3\nfEgMAPq32mYXDOqdgmy+UieFth/CfBpnqof98blL94UIDb6bUuWcy1I+antvnFpOz6XdBbS9XKIk\naXMbO+LW3KQcOGmOdIVObklbVA5HB3u1qPP7Y28/Q01wX2vqKssHvtlyLo2pTdt7b0RaQHFMnIUC\nSFgMIE/wjttF72JEphTPMoZAj2FMbbtiY4/ezyQC+qaD3WUdCJHCc9gWcr/QaMEN9aQibbAb5tnx\nMMXBtvWbqhaWOhpRgYWCDFHBOWRxDY7aHlYLFyoty+YjkHsmm0/lSnRBeeSQKdoHKnk0xFYL20jE\nawAgS5rF/2thvA25b/e35oTYIYCEM6X0E0IpugFQiroetT2sx7AcQGqg0/DyzqIgzLd17S2b/JzZ\ntoVhvjEcuDLaxPd/qTDM59HJhbv3Tdurp0Vsun6yc4rI1NriTPWD31PkMhjxXj6F/I4i3dO262FR\nV7CoK3FPxbV5UXEeJOHJEyXFa11iS2aNFzrbF1b5JJlNN4yRgRq6fjBPBylJDpAE9e2e4lDeSjmX\nxhTljVjIVFNXaZhvXByokKZwmkKYr4wzZXmKlrTE28rBuJSAPrVmVkRAF77bZY7tQaG8kdMQzZhC\nbxEg3bSxuCIdB68GfdS6qsuLpsp6U23v+ls0lZrFthnbK33PAXKXDbSYoyZ74ts+EKyljbRT0B3k\ngK3H2lHrRa0fk0MUKUA+zJdTLqXht5ySwDnh2+ky/RgoUdf3sGzGEJKC6KJCWS8aYqDzMJ8z2DHM\nlzOmtiMis2yqPB+yD8hU7kzD1aIxEdLgCOZROwCS0TmGJAGMEgbEuZ0Sals2tTkPtwTxsmqK7S7L\n0Gb+PW28zjh1z11qkzsPJcZUQKbyzz+HJuX2CamtvbUcsqRCkVD8W23XP/tpTjyu8f2JtJSbIefS\nmNqMoY6qkrMt2q6HqgLYWaTweEsQB4CpyJT7LqIb6nEy/cms77YfzFBOPCbsazGJ/4XcjaWBOpRm\n890gCuU0RAqX+FCGX+jxvWI4ho6DKr5hGLwxtazrIs5UU1fQVLrhhZypHKclXI9zTw4fdIS4LdUX\n60aCNRqN+WQ5AAAgAElEQVSU0jvZdtTYCp9jdiJFpnLcpVJjKgnzKahijnzbZ9AizptL+mEIWI4z\nhc9JRdwIQueRKaX+2d6qKTOQIkWdR0dxzltGijPQKvOdeuVXaPT4MN/CRq8BHJIyOcyHnKllbWRF\nD36fl50Pdw94T6Xkd9QPrg9hHY6O1FJBBAPCXBYyBaBzM4+aHrXO0HfhNntfztUh3I73uquELPm1\n2C8dsyQ0IjJF73hayrpRnZhbJefTmGrRu9M8hwGWdQ2Lpk4s9yTMdwwC+rKpxwwXebIhorNXmOXF\npVUUojymsKFM8RAOtiybTySgh//lqkQDnC4yxQ1VNFw0r+mAIFN1XcHeqokPSiUckKWySVFpuwGW\ndQVNU+nhjbbzXJWugDuxJR6niASSf4mJFeM4dr0xJRtcUg01GZmyjQi8NqdMc5ypJMxnIFM4H6X3\ng0pLK42QGm1GmK8bQhaYYSQAgN9rlk2VlIeIjam8Ub3teliO89hlHxpGUtvDoiDMh4aJZUzhPfp9\nJbNXhPlSw2ph70UtIYHnlLsfz2hU7hhV8ylSYnEMMdOy1DHeeINWdpTaHsOrshHbdsNYsqLM4XXf\nwTWAZTv072zb3o/PythdFRjkVFe2vX6UE96HS3io/HetawGc3pkCSFAwYw7z3QbiF5nCfUELe9nU\nyeLmYb6pmQh15cKH1uGfXulNDL0BOO+8H+j4CsN8S+chlJwGD+Bg551cmG/cVABsODkolFPiTAnc\nE1QYOB6+gBFpQ9lbLaIwH0VbFnWV9czbrodFU8Oirg1jCrP58p4c/XxfSVPuybuTxleCLmz7QQyF\nTkOmYgL6cvyphcRpnSOAdC5hiCNXGqEjY5eUjU/z1rhZ3ljNoy9t32eJy5w7trdaJDzJA8KZWi1S\n543LtuthWQfv31rf1JiwOVNjyGw0OqQ9APeknAGJQtcLrjnNAOiGwRveJbwlrAfmsvn00Kh7Vm69\nikWF2V5eSoTGUKu2trsRlda4lcipWha8wzDW8fmXJEf0g2tfee943+uljVgCYAi4DvPNMKK33QCL\nwjBfVN9wSpgPo0bLeiag3w6y7QZYLWTkCcC9sOW4CfAXxpGpSeS5cdMCALOQXUeMqSmZDgBh0Vmh\nHOn6vQkbClbj3aWlERQPCM9ns9o92LR+gZyGrJd1cu6c97AUwwU3Z5S9VRMR0CkHREM0qWxHQ7Kp\nDWSqizeqPKF4VPYKNB5l6RjE11AaQTaAw9wO7aXIlJ7Gj88qIaBnOFMaMkWJ92Y7NPRmIKU749rW\nELCSkBPtS7uOhzv3Vk1yrA7N5nPKN2ekB1QkN0Y3B3UEHoWSuQFk45Bm/QLk94lw73bGLwCMvLJy\nlGbrkZXKzIDcdgMsF24NighSEmUo28vR2daMJWfMuHUt9YuZiMs6/w5pnwBgZieG/u0sTroPlDhw\n1CAuDRcDgJkdHiIi0+glGDUqzYC+mXIujalNi8hTJcLKm84tBoloTDlG7topxtQQGVNqNl8fNiIr\nI0ISb4gZSoUKfr47oXAdGoE7S2IICBlWbT/ATgFChnylCokIJ5SdZZPwYY7GTUHjTNEK2wBoTFFk\nKqAtGheCStv1bg4pGT3Y53qKMYX8hZVcMT0ypiRjokN0SX4nVqo4NwzWxmYW+DJN9B0rzFdXQNAW\n5sAwB0FbE33vlGddyddg/wusvaQgUyUGQ9sFXqKmYPgZhburRgzzrRb1yLEpCLuQMB9Axpii+5wV\n5utCPSoAhazNnk32gFwa5suMte8Hb8iVKFb6XHOlEXANivOhm3ZPKNsRddZC+Dlkqu2G6B2WkO5b\nYnzkxophRMvYc201RQT0UlI5J6DbnKkQEeky4UP+vcWYeToT0G8DofwZTemsGnlz40jOtDpTIQPI\nCvPhAl0v8rVkkj76WGGWZp2VeBMoG6JYrQ24lAh/g5x1eBoibbDb1uZMoXeOsr9exMgUDfMV1Pjx\nBHQLmWoDAZ32ocnRuFk55ZAJqxrKQyuNwDlVUZgPlSMpxKkW7Ryv9chUxpjadPaGTdcDgB5qQERg\nUdcRGZ/fn1ZTiRttOWQKjcVeCY0nZxSKYb7WP+8yUrkL8y0KFFZpmI9ypvDvtC2GeGfGGQq35p2F\nfgjPqMSwwD0bs/n0g46d85pDpqY4kgAOscUwn8aZWozvyKKRLBq7oGjcJu7rdfS3fO2ISKoEdERo\nG+gH3TnBsdJ9055vAyxGvQmQ4UxxPTqx8n1JaZCbLefSmMIXoqW4o+chZW15i/o4nKm+95vg2pgM\nLVEek5GpTleIkoQaMyPkXDCpPZGebMCSIdB2fREX4mA8w+u0RKqKHAxoGVo/atMwH1b9BqCKcSQK\nZ4xOPMpD28jdmNymV5L9AuAM3dWoHESPmHBPLOKpNjesGmoSMmUdk0Ovzd0f3pcWSuDGlLYmEBGo\na6X+j1fClRim7LgjYnr/vT970MrWBIiRKR7moyU5SrL5MMzn16sVdikM8yEHyD5nMzbEc0TxcKSQ\nzasEcPN22ThEsWQ/TZApNXzc+zUoIR9btpeX1plq+xDm02gimM2ncRcXNUWmykObu4Vzs6mrkROs\n7wM7BTosENAL5hty7wpCtj6hYWpJjNFhREL87STn0phqu5Ggp6S4o4W9EBbDlnkzU6xj9GgAnMem\ncU6wz/Xi+JypKQT0ZV0G46IcEc9QC5vhWLB4nbX53ti0sLc8HfI5wIhMtQIBnULQAl9mzYypAynM\nt8QsnhwyNYYCDGQKaxVhv7kjOtBL1NrsCfdEzuYbNzAFteQKU64zlSeg06xVgALOVD9mndWy1+2d\ni0woqO17aKpKJQbT+nEiMoVKZpH3/inPx0IeAUK4c09Ao29sgyOxVDic/B6iMF9xVpcd5qMIqfSe\nPJm+oD16PRYYxX4k6fsB6mpEcgqcOTqW9ZjxLJHmvdOsIEjcmJLOaZUEw2gq4jUa9SoBfOTsWnzT\ntE0ecbCRKUSI7Kxe2xkAoIk7BfOti/dYG9k9HijRju/U2ldvlZxPY6oPWQeSRdzRbAhN4RSG0fh3\nEdq1aguhh7xe1lHhy9I+AMrheNycF36xFMDsXdjM8tl8dVZJ3DhlZGpXOAQ22RQynKn91QKua2G+\ngmy+bRcMSW3Ru0239so2SwZtg6cthbG6fiBZNxJnKPZIE2MqCeUQAvrI70Jem0VAx2eL3mxJnamY\nVJ1DprR14wwljTO17Z0zU1XII5L70ThlcVsBdc0ZU3j/+6uFeDYfKpRFU2cV+mYM83lUw8yuIlnJ\nJkowotMFYb7VYjROsmE+Whohj0whklIU5iPGOoa9JJQUnWIVqUzQnnJkyiFLOmcKjThpDvEwX1k0\ngK3NDJ8Pw4zSfOq4DiswtIsMJB/my5dGwHFN5R57oMPgot4qOZfGVNeP5f4VD6sbnKdkZfMtmwqq\nCoqJcwBBaQDYnr3nbhwHmZoY5vMo3TEWdsyzSBXrtgtVwC3FdLDpfDr6aQiG+ai3mg/zdXGYb80J\n6CzMl32uwYPS3mF49mWo4HbcxNUwHyG+FiFTCh9Q2rB56QjrCBwcBxpeuTDfph2Vj2IgJJwpZS51\niHA1CjLVBmfG4kOWOCJdFwxX7f3SOlMAIwGdZ/NtOo/KrkoQzy44KABghpspvyRX5mHR2CF7fFaL\ngvVM21gvGhO9BnDvt66qovpteD0AwKKpfLawxJtqe7uEQaBsTONModHeKMZfQKbk97kdw3z+uRRE\nN4Kjk+eWobGnzSderNQ8BDshoBso1jjfyop2srDxBPL/EvfAiUDDWcu5NKbafoAaCYKKUsKwA5+M\n1CtaGIpSEprNtzI4J155LKdzpoJCKIOQc+Rf8Ts0zGcsHIrw2RXQO3+kw2kIhoPo8+WlEXIE9L3V\nIuK30DBXSTimJXPI4vigcpLGlLSJPKxK50w5zpCMXPlCeUpWHCWm0r8BAjKFYs3f7ZjU4K/NEOwx\nfLmoc8iUjQShEquVqvPUmZH4kh1bO9bapqUvrOOCAGidKSGbj4T5FkpCTHIPiwpWi4LSCKSMgqnY\nxnlonaFIeZIlhyzHRTszBHTvBORLjuB4AZxhh4avVB4BUQzN+cC9f3dVHm4DCBXOJf2An4c6TxJn\nahijAXqyCJcpERG/92gJVonTYLflIhAl842H+WxDHyDsNaWgBOU7lxZ4vVlyLo2pHpW84sF3/QCN\n95S4wgleUa0oNU1oNp/l2VMC+pSCZm7sowc5GnslCjqOiefvZ+MNSoJoaZwpT9Q0kKkzyOYDiDlI\nPHOOKoy266EfHFkWZW/lKivj+0VDYMdzpuznhKiThUy5RIfwDHMhjm4MTzd1Bf0ACU8E521TaYRb\nW3lw75fObTywF8UKHXXd4GvoAABUlX2IbkuUDx0H/RwA/IauGbJ4/1qRRiRkA8CouG1kylIGzhCu\ns8cFuXGjMSWF+Vg2X2ZeIXkZ+WVZ5bbIh/l8Kv04D62Q2KopC3MfEUMyrDkle3l0AlaNvB8n14/j\ncyFy17aETAXOlIIQEaewZK8M4wX/vGTEayCIvIQMhWxxHGdO6EkV2IYmFPGW5hPVLwB2Nl8g05eH\n+UpKvWyNvcaSNmMg30o5l8YUTVuXNsJ+cMiVVCE9grsnIlMI0QPYYT7qiQ/DtFAijgd5FbnxOch5\napgv3Si1bD6s82LXmWpP2ZgaN9g2DtNRozE6tZwpPYBw9iKWR6Bhi0VBWi5C7VoZAwAalsvzXwDC\nu0LUh28mOG/dRiOMKZPe3pJ55/ojz4hxyqy5j+uLinnumw/zoaceX4elB0LdLh3ps9Y11l0CADHT\nquPIXMZQwb5KSyPgYeK0XepIILHbPCKmm5KqHrLG+sHOglxmDDSKyJeEuakx5dFgxVHrewgE9ALD\nQkSmFJrBsqlVpxfnmQ+FFu6zAZmS9zWMbCxrObzq30tdjoj5GnEFRZApp0sz5gDySC/2syTJISWl\nOHJ1xWifuVC5NJ4FooKFxu/NknNpTHkPXvFgvYcrbLj4t8Vd0WQzKkMAh4JoYY+QzTdtotHvomeU\nLwQZczBK4vc0m6aqUHkrYb7GnU+nKRwAgBtHp10aIeVRYLYeEpTpQufhGADHmQIIR93wop15IxXJ\nr7oX7+siFaQdA5DnicbUkM7NxXh/0vPmYb40zBXQN9deH313SY0pQ/lgBWYqrmKxcezHQlcufE6b\nYdNGN3Cw/g4AiCGakDWok/hpX770hfLejpiR7g87JvOSlgVZNjUMhtEDEEK9AaXLXVtnw8htP0CT\nQUi3Xe+PwtJS/vn1VRVn/GrHCTlkCopDNzhPm7oKBHQhzBeI2FrRztHxbMr2ytC/XUNu27vEkoXC\nWcIw3zKDtEb34kOSJaURBh85GQQEO0GmjL0Z7zWE+fRrPb+qhDPFHDdLP1Dph8ALnZGp20Dopqtl\nRdUeJuUbLobRdKKrJm0XeDk2Ad1tXMsCGDb9Lm4QdVGVWJrx4/7O98VT3zW0AL0IjeMD4Bb6WRTt\nBIh5FBRZ4Z61aEytmDHF6kxlw6c9LbCpGB2dHd7igpu0iUxVxiZP3lsjhD6sjKHEmFJC5HgfHJmy\nFHAoRCkrF9xoc7yaljwfrWgp9iGRqD2x2SDxx/dYq44EACkP0GBpBId20pIbB2P1f4CwnjQjte8H\nb4CXhF02yK/KXBsScnSE1D075JvlOVOcHwqgO2rovK4KuIgA1KGlnKnYUB+GwRvPetFOjDK4vbI0\nOyw423nOlFjMeAzzlYRqUWgGdVXpGa0ASK8IHMSEG8mc9dzhxTSsbPWLNQtLsvmwz9VEHefLUhQ4\ntDdbzq0xhURVaSL1w8iZMjJ+ED6eSkDHCY7HcWiHimJIw/1dDmfiBpGrvh366mPvdWKYDwAVq84d\n0AjRAG6TdufBnWadKTcuWtOHEsxXTR2FHHwIr6HGlBsPktBpReeFAt9ToZwp7d4RESh9z10/Gh3K\nJhl5zCIyFeauZADzo4hiZCpUVwdwxkivhKApAuSvt4ygjof5ZE86oAyWUga9SCMzqBNkiqDOWkHf\nMKZQuFGd2wIBHSAY6MMwwEFUZ8quiI1rszhVvQ9zECBP3NcSAADAF1YFgKIzBNFABgCT2I7vCcPT\nJaURAmeqIiF92TGwEjYo/3XRVEV8Uezf4oLSDGkrESKX5cjbrCv3nHJ1+5CDWNfaesK9bAzzZZAp\niobnsgiXTe2dh9zcBJhuTGGm/YxM3SaCxoqFTHk+BJsP1CvSiK6a8NIIADLXKAnnHAOZwsWe++62\nDRsDQBk/ixbtBADVaPOFKxWjFSB46bvLs0Cm4jAfPnOegm1zpuIwH2a25JGpIfsOaLYjQH5T3XbB\nCcDvR+0NbrPVnIQIVRUUAQ9zWciUH7OYet0nyJRlBPnz5hRPvSMK11IkHSJTlZISHoX5JM7UqKQb\nvaAvgFsj/QDBUTCQR4BgJKHRRA30foAozOe+pxud2F7gTOmIL5LkLWI5tkuzSrW1HPhmBdmsBMky\na9Eh6ljZhmk8lrDHrZXSCCkKK+/zABi6LE/2wVIOWqjbG1uNxpkakaPCLF6AsSwKCVHnQsHUiOYh\ntIRGYmbd5ZMTANx82zKnyESmxjGtMu0m3/O60T17i194s+VcGlO4GBwxUfh8CBu3VhphYSxSTVDB\nApDDX0WCYOwpHocztaj1gzjjMYXaRaV90cweAD2zi3rG2jjQWDkTAvq4wXa9UyyYrceJmRZn6joh\noK+aepwXBWG+Dp+rvKFiGIIqu5yC8sUAlQ2oJ8iMlZG1rMfzBTnqiiTXgjCfZejTeU6vtzhW6EnX\nVbq5x+E3vZBtl5lvmD0JYNeZQsPC4rphG5axTCuuA4Q5jogpzk90JHLKNSS/kHppmSSWEmQKjdAc\nAX3p13sBMtUHJFPiKfJx1hnDVPpOU9fJWkfx++C4XjRuLI5PK2Mg9j/YBXnxeWpEfU6tKCqNQDJk\nc5mH1JHD8fDxAYT9zuIrheQEWz9QJLCk5AO+n1UBbyv6Xh+QKTf2oq/dFDm3xpSzbmUkhiolzXvH\nSWPFkKV+m7rAW+sxa+s4nKmwgWvHKER9DeHa0r54mE9FpgiSoi1YNKZOk4AevFU3Tm4saZwpfpwM\ngCPHAzjO1Dpzv1RopV5twwUIBgKATXgGCIiPhkyhYVxXGuIakCkpBGGlTGNWD4oVEkLPmIqVTk+v\nlzK6cFzIB9MPOu6hseoKdbk6U2TtGBwausasUD8aFFi8lIf5DpgxFQpx6ggeAMTHyRikcgBgYWTd\nmKVcF/E8uZageiVczDY2vjWOKOXDWdzKeLxh7eBa5wi/D4kSFIOLN6ZG5VySfAMwhtxGI9VyIjW0\nP9RjyiM4oc+A9lpJGHhfuA/g31H//tkUlEboh3FN2ddGmZF1HvHC/WlZMAYqSEAPzn+5/j1rObfG\nlMUtCSnrgsIh3qFVY0btd9QxayPMh0Ta4yBTOCnx4NDcJMU03ynIVCjaSb18+Tn6arWZMN/+qXKm\ncIPtovFGnKlMaQSsSo0K76jtfPirmIs2ooMaOR8AWBZVPnSIGWQAqTfX9wB1rXOGqBKSHAX8TiiN\nEBucC6IcQ0hKmr+9NxBRLMMenRsAEA9n9Ybn+KxMhKUySiN0lPeTIob+nVT6IbH0OkSwtBA2opMo\nWJj2YEQ7uSOxyiAV3psv8P6psa4pVYA4ZGkR0GmNvKI6awyd1FAaatCUZkfH2XxYU04O8zmagXzv\n4Rk5pLYUHQmcWvskAm1PRUer8nO1JMwXjNkmU9wUS6hoCDb+jfuZhUwhatxUGWSqDcYRIswW0OD1\njjE35e+FWnJTvncz5FwaU3ggaqPEnkNWVPp5RGys7ZR/LuXIFCOOFsLPdHyINuWNKfCGo/u7nIC+\njJAa2Sj08L0yDKzjdJZhvqMxJZ8iU9QLpaUefBtjYcsDEuZDI6OkvpgvLlfpzwYghNzwO7k26Sad\ncqYQCZTh75h7lBo3qEwWgiGOlZBRbH5NGubT0sSxDVwXy0WKCNFwjEVSpoiAVhpiQQwCrtxd+B/8\n6QhWtiIAeCVjhT4ompcgU5vjh/lySLI3DDOcKf/O68qHkeQCvATVK6jxg8d+oGhH2uCrDvXRJiJT\nytl8gV9Wq/t8WA8widBM0RqVK2pyloKRXRIyBXA6gM5dM5uPlEYAMMJ8Tb7MQtcNnjLivptBTTFb\ntrYL0KLe8c9oijE10fm/WXJ6cMDHiAxD8MQsjwVJd2ktGmdRe69igqHj2nW/40TWDhWlpL8pUGZA\npso4XZ03LPPZGigeySEhE2nh9AOWRtAXy6HPkjvFg46XcpgPs/WWiwLO1IojU3GYL2dEU7KzOMci\no7csk9Lz24xNsq707MkotCjMba9cqrQEATVEsA03ZkGZCGE+S1GiEeTaTb1uil5YR5ngsSRabS+a\nru84UWk4EZWcVfMoEPlrcy5wnhmvXeY5U4yArhtTwdjNKZOYM6UjXpR/tDDQxk07+M9LDIC2G5L5\nIpYR8AR0MDNf5THrZ/NR5a6G2kkx2Cn8154goHICxhChLlLWLM53K9GBypagvTm9Q0uEAKQINo1e\nSJ8n/Ub8K/k6Oo8A5PUVX8/0zkRjyo9ngv49azl3xlQEfxuLTPOUqKIo9aT8d4kHvs5xpo6dzUd5\nH3lOV+e9rPK+Niybb1HLh06ip289J3qG12kJz+bLcaaOBGMKDbJQZ6qLOGJ5ZGo0ukHPjgLA0FUh\nMtVjlpBCQPfGa55wK3GYonpObDPkHBhftb0wzKdVg8Zx4fxbCpswDcdkkakGK1PnQlXpeKJxGOhL\nMVLGDApeZ4onX1hHM9F+kfju+sjzuqyQCD3RwVJsHcvmK6tfFyNTGhUAx1m6n3qjciTiV1UOmVIM\nuQSZKuRMjcZQXafZ3vg59guQKnxEtgDSzGK1T4Jy5o4dQg6c5iDjOsfIgnXbSZREQ5cJwok/rT2y\n64MOpt/PidfNE8j7N0vOXZiPclUahRiNnsdSmBCRdzvBmwFA8pz7PZRGkE47jwmMx8vms8mxKDwG\nXZbNF/OstAM/8XgTjRANEDzIszGm+qgPb0zVcmkEOoamdmdMHWwIMjW229RV9pgfDLnlOFNoIFRV\nAWcqUxqBhgG18BvtMzHGxu4l3hHlbADQkJSCTInZfLriDwR0vf4VkqktNKYWxu7vIcpIEwryRkR4\n20jCe7IMAG5QcAMdUU+cr5aBiu3RfgGmcaYsg8JltOltYi0qALv6vR9rH5As9x0ZqcD9t67LCeie\nMzXyjtbCodvcSMxxpqZEGfp+ILwgO7IBICNDkdFRUmeKlEbQaBW+fQzNVXKYEV+DJ6ArezOWOyjR\nRRRpBwC1LEQYQ+8z5gHKw3x4ru7MmboNpITwGFL660Rptn0Id0zlTNFYuaWMQlx4ejZfIOvWKnck\nun6IPY+S+6FEXteXcsYhUW7aYpFCbCcVVAyHnIAehfnCeMLncahxb9XEBHRSpBTA9qb8eWNZw4bA\n/Tm0ayS1a/0j10/LnqSeuGTg4t94DAhVvhTVcePW5yZVvP56g7TMESEtmw+rTufChSoBnztCCTLV\ne8RgYXj/HsHL1EbiBmhTO8WPPMGkNEJGQVADKZcFFR3BY7QbZSdbaGNHQ1MlB6j30WHXLiRmIFMT\nCOh87ewsG7POlPaOQpZoPkMuGjPZM+V2e9WIxZIoniOoEPO50ILPuaKpPjRnINgAtGCmEjYfv2ad\nuoBCkVAco0VPwWdYK6FQTVoSYqX93g5y/owpEsqoFWMDPQ8pY2bbEV5FQSXsqN0B/OQJNUZkb7Ge\niBb58fWxR5YbXzem+YaNNN/XpuWKVd6I3P3aYbGzMKYA3Pl8Vpgvx5kCANhbNoTfEjhTdWZjAUBk\nym1EUnG51JOzOQbYX9OQysZKmKrUE+cGB/4ttUENERwvgMzvkc7mswi+EWdKQISi9HlDkfc9LdqZ\n9rUhBiGiK/S90HEsa/19UDQnV7STc8f2VmFOhTDfwrdH20/aI44SNptFppqKkIcNY4bWrlIcPMrZ\nySEJfL4slfpgNCmiPJsvNqbWizo5m49W+29qmYaAHLuqKkPxaf9WcVzO66FbPF5O53sJKtOysh7m\n3tPHhkqKQMfPT9t24iK/dliNrlEAPeGAjhHfOR1TTrxuVvbAWynnz5himTgaZ4pav7FSCRtyXU/n\nM9Giga49yQhhGQsFnosfO1koJd6W97KMDZcLrSbu+pLj/hjmsxA8TmY/LVkvA/QvcqaibL442w9l\nZ9XEYb5FGYKAn9HwKb90SzYqbDNL6u2H6DiZBL4f7OxJ6olLXjV1NHhpAHquHQDYIaEuRaasdO6u\nC566eAAxMTyt0gjImbKMSZ9FJTgqFCGzwnw0NGUX7UyP1dlbLbLZfCWhu8qjnlroFN91GTKFbWrh\nWI7I5wwPPl+0bE7/LI3EiWQshDMF4JApTpfwJWwaPeyLKIdrawIy1eeQqRjtp/fNEZxS4nsUZjVI\n61JoTlvnpehmzJnKGPqF93UcegmOPcfvu1Vy7oypkDJsbboQW7/RYhiIAiyvTQLgPBQKgwLIFdC5\nZzMJmSIbTSlnqp7YFz3jDED3lHyJCYMLcVbI1HrReG8VT6undabofUp1pgCEMJ+vM5Xx0pi37a7V\nSdUA8llxXPBwXe3MLeQTaNmTWAwWPfEU/nc/ayGchoUGUayDT7EeFhUrnZuuKSlTDL/njEA9/JZD\n5uLCh6kzQ7P5rPAL/rvJIBo8NArgMvcOti7M5zlTq3helYZSLIXFUUi8v+Q6jpAqaDZV5iUIEkcn\nFwoBPYSSXN8lCAXl0AE4ZOqQIVMbEubTnDl0Wl3/eR4YStvTEzTSNTgMemiMo2qlRlzXUwK6/h2P\nfDW1imDjM8b3ozm6FAnNIUH4/9qvr3yVdkR2rTFwCfpqOgXmrOXcGVMBjqxHbol8jQvRpIuB1k8p\n9SpQsL4VQA6ZAud5TqwO664N5MyShVqarUFl2/U+EwRg5EMo99FUdihEyqQ7DVkva50z1SilETiK\nsJ9X5oQAACAASURBVFx4fktUAX3Ujyq3hXBqAowdX9NyJWYgIf47mKWDxFLWP+UTaChETRQi38C8\nEVghUtb7+xwGiJVjneP8xc8yp/gxJCFVHkdvtBqTQnSjLKRba6UhfBgPQ1qkLYpMWWhqCI3ZYRpK\nGkahYb6DTQdNXUUHCLvv5ZEp/KlnNhKyulEYsRUQUg1tjAyAXGkQVh5jqSBePsxX2TW74jHHz2G9\nkJApNBj0pAWKoJYacgDEaaldIgoVijiLkY0+XvelRlxL1ohF34iSFDQCuo98xGNK+iQk/rp2STI6\nvyp+J1b2LkAIsU4lkntE6xhlg85azp0xRRdio4TpLAiSZipNSael9a0AaJhEhr6x7grvPyfUa9aK\nylHBRZqrcEtlI6Q968gUqFmTAMSYOu0wH0Gm+HExWtFOjiJoYb4mY+RSHoiEbtK/oyJ3hUU7NaUb\nsowUY4KW9RC8asoFomjjtosVrvtddwa2jHzs7s9W/Ba5lhuB2lmHuL4sY7Iha5ePP653ZVdad2Ox\n0d8tMygAXEiPZvPtLht/3EzOoUkVsYFQjE1guJ+O22pTK1Yac6b08xFRNszhWii1qSjXpi5GpmKE\nbmeZZvPR403qWuFMUWRKCUNK4lGVKn2mdA2JyJSABJYYEnjAL96TVQAX29WoG10fUFVs22qrIXuG\nangJc9PSJb68xEQCOo/azMjULRQ6mdUK6D1yfVKlSWvoaMUBxX7ZZLPO4UonTLn1HfgcZQsVvSwr\n1ZfLpo2z+SRS8DA4NKMykBLXluNfoUI5LXHp0goBfVHDhry3o04eAyWgi9l8KtRub6gA6eazzGzm\n/mBkAt/zTRC5fnVViaepd0R5SHw/NMCw+j8qv63Aa1sIyI5vh2z84Xp5rXEnQ0J6cI4CoCKRHSAA\nOxU+JrqnmWt4xAWAbagEbpm9xraMWwgAsL9eeAP9YNv5sgg4dhynJJwrZCnVliDUVvgwbVPOusNz\nDwHszEzaLjWol4aRBpDPjIzHEr4D4ByntGhnATJF3vcUzhQaYRLHi98PHS/9vZRbRL/XFEREaGhO\nQyQdl7U84YEeWJ13MMr2M8qnBXhpVEA/d8ZUBH/XKTkPICglaTHQIyJKSg/QNrFfAJtsGo6zsePU\nYj9kMWtkUiqc2FhaZ4p6nVIMH//0HqfS7KbtfWXy0xTqrXJO1ErI5pPGEHOm+sCZMur2AMgbqnre\nnC+Vkc9+cdcbxNLezoqiYS7pqCGazUc3w8DDI8gUjkGpNM7DfFqqNA9dSWEPzteRC4UGNFBC3YZh\niNCVEOYjiq4rWwtRaMpAf6VK8LurxoeODzZddIxSTrlxRKZEudH5kjNC3U/Z6KGGqMQVSq7v4hCn\nZtBQFNeiA/Dv1FXg50h1ptqIMyVzW7se4tBZoWLG+SgVx42Px0mNWIpqYr8lzrKLlrjfrSzysPfo\nTh+t4C597u+zi8dahtZShNPez6y9TP3egEDDzJm65VJySjm3frsoFBB7r1PgSfwOQFCiYiG7HknA\n06FMDjNnkalhKNqcqWzaHlYEeZAUYMjSAfXYHgCATdedOl8KAMN85ZwpaQwY5huGwRlci1C0E0Cv\nHEw3VNzwOVLEQ2eUoyRJ8DgrnYA+BJRRy+ZrCKrKr8HmaoYmesXEMjhdm5KBlBKvtfCcRxnQ+1VC\nJ9QJkcJF+Hh5iJK24catrz+KqFmKPUYe9bm97QTO1DLmTO1GyJRdnoQjBXboNIwxpMjLWXoAEKNO\nWiFWolRzTpqrsRWHhc0wXyZRhd8brbDvsvl4aQRcX7VqBGBCBt5TabhtGMj+qmXEVuA5STyygf0B\n2PwnKnTtWs+f7v9aCZeOOeuaIcOpCCUJD01knOpzBHmSJWVmqGAS13GAhrOWc2dMUZhVC5cgBCmR\n3NyJ39SrmGZM4SJCxb4RJkOwvqdDmchTqgph89TrL0Smohoy+jlvVY6AvpUNmZMK9VZL6kxJY0DF\nd8Q4VznyI91QvSJTwgG58BUKnbcLZd5itpqazdeFCvzSNT7MV8fFM31mVHRwrYy4uXGkpRFKwnMA\nICI9FFHT+HcdMd4l5IQbbVLRXK6wsl74eIahroyGNKmB1pnadrBDkamM85RwWIysLop8BqfMui7M\nQ624JjUA+iF1EKikx8nIiCJ3/kr2OmpcA2A2Hy/aORqeBPFKar2R7OpSIjhNLnHh9Pg5xPdTR9/h\nnwOURzd69vzzhr5+Np+nsRiJCQAyny53Lc3KzSJTTX4MaT99RECfkalbKDSFszEUXUmdqVLjg7YR\nspbQspYJ6BQmnpKxkKQwZzIq0Mvy1xdm861YNh9/DhQpsAjom64/1aNkUNbEW02Okxm9ZNwEed0s\nFAzzIZHdF+3MbADRhuozauJrpGw+C5kK9dFqlbTZDymqFLUxxIUX1TAfa8MrpkWMNNB7je6tT+sr\n5cJzlhGDXqw2bnfvYX1JToRkNPDxc4NBVVh92EMsR4EfDg0AsLsKnKnDTQd7J+BMLYwyEbwEjPuf\n9fztPSDiTBWgCRTJwrFqlAaAEJ4uK2AZh0/XAgGdV0B3fcXtUI7clBIFAKCeZ4p7Cjqz/HM/DyfU\n7AKIn79FmwjvU09gCtl8+Fxy8y0/1j5Zx7nzA0d0bIJRhPxKq+TMrZRzZ0zRFE4JYqQvTNrcKO9i\nEmeKLSKTM9WHLDj33Qn31w+RwWYWTiNeFkBZyjOA4w/xGjJmmM/YqDRU6KSys6h9mI9nDGJ/aCRs\nWN0slN2xMvWLB1sAAH82Xy7OTxUEctqlMgaurdHAy6QS05RrnDsJstQ75Mk6TsYT0IVrqBFIw2mU\nf4ISuGCK4mXIVI4zE2/YPDOLoyLymsH7krK3OP9D2ow5ITmLPNZ2+RFuUAA4A33T9dB2vcvmEzlT\nmRBORAjWrg3hJMv4SQ00OYwavYNMcVEA6fgh2Vmg2cel+w899gcgDukn99XoirdjjmRJcWSKSuIU\np48hOmEDnR7yPCVkqtSIo/u0NjepUaOVUEGuWC5UlvA6jfnGkwJyme70UHbalyV4SW5O3yo5d8aU\n5LHRzRnfDZYWAIhfGCWgTyn0xpEpDJmI2XyYlTW+ndJMB+yHKkxrssmbc76vtIBjuhHRzDDt2B6A\nszOmXJ2pEOZbNSFbL4SoyOfCGHZHwvnzNzauzYYp4iwJVCd5imRiQ5HQjU0rY+FPVFfeIzdKEmSK\neNW03AUiexHSYFVA71PitVbYVSpEyS/r+yGaozLCAf5zyXBLS1HIqIEnWRtrga5la405BDd+Dkg4\nv7Ht4MamZZypDDLFDE+TM0WQTyv9nNeZUrPuiGFYogA5Oqm9/0BAt585b5sjU4dsH+VFO6XxHguZ\nYqUcAGL9EYWAm/TzNJuv7EgyrLUGMDpCip0iIVMiAb0GcfxU0IHLrT3XR7yOc3Xz2i7O5ivL4qTJ\nY3mD/mbLS8qYet39j8FnfNsb4crhVr1GUkoSDItpzwA8tTWURrDIp0m/rKgZTiSxzlQPkyca7acU\naeKkQWtzprLthvg4GQEBG5CEXempyQBjiO0Msvk4AX0VZR8iMhXCgHKYzyFTl0djClGEfNZVQKY0\nKN175GTzseaSJ9QabdIyF3L2Uu83UOka7Qw8nBPUMNDO6sKSGKjAUdQzCiUDQUCmcI5qxkswcEbe\nlYG60Z88bT1GpmzkMYdMbcnB5ig4pw42HVw7auHCeuE/y2ZXCQory5lqbH5J8vwVNNuV5dCfHZW+\nHzwnBuU0CegpZ6qBTdvH5yz60gi1GmqnaE9TUO4BAOLSOoL+iJJPBCM2zMM8N4/3G+Zuwd5jOHL9\nqCNyRjH+f1kwVtzPQuRFP/IGxxDtZSXIVKRT5my+M5WuH+Bw25svJnCmiGVO3rlI4KOhgKhoZ74o\nZtpvDH1rZ/PVVZkHmHy3pwUO7eJ6vFyDRWilIh10nBy6myEEo9wUAjrLGPQ1vsbFfrTVwnzOeHru\nmjOm9rgxlQnzNVXl0TCpCrFrC3ybZkhWQFT5M0ejQ0rZxjYiIrcA/+NntNzFVkKm/BjkxIOEgK5s\n7Jw7JoXoaH2sRS3fGypSZ8AK/SRG2/E5U15x1JWphOlegXJhxxlPVw9buHbY+r/pmPKcqTwyTu/X\nMtKSemfKuW88BAqgK8BtH1AhlFwFdJzX/WAT23HMcTaf+53yptq+h6py7aJdL3HxjotMRc+VIlOs\nBhlA/JwSZKqwWGjChc3sPYs6cMWkjMOqyjvrtJo6/tTnm7s2RF7s50nLS+DfOaHP/u79FXz9F30S\n3Pey/ez3bpYs8pd87EjOswPITzYKkwaFET7fkjOnSsNicb9hc10p3hou8qnnFuG9RFCrpaCTarwT\n6kwxzpQWMvKbpGZMdT3cuVpm+5wqO8sG2n6AtusTThTPRDvqeri0ky4FDME8d+3I/b1CzpTtFZUQ\n0CnHBwBGr9xOJQZw71TKEOTnAWrHqVgbMi34ShU1DZmgWGnX2D4VyrNZNOR6cl8AMiIUhZiUDZ0X\nHO1GFKxiDknCmaLZfF1pNl9QHNZ7o3sFCs6zF25s4Pqmg4s75chUeFZT6v7U5nxNODxNJVIP2j4U\n4cQTAEqNPhyz5Dh2QzxvcUzcCOVj5sgUgHOKsAgqPaUBr5VQ0bAeAnJqFRCmqLNUQVxChmJkiqGL\nhTqElrCpFWcJgDon+hrFo1z8885xpigNJMuvCs/TOtEBx6Bl1It9EEDi3otr+Na/8pnZ79xMeUkh\nU37yGMZHVH/FT/a41gyADpPyM6qmHEGA/aJoGVz0gGDef04mcaY4MlW4sHlYbFFXSSVsyr+xPKkz\n40wtgreqhvkIp0rKKEQk6rnrDpnaH0M06BRrIVFKQMfXLXnFAJwAm0emtPpjMRom18DihRf5NTSb\njyIJUphPDzWCb5+Kxgfi2XwSwbwlaKvGv4t4aoIBS8OkACA+wxiZsop2gh+rtWakEhEXd5zj8OQL\nB9HfdGy52lEWWV+61grLyW2mytdl/dbRtVZ4EwASzpS419H3VrB/45hjYwrXeiCh0wrsWvYtD+sC\npE4Pl054ruI6jD6PIxu0vxwiTccaoaY5VFyhsQCAJ95r2ey0z3is+UK2HuHMIG40dF+ceOD3uOyl\nt0ReUsZUyF7Qr6GegXQ9rQItkWxpnalSwiRvF0U61BUgpLhPLWiG107mTE00DjnS09Su3gr1LqhS\ntQiTm/asinYSY6rLcKaUMWhhPvT09YNw3c/GeIcSIlBi+GoZMPgrlvzQDI4QAtZRJXQkcOM3w3wq\nMhX37dERtRK8jkwhvwIAVF4N3q4L7cRt099TzhTL5mv05yPdI9Ya0q7jZxTesesM8mBMBWQqd5is\nhGroSRApWVdqlyOk0hE1vIZQ7gQAX0qDaL2looil8HVuv6PEcQDwaFQU5iMFUwPCH7fDCxZb98TH\nS/dn2i4v0eG+k35/cnixIw6F4SSXEtDrCrKokJTpmT/8u3A/o05/oUGpUQhuF3lpGVO4iVrIFPEM\npOu7yLNI4fGWVHe2SKpJv8QDQ8mF+TTv35K4EJ1crI72Q8dUikwlYT7Bo+wHuqj1d7LpzuY4mbXf\nYDshzBdzpjQSPJKFn2Vhvtxp6x3d0CoMMbBrElRQL/4IEHPuLI8YeSJaSMfybmmokBKGg3IkYT41\n7TpWzihaoVPOtRDLGvTxQcf9IIds8HMpPC5VD6ffw9+pF66tnagMQyWvT0RzarbxXxqRqA+jMbWO\nw8vWnpKknxuFXikSLil1FNGhSp5/yp1x9yh2TTIE02w+/jyp8VGKxFOHESA4TrRwJ63Ajq9AKgXC\nkamSvvF+pHYlYys22JlhWmpIDKw8SGbvsQjoCVdM1Q9xpqc1Vp5glTu4PQqxGmFL6d74UVW3i9ye\nozqm5E7BBohhWOl6ulGK2XyEvyFVwNVEsqo16LvreZgv23x0fzjXchuEjEzlN5N+gAjJkdCXKMxn\neFJnVmcKSanbHo5YHxiuQqWhjQHJwU9dOQSAYFwFI1up9TLQDdX9zzoQFSDvoUb10QRSO/5qlaKg\nYQ2Jd8GJ3nh/IWyThvn43JQQWPp3gmQJyFT6rPpIkdDv+X6ldS0oubTOVGxwlYR9uOEmKSMeIkG5\n6I2pw+hvFJv4HiMKZZwpG5miaCRAejqAdC+5EwBawfgOaDB/t5CMMweO4xmUKBSFRtmSWnhquIsY\nZVYoNLo3aqwY2XyxEWvPwxIH1s1N8p0TENCRRgJgo0L8TE6rdpRslBscULbXTCGgn4HvfSpymw7r\neFICE+eyXGJkKt2EaDG6sGnnxyYaUwpMPwy4acLY/hRkiqSRZzYIKfSRW9hITqUbpZkiXNkkwyOF\nr3RSQVLqISJTZphPNqaQLPxRb0yxop3KXhEpWyWbj/Kq8FqzLgtBjaR5F5+FaCFT+obcDxT1COMJ\nNZooMjW2qWYpMmPKUGgAQMJrKdoSE4V1BQEQjHfe13Gy+ei9S/dYIz9NeG2Uu0JlZ1nDsqngyefT\nMB+Oy1JuNNRqIQURAm9kTHHjV0pa6QSeD4C+z24E43uhPE+qIEtDbS48F/7eISg0Ci3loK1BSnT3\nazpTGiYy2k39IT8naR4Whfn6cM9mnSkhW11yPGjiSw7lKuF18qzcXKkJHuYrK40QG/63m7w0jakC\nnpBWx4kiBnKdKVpvJf6OJZKSkbxAvDYiCJZYa+S71HMFMLg9AgE9V2dK2iil5xiF+Qyi45kT0Ld9\ncmQNKqQNNaaaJmljf7WAugJ44cYW6ko6Tkbx0iICumxIJiHWTLJATzZh1KeD8Lyt42QiIrfQX98P\nPo2ceovbduybvHOfWMATD5QNzwo5YH/uujIEISHPj19pIuOd3LuQ5g0gIVMxciU9R2qANFUlItOU\nu0Klqiq4tLOEJ56/AQCpMWUjUzFXyEIKuNJ3XCzBwGZ7wEIoIhmKN8YE9LwhF2f8AqTIFK9cT8ek\niR7mY04vOdTb9ZW2442KTIYi/Q4AsESHVH9oYTaxWG+mz2EYRuMD56b+jCgyZSJyUf9yvyE0Pr53\ngwfVJ/PIPh2kNNTIv4PjuB3lJWVMYUqrFXajm7cc5nM/JW4KTuoFX6THDPOpxhQv2jnBmOIHYgKc\nLjIlHS3ix0k2yjjUpd/H2RlTgZS6YcffJGE+pWhnXVc+DLO3Wvj5ZR0cC6BkKClGhEemMp4c5ctI\n2Uk4bysk/AtN8XCZfBwN3mMgIvuzDfl5e1W6EavIlPIceJarxFWiCIJGfg5KTObISNXD8ZlE/SSf\n2waI+qzZ8TVU7t5fwfXxfL6XX9qJPrOSQKgjh/3n60wFA8hCpvwRVEL/3ODNnU3pExYEZEp1Kmp6\ngLfYbBgzcRgBYn4kCq3xhdNWqvVW8r553wB57mIU2cjMwzwSB9F3LMcrIqArxVq7IUbE1SNiEgek\npK5ZCK1mkSnKkyzQcS2bq7ebvKSMqRKOEd28RWSKICq+iF5CxLXhY0k0zpQ04YZh8AUfXRih3Jhq\nibeVg65TvopNgo6+U4hM0eJwUsXuth9EVOikEgr56QT0becKvPKK7lQujdlX0hlq6tlt5F1roWDJ\nkzPPshLmLW0zlEaQ0R03LmY4C8oF19CSKF/JgAZwoQT1fD8NmVKup0qf3xsPCbjnEd+bqOQExAAR\nEv8OozpTffR86PeiviiakkF8OGcKAOBVd+4CgCOfX1hPQabiY1TsbL7UUZJCKdyYlY4B4en8VkV1\n2iZdcxrlIMogzWQJ0nuj84vyI8MYQvV5qS4b3pc3Kgr7FukLbK5ie1ooGWCiA8vQLIs2Qeemhkz1\n/eDLC1j8qzSLU3/nwTnEduskw5tfTx2kEmOK75m3m2SNqaqqXlNV1W9XVfVIVVUPV1X1TeP/766q\n6k1VVb1//HnX2Q/XlpKwm6TopMkunWjNs1SmhOEkJaMdbtuNnCm8fioyZYUypDF5qLvOH/aJJ4HT\nTb0RFjf+SsOl/D484nGWnKltWhoBN7lt1/sxaLwtzL7ap8ZU5r1H5xIKKIn7btxWblOlSq8S2oxq\nWykbJEWmJN4FzT7DzbAbjU2AFF6X5iZFdqlo4c4UmUqVGq9JA5AqRl6Kg/clGQ3umcRrnyMVudpM\neJ8cDecKkMrH3enQqFfcsZN8ZhlINAzp7kHn23AOi8bF4spdQsu5A4Vj0LldBjKlZJBSDlKegM6Q\nKcKPRNl0AyxZWF7KJCzlgdHvuOtlBDQy6tFAY4VhAfKIIb9fOkZtDdBrF/QEDyOLsRbQ5TDWuCRK\nU+dLI9Cj1rQx4vV1tPfJY5D7+Bg1pgCgBYBvHobhMwHgLwDAN1ZV9VkA8I8B4LeGYfhUAPit8e9b\nKiVIkZQyLB8nk3KmeHaDVr9EEg3R0YjC1hlqZj8DNaZSz8gaU13l76UT+BASwTUOu8gbFXqSZ3XQ\nMQBBpoRsvk03FBtTNByT23hpRo+KyvlN1/2dy+YT0S7BeEUCtoZChLkhb7K4T9GMLel4EBxLGkII\nyoZfSz8PfcbFNGWeSYpMcQQhLsUhIQZyPwlnqon70dYnXqMhjxISjfLqOxwydffeKvnMOtKp61Jk\nSjv/jB7nhD9FlE1ASNPCqmgYxuhhNsyX2SNc/zi+yjQS+JglzlSETHW9ULQzbodyCK2Du6ng2LRE\nB2rU41wSs0qJYWohOPQ7XO9ovEh3jUy/wHug0Qu1zhSbw1VBeNGDADndM9A1PS0j/mM2zDcMw0eG\nYXjX+PtVAHgEAD4OAL4SAF43XvY6APirZzXIUinxLgKRtyYbasybAIj5LqESdKxUvGcyAZmiE2Gh\nVIkdBoJYGNkWWj/B4h//l4FxYw/B7oufMg9QUBpBeS9HnfMkzyabLy6NgKEAgPD+8KgZAN2gwzDf\nK4kxlQtzUIOCH2fir2FIZa5wHVXOUoXvgShPx+ORjQBvTAkbI09XBnCeNBLQi4wpZcNTq1AnCIpt\nTGmFeamSw3VJ5/1WQGqkfkqQqbgMQ3zftC3aH5VPfcVFAAD4rFdfSj6zsvl45W+tBAYA+MKMVWZt\nc4RUOvbFE5EN9DC6XijaaSl2dy90HykI85HnIBftzHOmJH5pbq+lfMhsNp9gQOplJsrWPvbN+/Xj\nkwjo7L6HIUaFcpGLJQnH6chUP6LmTPcYbfvyDEa70nhu1zDfpLP5qqq6DwA+DwDeAQCvGIbhIwDO\n4Kqq6uWnPrqJctzjZDSYlioU+l1+evqkTASW2pxDpkohUDp+CuEC6BsEXXh4fW5Sc2/FfT99jvgr\nfc78OeUMmZMI3WAPNp0/Zw8g5kz5MSjFS/Agzbv3A4qQO5yT8hbUg44F6H5qmC/mqIHv0ylZSM4Z\nk7lHQ/w7UaoAozHV9a7kAtvEJL6FxmsIygrE6+nmjmOVxq2hF2hMUoK+dGYaX7v4XIdhYNl8ddJG\naAtCXwryaIUkvvSzXgFv+0df4hEqKpZD0/Z9jGwbSAE1jH27wtqWENKksCpPey9EpvhxMjiuqH/q\nvBZwXl0bcp2puGhnDxeWTr1pDo0UPrYKTQIQ+kItZ/NFnCVxLstZpaVrP/qO8D4pAV2LnHT9AOsF\nok0AA5QhUzafD9h8q9UxAoyAAdFTmccetcUpBLeLFGuxqqouAMB/AIB/MAzDlQnf+/qqqh6oquqB\nZ5555jhjLJYmYzwAxJNZWrz47qXF4DeJcaJoilISCr+iaPFyCsPW1TQCOo+HW+OjNUkACpEpKcwn\nePE0zKehCWjInCUydbjt4LDtvHEFEDb2TTdkDbpPGI2p529s/P+00B1KHJJz/5PTsilyEA5alYQa\nKYi+yKURQESusE+KeAJwg0xApsYwH0elXF8paiodcuvGDUl/bkz4uWzk4HeSEIdS/JGuWzmbj4eq\n+vHacRwVv3/bAAl8nPgayelAqesKPv6uPVEp5LL5EgPJMOgpOugKDMuOGwBFppwhLvHNEidSNabi\n67F/9x2Zj0VD4nkSeCBQA8hFO+kZqpLRg+3UhXslH29Vyc+B3o+EsnJkqoT4zmuBWU4yz87k+wRA\nbIyWHJpMS0xoj4fyMd19jf83EiTw8lIdRx2m21GKtFhVVUtwhtS/H4bhDeO/n6qq6lXj568CgKel\n7w7D8KPDMHz+MAyff++9957GmFUpsfJx06X1eqTwVF2RbL7x88RDU4wESTgK5PrQzhkLBdpKDBwq\nkcLMPI8EmVK8Vyot457gfQBwDk/wIjRFqqXcn4YgKfXK4RaGASJjCvvbtn2WBP8ln+Hm7Fd//mv8\n//ymr20UEQFd9iI5cmBV3AZIN2GOIoZNnjxvIfTEkalYEZAUeRJ+2LaDaExJaBpHmlC0MB/nWEnh\nlijrSjXKUgNHQgQ0zhQPX4e1I5UuoSiYPB6tEnxOcgZSwwwkbb7Qwox4rcX/ogR0AIgOLu8mcqak\nIq9aoVspC7OEgB6tncZV+6alEeiRVxKHDgCi7NXJBPRKyeaja99wMo+DTJWQ5XkERKsnR7P59D2n\nh6qihpdNGaFzE+t2qQT0ITZkyzhT4K+/HaUkm68CgB8HgEeGYfge8tEvA8DfHn//2wDwS6c/vGmi\nKS4qEjIVe/ihLb6hphsuZPsL/QYjDUUrjZBkOhwXmcogKLywYAk/i3upAHLoJQo7KZ7UWYb50Ft9\n8WALALEx5TlTfT7M96o7duGx7/oyeO2n3OP/l3uuUhmDJJOIIQc5rzz1OOPwrw+rGqEnWp9HQm+k\no4jafgB6HiUVqT6MxmtQifjsviREKM66komtg6jkYoOMjoOXDdGUXC4DTkM0tONkcmJld3EjwjyM\nOQm7yHSBfnCFWiv+/IUMtJQzlUE0hFp0Wg2rKOu3gIDOFep6UadFOxuMIMR9hXaIoTChb7wfjzoL\nYT46z0SUDw3TDP+SfkaPgNHGSp0KvFZEqMc2KgMVavuBoU0ZQ5+FoK37wvI/eF9TAInb9Gi+Is7U\nfwEA/xMAPFRV1bvH/30rAHwXAPx8VVV/FwA+BAB//WyGWC4lnk1U/FDwLOiBsVo2X1ikOtzKhL8U\nvQAAIABJREFUhR8f4sZbJ98dBnf2XUTOm4JMkQ0ix0EICz94cFlkSgjz1cIGHIWdFEV65MN8p19n\nqq4rWDU1MaakOlODH8MUgy4XEqBFHfGSpLilELIB0Ocu34R5BowUehIPduVhPuY1hzBXIOlvuz46\ntJaOWTtOhoewssfJsBAGD434OZpBuGhKOn3mWqgKS31M8f6pAeLDfML7pfdTKk2tl0ZI0CZjvbpr\ngVwrz1f6zgFirhy9BscGIJP3qSDaK5VP0ZFJSuieRkAHcIU7teNkbIdmHF/hXh4hwMJcxF+pUX5S\nZCrh+xkRkVDfLCRJSSUhqH7RQ3dDss9r13LDK4deUsCgMhCvaNzHXFM3S7LG1DAMbwMAbfR/8XSH\nczKRPAUuXT946FK6PmRFVf4anBCcVKrF4iWRwh+SFzoIi3FKmC+GcCEaNxdqWOLYch6CVD/HImJG\nhGA2jLNEpgCct/rCDWdMxQT0yvd/nDHkjNRIkVbud6n6clOlm497vqlx6TcS9DhZmC+qOD82y6el\nTEAnfQxyqvi2G0TkTq4zFc8pf60QvgOIwyK035SAju1A8rkbO/h2pOwtKc3brS33ADoNuVKQqbBm\n4vug19D7KRWb5Dsk684qisivFe9liGs24dqgYb4tuxd8vsdBprT5EheZFJtVxwwAsLOoWWmE+EB6\nsW8Sai8N89H9WSqeyUtS0DmG4wIg2XwZlI9+Ro+ToX1J19J9QrpvyqmyEgliOkeZceT615+nBwzI\nsy8J83FD9XaTSdl8t7uUQLUdsaAlAjmPy9JUZZ6losXiJfG1h1hoR/WwqzCOY4f5cghK4iXlNxP8\nPEp7FhQg/opV3KVxSOf8nabsrBq4fN0Rx2mYrxpDCm2fL9opSe4AaorKDSC/A0p+Bchv5gkyxcJ8\n9Hlr750inp4gysN8CTI1jMhU+o4c38JGmvj9JXWGkjlYJ9dRD1m9tz48cyl7SzLyKGqgIVNagghX\nwlqYTzpOxpKqMtLPiQLCvi1kir4DDcXiPCwrAy0UZNQzHQHk8ikqMiXUZMvyltiYARwydUgI6CUH\n0lMDoIQiQsdGEfdoDTH0hIdXO8ZDytVjop/x43wsAnpUWsdyqqz51qfHF1lFOEuRKUpJCGMQm437\nYLrxdpPbNPp4PCnL5rONDR6XpQYPDxVosXhJaPgQxToHi1rtU8J8krdVbkyVh/kkZEoj8msViCUP\n9jTlwnoBz10/AoA4zId9bmk234QjbXIlJyIFYYSlJAK6ypcZ4udeVxqiSp0EPq44sYGPKwrz0aKd\nnZzNJ4WkONKEojk6yWHbSvhRIsZToVwW6wDa6PDduhI4U7GjJKI5HeWcyGusY0qtVKxaPjyLDUM0\nklfvQpF5FItzqzBzixYD1RJvtIKhuKZKkCmqIEuNKb52AJwzdLSVCehaxCJyLgSkVuvbtWmfoBFH\nFuJq/pLRYSNTve+Ttl1CQJc4URQVsgyZbRdX3LcoJ10fc6a044MAJMDg+NGd20leWsZUwWKkWQdS\n7Jm/MHq8A6/smzNWqOAliWfJxppa7VBUgwOFpk9r8DYKV2RVlYdbfQG/zEYZEzXxc9a/ceTGacj+\nuoHnrqXIFIBTyicO8xlKDyBOYkgNm3hTyFYMZoeO8oKNNMwVwnyp4uKEW47K+jAfboadC/OppRES\nhAjvhyFTigEqefIAMVGZ1ldSswIzz5wTc/Eek2w+jkwpxz1Rr5reN+9v6tyeFObLKFWOOEn7FOdW\neWOVEtCZE4nP0OLPAMSIs8azosVFSxN6+j5VqI4zpRXtlJ+Tczzd7/gMcn0PZF+T9v8kbM0cVP0d\nWqURwLcVfUfhwAHEBPRkHyBGuVV9PCl3oMwhgDSbTzs+KB5j0Dtl0Z3ZmLppUlIrhGcy8Ou90YOb\nexM8C17ZdwpnSoIoJc4UX4z1VGSKQtdZZIoVkFN4FVT4SeL0dy3Mp1Ugljbd05T91QJubJy3yo2p\n1XgG2Waswj6JgK4YSChxTajxf4ISaZhiB7CQKfBtAqQIBg0/aGENGh6RCo/SkhyeiNwPUciEihWm\nVo+TUYwgzlWKHByCnmgODDUmJcSYOw54j3gNNwJR+YsGSJ+WalCLdk6c2y4cJ39G68/RscpKNb7X\nqpKz+bhyD+89RlMAypQ5QNgj4lp0cVv0nniIt4QEzueXy+aLi3YmiULCO0r2ymzf7id1WuK5KiFT\nsWHK0VH8vyaep8rDlgbqE9EBpPsmDrdV7oDXCrMc8yisjPuLMJkp78xdm3/uALc/Z+olZUyFDVu/\nxsWBOf8ifN4zo0f0XtkinRLmi73FWig+GFvtFuwvSbQ5ZQidneDxZI0ptrHi97BvFInDkhhTPnxw\nNtNwfx0ogbvMmFqOx2YclwRvbQBUcWvKnxPQc5s5N3y5NycR0MU+uVHCDI6kREHXQ6sgU42g+DXv\nUc0wxA2SOC8AKTKVqwdEw/MiYiCMqxHXNkfIFGQqE+bjoZlSaax5xQyfYKin19IyFwDOmBFRAqYE\nsfwBrQSecKYy+96WOZ2uf7nuEHX+cicLaGMGGMN8WtFOZQ0OQ7zPWvfkx0ucBYlnJYWteWak5Ihq\nGZx0TMkaKEGmBNSnJ3uPhQrRZ6i15fvtZCNRm3OuPfD3MyXMd5sCUy81Y8r9zB0nE7wR9z+pzpR0\nphU/6Lg0zi61CyDXmQoEQryn4xftlIqSxteOGz7xUnJdBY87jqXzfqQwH38tx63FUyrUmOLI1HJR\nFR0no4lJ/iWKWyO2cgJ6Fplihi835iiiKin4YRic8jCMkoibRMazYVk90TMwKlrza+l9oPAsRa7U\nMPPH4lTRe42PJUmNe85T89l8CkImF+0kyLES5gsFcScaU1PCfAYyThUmXiu1y+udSaUROGcqX78u\nPqcNIK3rJd3TFAI6N1J3SJgPjwbCe7HOc6QKHf9n9u0VOi0yKjmRwTmgbbZC6AzAvmeOyJghaGZ4\n1ZVdGqERPqdtLZoYXbTCfFJCjVWnLZRGKDSm5jDfzZMcMRggjgNLii5FpkI2HydMaxC/JANr131f\nryBdkm0hSRSCyIQhU2Qqv5EF3piwUTLFjOPXkBIfDjijMN+FdTCgEmSqrmHT9ceqMwWQz4IBiA3J\n5NiVflA2Vdky7xjSwb05qc4UHR4Ng0X9sTa8MRGVRujF56Mdlkz7CfcXf86vT42YIfqZq/+Ef1eK\nMen7UZEpuR9JYdEQrRrCFhI1SsRSLLzOVA6h4KnqUrs6IVoI8zF6g5V5yu/bh32kMF8GdUzuTUOm\nxjAfOr0rnigkcodiXZDjjFJjRV5DMLYH/rokyaPQ6OB9VqRN15dhTNEwXrJWuAMt952WRjCKdg7a\nfpZePyQ6TqdMxH3Ebd9u8pIypkoWI+USiGE+7lnUNJsvVv6VYIzp/aZKpqmEbD7i+fD+S0TanHKc\nKcobKE0NzqU9U+WtkYZ5uv9py/4qIFN37i2jz5aeMzW9NAJAJrMFF31lENCHkyJTcpgPz+2j/3Pf\nxw0sjB+Ae9Vho6ZFO7UwX10LiIyCTGlGJV8XfC6Fujm6EUjvNQqtMi5LVUHyzLnRxrP51NAYR6YU\nztRkAnrGSM8d44TSs/llIlP0mQjZkmnBWHlO0zY5IoftWiVCSgno3FAEcIV/0THidAx8B9RQ8s5t\nYqSbXUcKvTSbL3qWHTdedW5e6DN2BHKJB3UV9IdkqMTE+3IkVDPIAVIDOjdG7Bt/lnCm5tIIN1FK\naoV0UWaQ+58U5qOeclIBvebwcX4ieOOCTbh+YP0zIqxFSJWEpqjmOF2J118wqbdss6C/i6n6tb75\ntgLKdZqCYb7dZZMS0Be8NML0MJ+lTAAQJXL/k7KYpPo+6nl/LCRbVcwQEoxXydiyjJJuGIL3S4w7\n7qGiLOo6izTx+5OeA/2ce+o8XObb6Xg7Yz+VnBXGs42wLQ2Zyh10TDOR6DhROjbuUsmF+Uprk/Fs\nPunoHxxnHPoUKqCzdeqN9dNCpvy7LSOg90L7O8vaV0DndAwpmzg14sN4cn0DxAcdywhxcEoiXiLZ\nn12/9rqnYy0Js3ZDWrU8TdaIq49rj5uGSgF0g9yNsY8NL0P38FMSSjlTtKD27SgvKWNK8kC40E3V\nqjNFlUrI5pNJqiXAkRTmk8JjiRdSlRlrKHQTzSFTktef9QrFTJ10o4zrsbj/JXWmBJTrNOXCaEzx\nGlMAzpg6ajvYtM5Q4BWVc1JVhpFK+WLKO5iS5o5tWmnKNDyNc5dv4gAxlwIgDgUORLEtCXdm2/Ww\nFJC7uhayUQUElv6tGl9K+JFXLs+1U1XyupaqZi9IAkiS2Wq8jyhjFp81u+y4yJR0lprvd0gNJAAt\nzAcJMqWFheLjZHAtp2G+hpcaMBA0ft8hS5PPF2LQKAZX0r4Y5mv82Xy4T1t0DO40l1BEsG/8nsTF\nStYZR6Z6RtQuOJsvcYQE45D2T4F+rEUWtUfmb1Pr5XA4v0tCuWi/kVFu3Bd2V0KC533gPd2O8pIy\nprR6RlQoL0Qij3Lrt6lJnSmm/H0svgiZSidCI0DqSXzc8FQliQidmech8bOGIW+MAkCSMkvH7toO\nn2mp+mcd5nv5pTUAQHQAKsp6PH7iqJX5QDmxvKmYLyYbU1P4LwApwdOlNJP2hD5pU1JNMTpWN6bw\nLuOinYPP8qIiGfp8TvH7U+tMEU8eICBPyTEvjdwO5WHIIcwMMqUkl4icqQGSNXZanKnGMtK5AS7s\nXyjDIJ3Nl17Hw4HiQccMtcvWr+vTMJ/GDaL8M3+yQBaZShXqmiBTaXHlMqfZuif+vagEh8TNIwhn\ngkwJTpR2wDnvE8BOLEoQSWE+DWSdW0lHSTafsoblfi1DPwYW6irPVQOYOVM3VeoCqLaNqhen11Mj\nAMAtSM/fQI+Hh/mKOFNxuwAZZIpsXFOOk6EKMZfNN+VwV+079HcxzEeRklPilZTKf/RxdwAAwAGp\nP4OyWjgC+ua4xpTBbaGhK82gTTy5TNFOzkNxXqJivEqeOA9rCAZXT8J8VKm2RgV0idxK2w/3JytT\njjJwpcvDZRp6QdeXNI953SUAXNtyNp8ZQiPPqVIMGi3cmRMtHAcwru3oWcV98f552KVE+fown+Dg\nJcWKC40++p0k+5OgbX4N5NBxwvlB2Vk0sO0G6PohqcCuVdWnn5VQRADidSRFQiTObYxM9ex55/dc\nvqZyBPTI6VLDfO73qtL1l2a8a2cCUgfbzoaNHahSHUdDrLejvKSMqanHyYiLgYXjGiGbLw3zTUCm\notov6cbFre+mLiPnoXTE08uNjy98LWTB2wdQwnzCSfMROsMaljIDT1M+8WX7AADw8ovr5DNEpjZt\nP5kvBaAXQQSIQ1faOX78nDW8TuNOcM6PQxFl41UMc/FwmRL6CE5EMO42XcydQJHQOR8uY6FbPdwZ\nG17ciEk2XqUdKZuRTjeqQGhfCWeqySv2YaBUgbj/cF/pOimRptLDLs7wCX9boSlO0taQVB4ODBXQ\n0+NkuEFroaiaMS2VxqjZnMyG+XqBgD6G8o/aLikGLNExONqTMxDD98BfL80zepQU/jytbL6a7eta\nphw3opMw3xAbMhb3LSqBY+gTzmOzCP08zFdXMrqa9HFMB+VmyUvqoONSZCU5MDJaZO4nepw04wdP\nUueVdUvCcBJ5ziopEGXzTUKmyksjJPB9gXEoGUDS9+imo3HLMPNkKl+pVOq6gtf//S+AV925m3y2\nWjQOmVLS/nPS1PrGS0NX9SBv0vyctdy76nt29hVDGjwyVdPSAOH7nPSp1aLiyNR2PJtvJfDauNcN\noCNTVn2o2MGIFTVPktA8+ahoqWAodn1qEErZfFy5anVyEiWs8AGnRrAtL30KAb0fUlRBvy78LSGI\nLTuctySbTzOmRWSK71fGfqrVGsJs3KNtn1Rg98g4XS+IZHIkMoeKkRCVZEinzrhQAb3gmB0qSSkB\nY6y8Sj5HsHGMNLypda0b7+m13IDWkEg67riwaF7HaWVXbhd5SRlTJcZAzJmC5HpauRsAFUZ8nEyu\nsq7c7zhGYcLReDknoJemjaLQeHjO2ON8lZIqwJIBJHmdlJOgee9bBfE4Tfn8++4W/491ac4izCcq\nCMGQnEJAT5CpWi6NQDd5MUuUhTVoG3TulIT5pLnJN0o6Xun+0jBTvAkHRC0+tUAvdisX7aTFelEk\nZArvMxSZTJVBPwQFrfEBcTxTkSkX5pM/SwpxGkq1Z4ifms3Hn79ynMyS3YdDEwxEo04NV/yM9x/m\nXIrUJ+NV0AnM1j1q+6QCu5V11/D3mEWmwp4pOS1oqHhnuDoFZIqjaMZYKbqM37E5UxPCfFZYeQIy\nJZVGKMELJB16O8lLMsxnIlOk7H0lTEoOJVLvlZ9LZxFAuXDSHbbNxxv6B9/XZGSKGIK0zWRMg1Jo\nzeKcCRtlIKQSo5AsGP1sLDnl/mYIcqaOThLmUzehMDdw3UvZZ7yoonQdCkca6koOT1eVEn5g80o0\nuMjcoYpNM3qluUmNGn4tHacfl4K2oOMSsvniz9NDnPG+5AxKfhYi3mNApuK1bZ16T0Mp/v2y63gW\nYqlYVaa5wjLDfAR9ANCN/xICusaBMhE0dtuas+AU+3g/BQR0jWeJyNThtgt1ppgBLhHF0zpTZcZU\nU8lZylJ2JDVMOTnf4hbR79D7yGeahr8lgnnMmcpkj0rzTTGmpNqDErE+RdoKAQlBh95O8tIypgqM\nAZo6GhCT8Dm3fqn3uh0XQpVRlJJgCIUesSBxjcLcC1Z7rpAcFaqkc9l8UoaYG4NljPbixur6oYo5\nfCZllwGMyNQtWhmeM9X1kwt2AthcNhq6wiKayZEOfPPJPHuaOAEghfnChmsjrjoy5RCX0Ykg3Jlt\nr4f5JKQJP4uuVeZiEo5ihpCGTPF2aF0zKWTKz0LEvnJ1plSSL1NsiXHHjLNSsWr5JIU4TWQqfa5l\nyFRqRPKsLgAbMe8Eh0szAKihVkJAl7KiAVxpBABEpkY6xiKeMzKSy/bKzFYeH3Sc3hMvweGMzvB9\nrbilVWdKSkqi/+fXRvtEbR8nk0MYi413hvyaJHn27C3HlI+bfu92k5eUMVViDNCiZhb8S7kjFJmS\nrO/Sop18Eki1OPjCsbg5XPj5azlPj2eIFXPOmGINm3r4X1z3B8R2JR7LzZLVooajrodN252gNIL8\nmZQmLCEXYmkETUElmyQL85EwnnicCjNyPI+EcaY4qnnU9jAMICNTwn3xmjhhvGl/OC4pzOez+RjS\nZbUDwJUcGRdzHLCvXDafXLQzJvDi/+LxxPdTKrVhpKvp5woyxeeLpK84MiiF2tq+TzhQmnGG31Ud\nLgOhzWUf08+SbD5CQA/FlYPBAKBwpgr3Sv89YrRL3LGkGG8Vn1/JDc2SPZeH6O0QmhDmS4ypmJNr\n8TRL9yjteCzr/EBqyE4K892m0NRLypiyJhkKXehSzDutM1WHOlNdzB3QiNWSyNlE6caFk4oqtdIw\nX/guW3TK9yUejnU9gOylSmRD+hw1T4oXhbuZsl40sGmPXxqhqvTnJKUnS8efyBC63F8a4tGdgJI6\nU2ItJqLYkDuEZSXKSyPExo+/VlH8HG3h3KqWh9+0kDG5P0kxSoUemzrUkON1obSDef2Yx6a0MN9J\nkKlyDgu+w/RarghrZb5yHlYI88WcqQRpMsPcKXrN64fRcXLaRIlhoSFTh9ueZF3rTjMPe5cS0ON6\nbu5//ASNFBEM3+eG5qKgX+qY5sZKk0hwnLJ+g7HNMu4nQIb43g9en9ExSm3jvyh3eQ7z3WbiERAz\nzNdHLxFAPk6GEnFpxk9crDLfn+93GKIQH4C8eSQF2gw4nUuSSWJArQCQZN2UcMB4umx8H3Hb+Jlm\nKEiG2c0SDO1dOWxhZ9Fkrk7FSmGXMqn4pQnKoCAu/z977/Mr27KkB8Vatc859973o9vdfuo28LDc\nCMTASA0yhgESBmQJC08YAWJsmAADkBBiAAyZIIQYWAJhMeMfQAwZGCQmHiBk5h7wQ6YtQ9P93rv3\n7F0rGWTFysiI74vMWrXfuVXFDemozq7KlZlrrfwR8cUXkV15VyfNMwVQJ5T/xl6n/7e/L4vIrz6r\nMhXfE8phc+1xMhSZumyIm0N4mDvUGhJoIUdoic0h5/udI1PmlIFdcY3Io/19VrLzMT26nRGCw6ZO\n3Id+XCG0/IzcfATpqv2J71//zI+TmVCmyPiyqRE06jqcobrx+ZChfL6/In5d69dv+8ptLrNa/3a1\nN4AduYR4VmNupX7f7pu9R08tQLnp2n2No0JtWe2b9uGa9ELXGihfSp5KmaonxufZVC0MiiZQUEgM\ngfBt2/q8GxNuRZVSOCkXRfNZK2QWmaLh7xkcP7k4720ANAlbfvXThqpHXsn35+ZTZer/+eWrfP3x\nemUKue5UojsGKxH+uA/9fq7OBWfuJ3mWIjIllzLJRrAu8m2CTFlDY6/DbVIqOjdhnimEtpQcmfKA\nUR+yHi1onAHdEtAvaIYJTmEWs+WHsDQB6GDlGfHv1bdrX0Pq5tt8BnRslPl8Z3r/r+YBvwKkCY3p\n1nZcI5aLkgsDEAx3Jqu39hdvqGoQfWeQqQ8TdI6jeabWFRuJlmah9Xv+2Qk87/RsPq/oA+O1lY3t\nZ6kbGGKpZf06VttF46hHptJs6WCfmgriunPO1FOlRhDJCZwiCitfyiLrfFNlJiJT/liNDMpE7fp1\ntZ1XZcpdqmKhtZlQNx+5nrqakvb8YmDbsQvCaHMXaYT+70M+7srUZ/nmiDK18sAA5LryY6Quun19\nei0SjyB4N6O1OHWtQZwpnzaj50z1C9XLuqZuPr9R1HbqJ7IeGcdq7Sza3vUdyLdEMbfl0DhGEWn2\nEHMUffdiEvb2bbV+MHTac0hm5bQm7uOCCeg0Ss8aSsQt5/OdNWSq5/l4ZDIz8t7OkZ+mfQgpLTyK\nOzAeaZ6pCzL17du5uapfeuXDo7Dani0z4+ZrLrJ2D/Z+7K2j42Q63u3U2Xz1c4bf5dtngSp2f5mO\nHk32ExalyKJhtW2RCy94Yg/1+9u9yVMhUyI5TC7Sw8p4MtRPC6m2DOgYmZpRdjxELyLmbD67KzvL\ngViUuA2HqhErXgVFiNl64DVbCRsr2lBQdFkgnwKL90uJIlNvW5FvPl5vU5xAlIwKRpEGm8gMMuU2\nHZa5XxdKmGfKITz2FtBGoG4+dBg1chH4MWiFcayQu7MFfShi5JApgogpAuLLeOXC96cd4L3A362U\nYqOh8Jzx0U2zkkbzeSR5gEz5jRAp/9X92ebznqzVnc0Xkak8mhUpkjPv/zRY7xgyZZN2tsTCfdLO\nznW5j5fL/UwjU/Fs1ziH+ufuj+ZBzzvLM4VyH4oQ9+7m24/Ime17hgqxNQotez7KO1e8+j7Muvm8\ne/De5OmUqVMyyUX6wbaiTcdtBn0GdMeZugaZci4UrVvEL/rS9S0jenrx6MMoQoWdi5ZH80UFaHeJ\ndItGuw/0nEW+TNJOJpZ0ftjNR5UpQEIF3CKUJiOL5uvP5sNJO/VdiMRFvl4n3Wd08xnr8rTsyBTK\nxYUsSpQCxN5j2EwLjibz7rdR9NxWIsrQuTkpMqUu/Msm7c4XY9FI2RqiZY4gUyP3CNqwWFl/jh9E\nsJzrUJXRyJmKqQ6uieYTYW5h6ZBJhF5196XvyY0vm7Rzd/O5pJ1onb8GFRPp5+0+h9y6180hpxyy\nqLeZPFMzRH3kbcj2t3XhRmFIjXAFRy87c7DN6fp3luuqbwMr0vciz6dMJe4XEWxZIPi3hY6uu5X2\ndt76aD6ysLN2PfSNDm31hzlm7qTYRrum9p1bMCIcxk2RKUIa9wtRF0KcWO/fZzSfyjcf3pcz5V1X\nXvERiRy6GTefHT/Lgrl+jPDveQqM72H3qNO6DpEpqBwRRAYZBh5t0VtkBx3zsw6N+wWUQaToDpna\n+nZqWwvc5KqbzyNlfRmmUIyEBY34tCfa/3pvCD1zZYn1z6IcX819IwMqNybwvaMs7EhBnIrmI8hU\nl7TzxHOT2fmiUlFB2vSlfXsuI5pDPbp7cq5iFEgiMkCm/NxN1gqvzEU3X/t+/z1bc1xd+r0XH5mN\neIv+fvqz+SYACYM+36M8nTK1Lrky0OU1ubwTOzh86KjNRfN2JtF8U26+SIBFlmVApib9yajvIzck\nm9ij1BJsY93gc7Qclv6aV5e360vK10aBOoJMVTcb/g0R0JGbr1t0B8/eK57BzWeQQOi+dhY9KuM3\n4A+nRX7xmSNTKKJrc0qiLx+On3FjsCEjPWIUlEDwPC0PROtu7aBw/ciZ6jljhGdk3l2aP+sGZCq6\nxKNVPiKg26m1EOXfo5EiNT/T2bn5EGeKjX9mcCFkym/YqExXfkcn+u8Vmfo2yzNllWuwMc9k4rYI\nDKaJxCNY7P0EpWMdk+4DWT557zU7f/ubHTtljXXWNMtDSIMyEDJFUoto23pfc96d+0WlRJ5Qmcrg\nZ5ELrGz8xcvC3HwN3ekyoE+eoh3aLVGjRpZlyHOVICCoDXstc0GoRL5C+56J51i0axe3WLW+oEVH\n2/m+kKmfft14Ukc4U9kC6F0sjFvkuQ16LRKf5NNblCjPFNo8Airr0K3eql7kl5/fRETkE0DvkOGC\n3Nm2PpRvC3OZLv3252ESNLgqgu16X8aP9Vpu3etvZ+n1mwd1pQzmGJsnI2GGB+IKXbO5MS6SR0i1\nbIam1H7y8e8VClYvKjtytXkqg8qnl3VP5bFnQDcH0i9urOp/vTE5WmvPWxvfeP/wCvnaH2MDniV6\nLn2brX8iOR8prCuufyXwla5w8xHUVPsyezSZf4enRKHrrnPr073JcypTg8now4uRm09ftM+A/gEN\nrkmI0g8EnJqhfnaWw6Qy5Ql6zR/Py19LQD9v/TOw1yIYfV240vkGuBhfSn7y1Yf9/4ei+RJ4HLmu\ngtIB4HgRvrD542diaoTL9ys+vseHFWMXd78Qfzit8ssMmQLPwKNbobxXEsDm0mUmd0oeTEOKAAAg\nAElEQVSEVh3btSH27X72e3PcHBE9N61HpjzvA3Om2rtjbj5v1c8KS0+CklVmaKZHwtm66FMoiNT3\nboNiXs9bPI8zWWeZi9Mijrb9awjojDezLIt8/eEkv/p8Nkk7uaKEyMwjF6O279dMb9TY4b8uEeVD\nqWWmkKkQhQ7eZ4nrCkKmrPeCIlPAKBSJSty2lYAaZWku/Dv0ii4TZHjdkzydMpVFmYigycDg3/r3\nyS64zs03e56TtosscP1NpbhovmsI6C0dQbM6av8SZApZE8nzewWpEbSt3vJrRGSGJtS8Xd8TMmWU\nqeNuvrnnigiWgVsxcMlGZCq6F/R75Nbw0Xwn4J7y6OlpXeSX31VkCmWJV8TNH/TKdAh0NJLPcyTS\nk5A9okbPOjRKHHTzAbTEc6ZO6+LcPjyazx8YHQyFo24+Mg6Qeys7fgVt+jBTegFcTqdEQjQlWWd9\nxJqtFynTPt/aDH8IuZK//nCSX722pJ0fnBehQyrdWqn9G7v5YkSlrdcbE1ZhF6lIazzWaE3XXE+6\nz5ToUnr3rldooostp4FANx9DTSHCDMbmbhjo5+RxMtsPytQXlRkt3y6YfqPzJ1p/MAP9ddvcBO2v\nyQT5e2Hm8B2ZahDoUTcfirKzEiLEEmh2v2aLqRFQPxE3DW049+Dm+/rXQUDvxli++Yvk0L3WGaP5\nIqJZ3apRefWbMc4zFVMjKGcKHQZN0S3yThEJ2uc5EqkGTEoMB89+K0W0BDIKPDdH67TRfBAhA3PB\nvl+Guh5N+9E2LF9fjyx2ZSHi5BXjOaK6iCJTDk254mw+5r5HyJRXTkZIvF6OSMhfXZQpn05DBBt7\nIoiAnq+1/rl6VAW5yu1zR6llppGpfcz13/f9i3QAtE4sZvyiekopYY1CBpi2KSLT5zdGlHyWd9wj\nifcmT6dMZbClCCEHk01JpA2IUkogVo4I3lYQlwRZlnHizJHzROwgbd9lbk9kFYrkbkufT8S2459j\nIzsTZOp8jFfyHmIVqMNJO8ljQu5TX7Tyqtrf2cYoAo52IJb2QpEpv4DVT9ucXzztoo+UKbS4Zm4+\nhNBxN59HpjjKoO1qszDPVsHula3UZ8My+7PjMLLnKFIRt2NuPmzQ+CNFRHI0cys9nYEpCn7z1zbs\n2XxIOcpIw4x8fwJzxpdlCqztb20//vb1x1ON5jvHcxG9x8LnOhKZW2sDwduhKkEBAe5FHAjBo372\nuauo8uC9Z3xNFKSEbhkFPOzH8hBlKswfNuZc3bN7XGao3YM8nzI1iMhAEWyehCvSBpvNl/HqknaO\nUg9YQZsMdPO59q8ioO8uSr6IWKGkwUyZIlanPzBTj9Ow9xJJuhs88+1LiH1Gf9+f+Obq65GrScW7\nrrzCLtJzfERy6F4kum0WhzhaSxvxryIBvdVr2/CKuApy86EzzzI3H5qbKJWCtWjRGXf0ebqx3CEC\nwD1tEyZiZGqF0UjFvF+9JEapbYcWfoQYimACeh4ijw8xR4hXQOyca+oVGD0Zafht26AbznLhVDY/\nV4gC28rH56CinKnP5yIfT2tYB22tnockMk9AD+52t38sbg6pMS6CD3cfIVPX5AOsAVbtbz/nPFiA\n5pK2adsS4cY2ioTVa9kJAn0ffnDz3aWMJoRXahgBfXeznfoF94MjAWudI0GbDDzoWGFssVr7nCtR\ni4Ts2wzt2KI7SiQiSP4+EM/JP/fOFUIsqaO8kveW3/2Nr66+Zpypuv2N0NLo5tPv+bsKljZBnlBE\n2BQBfetd4HasfwKHQWt/esucv1Pq5gMW7X6cDHAhIL4ORgT6fsXFviUIhRFrDJkySicL2jh6iDc7\nbBwdo5IiFFtEKFA/vTIjEon3Z2D0ZK6Z8xZdPtoHT+g/u7kyTLrsNmIrypn69vW8Hy+jEtxx6Hmu\n4zxTXvkP+4dbU60xjojaWiY9m2/r1/QRudujSfhkitZ/6IpDSOiuvLs2GTJFECdPOWAKXbw3rETf\nizzd2Xwzx8nY9+EnGeKNiNTB9eaiWphVigRBlMiy9HlALHl7BOJAaytZILatdIsOSxhoBUX2aDte\nKW0oCJ6ERzec95Kf/eST/PSrY1Mgy88SCehoE7uOgF6Vjh4VRUYAS0XhoXVUppjvbVkRRkCvn/6M\nQJZUDymVkBh+ahsqRqZwigVby7pGZI4jUxt0ZSEkRdvyYep+ymRKZSYsmi9LjTBK39CVLaVb9P16\nJxLPJITHySSuGeQyFamIF+LbBEQxQ2m2fn208tXHk/zhr17lu7fznndq769DPzDSN97Ui9vQg5Lm\nUaRTe+5aKhC1TyMAIFJEGH3DGw2n4IbU59fGb+rmA8Y2MorrfXj0kpxt6RTZLDK66xMYq/ckT6dM\njSybwGdZl7Do9tZKO8Pt1UfzTbjFVKCbD2yg+r/G2cL9hvfm0If6/xzt+BotuIPnh5Ap73Y6Wzcf\nIerXur4/cPR/+vf+2cBlmhUP71tB1msgoG/XHSfz5iz4xVmm+yJJDpb2mwdyBfoxajlTLJrPtq33\nxYYpVCqRm8kswqrMxDnb110VQadw2fEIjBn7zGHE2op5cTatBVIoRY4HV7B0K2hzS918gDujfbeC\nELvq5ss5Uxky6xHv/RqwucIUDgPFQst5+frDKn/7D8/y7esmXzlkyq+DCOGad/OZeld/XIsj/ps1\nvqiB7Inay/gInaDMkn0upkaInEa9Hv2+3wc4sJwZ22hs1mvxGhl4wUuLCs6ym3tqxL3J8ylTg8mI\nCHresmYw7dvWHyezE10n+sWInlq3SktvcOlfsmB68Qk/tQ32PEqJiqVIzgFjqRG8pWTrZi6GinJ9\nf5PjFkUuI/ZvW+mUj6po9mW84oISC1rx4eYnp6DZRRIprz4arLleTb89Wmb+yKL5ysCdZssHhRog\nONaFgaP5otKJUk1083qLSTs/OBe+R1xTZEpz/iQbzBHOFFOq0TEqaZ6pza8Dl36hfgZltnc7oUCR\nLCcTy7F1Au8tcFgHnoXMzffNx5fdzffVS0SmsJvP3dNgnUX7h72leJxMVKYgZ2rgTZlNOxBTI0T6\nRf3e9j/W8waMGDY2WVZ6j3Du5R1Kbukyma6Exuo9ydNxpjKOkIi6ywaTAURZvW1byDNVr5/jM6GB\ngN18rV8iY/ePFWhtJRPVIygz0XznrXQKpb22n7Q5P0fr+r7yTN0qaTSTV1KXRYrEBcjvN+MIKV+2\n/W0XSciH8sgUzDMVk3aK1AUObY7MzZcpU3EzjeVt3h1/nIzeQ0S4+oXYo1c4WWLOmTqt44OOWaQq\nQnNmhAW1pHmmCDLlx4v2ywpCzOsm2J/NF46TScbq21YgZwrlU/KpahiHZ7+vzM1nOFPezecjSRGR\nfeTV0Osy5D83xrVNkBoh4UyVEnltLP9gIMivMdqw9ruN360Ar0GJ844Z9oh/VssPkKldmeq/Z7KV\n++ZMPZ0yNeNz76wRpwz5yRKi+RDcOqFMoU0G55nqLYdrIgZR2HAezRcVr/o9b4stlH7SdgfP6qYL\nfO3fVwb0WyV7rt51hVICIE5NdtBq3Rz7HGfdMRUGlUSLUziSArj5vIviR5eUET4yau8vWFy9MWIF\npzQowaK1UUBat513PnJUpCa79ZtcH9iBkiV6ZGrO+rfPaX/WYGwfWfhRWgeRiCyK5MaPj+bb3xVQ\nZnw3X04TSTvBu2Rtq6xrPNC3bpC+3kyxuCgkoH6N5mNuvgyp1bZHRquPlkNKWodMnRpNhKYQcEfO\neEHBSywf1+YUr6js9croaR9v8T7t77UuokwBj4gIR6aaQtfuRWS8x9kI8XuUx9zJEsny//h8HSK6\nKZoyBSsYb+fLgnvyk3TuXCG0ySDLstXlUJ2JRprVllvxtk/Ies0WMxTaW6+N7kqPTIXUCN+zm+8W\nGSF+J7egoaSdXkHJCLAImWJuPhRe38Z+K6f9aHX0i/Y3nyoLAPGlRAwqYypBqQ5an9FzYKkR+oOO\nI4LQ143mrVc2katEROR8rnmmMGcqvg87b5BCKTLHcUTCXHcQSSHGTylxHbgmms+HtL+CQJFl4UaX\nTwas8rKu+KBrpyDmNI3L/YD6f/zpJL/4/Ca/gsiUuHU+KgAzhjFCpjKDxNNERCK64g9D9kKz94O+\nes6ivydPBWGokPb1xc27ei+uzdL6ZGVdCGqqc3pHx7Rvoahr5z6iv5k8nTJ1WnJicC3jLFinuds1\nV91QCtN6t9Sy5MqHrZchUyhfUECmJpSpAgb1mqEdDkFpbfE2zuQ8vcA9M6gXC6llKNcjiFfCrXjE\nDyncKIoq20jODsULXIitjRvLQdh/n1hEvUKiyBRKiyCC3+tWMGqgbUeEDiC2ZjNX94dXTlE0X2jL\nKnlb3IBfds7URvNQQTdfmXPzHUlIyw4bv4aAjsLaVzIHzyVa+/5sPnQvzEjbtnKJeMMRvwGZcojh\nTM4lEQlzR0TkR59epBSR//uXnwPHz7vakQIwhUyVOLejEdnK6/saIlOZArkBighZ12FqBHDCxr4O\nkHGBOHosfQtzvbI8bd7NNxNFLlLJ9T9wpr6gZEiMf4ki0WXgOQQ2mq8edAwm6QQy5aMstK8iHtFp\n9dq+HnbzJWiHJ1MykqqVV3Ke3snBzn0unr5/Km8b5l89gnj43MoWUCSCCARkKlemIlejr69+j918\nfvNASoB3UXz98YJMEYVXy2bGiC+PXARxEW5zEhlAyM0nRTrk168DljRuy4jUZwvdrszNt1nUtX1n\n5ShniiFIu1sKIgWuLECx9L8eGSwEsesI6IQzhZ5NQxLjvaHn6RHDmQCiej8AmbqkOfk7f/SdfAKp\nEWy1zc1nyiReDdv+6hBiXy80UM9lf6bRvZ8by3hsEvdu8VHCkcZS+13/XsBaofXo9fZeRbCrGN0X\nI/Sz0xhGeAFySd+TPF0035JY9/Dk9dVxfRxMqgvi63mTrQgkoM+44HyUhQi2LP1iwZL4IWG8Cvo8\ngJVV20osQ7JJoM1L7w9t3KVg0u+jSLboB1geIjI4ujNz89mxtyw+JLtZhxkBXV+331xLKZdomohM\nsbBtNF6yLMVobqLydjPXFBsevQgcj+B+6S1yj+yJjDlTzO1j5w1z87H0ACOh0XxAqWR8SrTOsQ0L\nKfUf/OG8YJ4yxb9trOPzO1HdI4UGRSyr/Pjilv7F5xjN5z0IyLDOvBr2up7gDTi3ps4Xk2dqKf13\ne7sjNA4EaTACeikowMrOz/q5J6Wmyru6JMcnfqCxWctjJbEZftqXvh4m954a4TFhgUSyKBOsbcdJ\nhngJ377WA1/9IZWznKnMzeej4EQMQXACLfLX+giM7Gw+H0arfWWSHSdjF0GP8HmlUxfr7+s4mVsF\nkcpVvILgeRVIcREZu/n85li6512VDk2xINK/x8iV6N91ceNOpHGm2H0ydyJTkLEShDgk/XEyUclB\nyoaEpJ09Af/6DOj+WJX+HrUvREk5ikyRDQu57vb3TJECUy/ZsLBS39xOpRTImWLrrD4vnBoBH1B9\njUKDztRTUWVKRAABHSevvJqADgzQ6Cpv5ZtyvKXHrozOI4x8W0ZAj5ypUWoE7bcVH7BiyzIXdPS8\nYPdljOYbG/Hazg/K1BeUFDEAg9krQ1vBBMJvXyMhT+QKzhSyLsDCeXSgiUS+lYiSdRkyFfkKIgmx\ndEv4EG4RjFGTS9jcapuPOQRPGVm8eAJ6Hp68l8uQqVJcRFt04+mviPDvx35bGOvvxV0r0pCpn5As\n8SyAgmdAn3Pz2c0FHTeDnlNxffebvSfwizhkCnABWcRmnxqh3YeVt207xAc8gXdn64cHk/uNECgK\nKCiBKfUf1kVeLwOjuYfnzuZTjgwiiJ9O8UBfFHU45eYDy0avTHk3n1euL+15NHMKHbH1ojxTcf/o\nOVMgNcLAGwDzTIG+jo2u9r1I4uYD7lqdh77ZUvrf9/LA6EF9YJxaL1vB4+pe5DF3skQymBhlz12c\nEsCSrn37VpGpEM23xkSESBDREylKeySOa/+WPFMZt6eHrHNkao/wIJwpbwF5hMzegi7WDxvNlyGg\nbvFD6KdI5JUwZEpdoj7k2Za0yCd287U2RNpmpH1BfLtvLpwpu0lZQUgmItarwJQGztIX0WSZDZny\nGwlyv3mlzFvkeQb0DSNTZMMqZlFn6QlYeoCReCW31Sdde33/3bMgRmP9zZQjm+DLyT5/POf9urn3\ns3Bk6mWNioffIEcRdZmb70cDZCpze4tE3icS72FARg3k3J6LUVDmEJyuTYAMMkVlJjVCiOql6Ob4\n+DTEPxPBecW6PuzoWP89k+x0hXuQp1Om0mg+sMhArk9nWdRH9N3u5kML+7hfPtu4tl371b7zCtE1\neaZQVIWP5ujKlxiW7PtjRXkszM2XPUfv6tqttAd283FuXr/4oWej31upCx+o7/LdS7LpWGQGLU57\nm24R1XeC+qTnNlJkCizEGRRfXb3+3rCbyXKmUD6umFHeJX/08xooNztqcK5h6wgBQ9F8ts/UTVKO\nuvku17MNy6zYLGs+2rRPTnm2/0fP/9U8f5H5rN0s/F9ELsemtBfnFfy93oNuPjtOR5ypdtKEa3u4\noUcl1bsPewVN+51E8xEEx9aJvBpI+QgegZUpkTkqhAIJdkXfjzfwLOvfI86UomO5EW/7fs8c2+dT\npjI3H3jp2Ocdrb9fXZSpj4EzNenmAxb4rul3k7z/7Yibr1+ceP+CVTjgZ+18CBCq45GazZ107p/z\na6KYPYJkVqxXUhfpFysPc6swHgTcoJzi1S3iuzLF2/RKAOrTL7+rY54pUyw1AoPiGaKUIVOVeN+P\nt2WJY7QiXKZvAJnixgzhTLENq0Q3X9hgyLFLI2GEYEryBUo9W+d8vUyp/3Bqeb5eaQQaXmcZ+qLf\nbRsq274bHenCUF2RHkH9zR997H6LARvtPva2iVvXt98joHPI1LmYPFOBgJ4jU8zNxxR973lBeQwz\nw0vbtOW0TREcEerLilyQKfAuYzCM7nGhaN+nwikE9yBPp0xlMDHK6ooy2Nr3pcjJrz7Xiz0BPSMi\nd20DN9+yLBdrnS9w1yBT+0RxvIoUQXEbkH6PpOW6ib8hN593u9hqGzL1mEOQcUZELtE3fiMD1mFE\nBFgocfud1VlKXJyykGi/iKI+/dm/96ciIvIv//m/H94ngv0R0mTvLyoJgLhquDUoKu4EXOvY/XL5\nbVOun1vszdl8CElCeZGUZ2Stao+6ap2HlCniumNKClI+9E+/zok4xZegPD6aUgQE3jDFnyhfIvEA\nZcYDyxQapgCKiPz06w/7/3/3p1/1/V1Y3rX23Qwy5d3SASF2498m7eQoX45MoRxpPNLUpUZYfHLf\n/r4ZKqR/+9x22h/fP22r6yOYP30fdI/r22SCIuLvSZ4uNUKGTLEol27TcYu3R6Y+uGRwi8ydzcdC\nxv0E9oOdRVDANsACkZGaWeQia6vxJ0DSTgAn+83N1qucqXuGbTNB6IiKjfYSqYjfq7EivXWownP3\nbPvve53OIsYZ522f+jb95or69Kd/+0fyt/7jfwHeoy2buXetwGN1AA/CIlMoKs7zobT/IfO/olsM\n1THRfChpJ0If0XNiiNuRsU2j+YgrBSkfMIfS5f9IwfbTuSbtrL/RrN0LUfz3TTjee+CxbfG9zES2\naV1erML3Oz/9FNr2CJJIzBKfJSzW9j8EF377neWZejs34zIioPlxMuzIJeZCy86ejcgURoXe9kCC\n9h3zXLCggBeicN/i5rtnZOrplKlRKgARNIH6SWYHe4vmUzffnIXgxdfbXb/FSR4iHWbyTAGr7apw\n+zUf1BmEj+Bur6ghztSjpkbILOhIQMeRjH5dYIovQ6Z4NJ9+FzdO76KInCl4S1Cg0rZFpQW1Z/uF\nlJi2mbNovr7uUkqXGsFuyo1v5Dcxg0xt8XSDyvHBG4fnkvhNmKUQGQmN5gOKR+1HbBvdLw5KwIpJ\nff5bV1dQaEG7Ivj4H5WXNbpefdm6HsZ69z4TFMSLR6a80gMjn0kizK79knNBvZvbIlN6WYgaTQAA\nkd6t3F0DLvHI8OqM2Ohi67/35RCnNhgYwCWof7PUIrZttI4gqahgXub7lMf0sSRSYU38GxogCFFZ\nugl2QaY+szxT40Gg9aKBgNxjIsfyTCHOVI5MOZ/4AAVDlqS9NnP3eAupWbyPOQSHUZKJ9YqiSkUm\nkClbp0ROFEOdtE8iHFEpCbGXCU6NkGVAj4aOH4MinjMFiOFLXPxLcVa0eeYbe977RqfRfGNXFjLI\nFqAkns8xAmtGuCsF3wN6FnCdW/p6ajntf1/nB6vMErcdUoyzfopEtw8akzPn1NU+499/4+Lq++0f\ne2QqeiBi2xME9JIb4yF1wq6wb1TRHBHQUVAHC7SqSlu/9mi/av/7+x4dSWQNDIRE178F3tcImQqH\nhf+ATN2XeE3cCpro0V3STzC1ItTNF8mws5wp7Of3cHkcaLmC07UBMx9zVMu7o0b8LISQ7O14q9NN\nav+c96Sd92xqJKLv3UeRiUQCOrJe6/dz1j6y4O0iuUcLOmtzhnCr7d2CTHkEDJ3dqOVRNJ9v82RO\nmz8XFP00JrKvZrNhRsAoAzpKjVDAxoEU6/eO5stQpBl+FXxXwB1Yr1ullIv7c0eQQW6kRJliqRGg\nm889y5HLSySijCr/7b/5T8n/+n/8v0D5w+6uHqmdTY1grgHGeL9/WGSKKfXj1AjIEGCpERB1o7r/\neCCKf+SIgL6ae+nKApRP2/Z5xWpb0dBG9XrZ7hyZej5lKoFM903MLTIlTIb2d+BMeTffii200PaG\nkSlv/bKDjmdcichqO60tAV8ov0VeU+0Drn8U9myv85PaK50ZUfURxCZM9J5KHxnmUSROQMfvOdsc\nS4nE8zxyq9VrEZWMi8IERZpuDiHqyxNEaYBMIfIt5EyZv+1mgw5t1TK1jQKtf0SghbxEYFC9AaRr\nRth8PxNDBikfTFEQwSRsTszf5EzmPHoHtZ9aJzpOplcaaHR1qlhc6iLj9Oe/9Y38/Le+Cd8Ho/ny\n6Xl2Y2QKnZHpxr+rU6RXFK4loCPXOUJ5tR3v5tN+n2QJ45ehQkzRRWWZm48F6YRnaBS+TEopst6x\nJ+N+e3ZQsmSKeCGMm85iluWdM/WZpUaY5UxhQmokoLd69X5E5pAp5D5ii572aebgVFve17+3s0Z3\nT3jOpl5m8T6KZBEoHo5eF39ivSo2EXGBbj6geC5uEbQID+LH2ONm2j0YN9/eV3i7UHBqhCzPFDtT\nL9b7dm6cncjXiQtvkeh+0XvbAycC8tQSKr5tG0SmgpsPKJ3LgqPvjgzt8eHFfXmkfKB56pO01v9r\n/wlidy40hQlLDZIfdOzcjCQRaabQIHL9jExxppK10vbZu8q9gmof54sJcuDu5pyAjhI+s+fv1/TF\njadZzwdCw1nG/cyNjpApr3AiJB3JVq5Dzr+0POZOlkiaZwrA/T75on9hEZk6fjYfcvN58ir1ac+4\n+Zwipv3POFMzGZVVMnKpX9S9my8e7/Ho0Xz8WfmNdHHuLa8wd+WIciaCOTBa2iI8XtGq/wduRTN2\nmYKXiRb184cqUwB5Q8qXncMo/xNSIPAxH5c6iGtI8/1UZEpi/p8FpEagh6UDZerAys84LJn1T918\nbp3z9SKFQqRRGewRKDOIWNc2Q6bsGgAUxMz46/p85bphUVgRjMSydA9WoJHojGEYzWdcptcjU8TN\nR9YK1H5x83xHpggqhN47mu/2b4hMAaeIVziR8Yfkh4OOv7Ck55ttcSKuiwT3lH1hqjz9ghDQlyUu\nfEiQO0NEQgSJh+hHPCYrCHkbR/O1v1lGZVu+1j+HsGX5vJ4haacIdol6JRWhn/q9rxM9e6TE+s2x\nIqraXuwbQoDsu2YKXiYo8iw78mEBroltw8hIGs0HlE5vrCA3X8aZOgNkShWCzkiYcPMd3fBtH2fc\nLto2OxR5FM2HUDYRi0xtFEFmUXcjzlQp7XkyEviMm+/aTTUiSLEelu7Bil/H8ckPrTzKMwVTIyT3\njBLOMncoWnu0X7X/zlgnqBBLWyESDXv2TnzGexX/DLUPM5ypeyagP50ylSaphBZ+74JRd4iKcqR+\n8d2biIh8fImDekLPuYS3kv6Cjda7bGbcfDD1A/FbswV/pHyJ8BwyHfJU+pPOPbesRYs85hDcFwCG\nILiNzBajlhx59uxMyfrb5VNAdIxTAuLxNQu1WGcE5URi7myRyKtr5V25ETIFxnRdoPsyGjrOXGQ2\nmg8pbVq+i0CDrnT/DPT7A8jUPt/775nig5QP7Uq2qdp+BiWzQ+wYZwobXbp5MoOrlmnv1tf963Lz\nMYNm8WNmIs9UHzXqFNSN5JnaijmOKyqmOQGdIJIEGfSKvvZbxPAHnZtvxnU3cvN5MPJ0ws/TG1ws\nStBLdu7nPchj7mSJZG6+fZEjIdQiEk6f/3hJ0qnKFEqNMM2ZQm4+txjG7LBzA61eK901e/+IK8q2\nY/szytPF3Xzt70jU9MfJPLabb8g16BTa6Aqo3/tnL8Ta79u0/9+VqTLiTCESq0W2YhsjQe1k1iOa\nK8jNZ6PokLuM1dO7lQ25noz1kGcKKG1a994OMlgWnEPtyNDeuU3e+k/dbX0dZ7C5oRxB7V766/U5\nvG45ZyrL1s8OQxdpz5PlmRpFttV7u+7hegQJIbHZ0Vu2/ezdl9L3zaffEInuZHuwNGwToL2eHlLb\njmNzR7BJ1C5DhTKeJkNC8VFHM5ypfi1jklEI7kGeTpnKOExIgfBuLe/P3ZWpz0yZmiSgA3eGyDUE\n9GET2M3HLBiwkGl7DGbPCOiBXAomjF30M5TrEaS5+fDC0pFAJboCRLCbL+ehtO8ifN++W9xvInxB\nbhYr3lgzgWhH4ubD7jlAxL+E5m8Xngkco6ge15ZFt2q9USHQ31H0nXXR2HZ8XciQEDno5iNufTZf\nkbGE1zmsYPtyIoY0feauKUU14zE6ecRvLcOVXJ8+wcsRd3Qt75R+oPDOENCjiw9lBeMAACAASURB\nVAqlRmh/tzEklDM1UiAROosSjKKxeXJz1BtNDBXCgRbx+DN7bZzHLEu740xNHidjqQz3KE+nTGVk\nPqQMLEsM6beDQqP39NDXo2fzMYjST6Q22C+fJO8MEpgbhChHbFE6JVB3ls7A830ilNtPlgzlegRh\nyBQeY90xehQFYosqJMt6+N4gPMp9C5mZXXt27B7ZpPY+ODcYe6eRiI+VSntm3rbFzOQLsMrFb3Jm\nIWeBE3s036YHHeP7s24+zJmKrk57/TXCovmuIaAzV6SIc7UT94w+71eTaNK741mwCkMp0DVoHqgL\nl0V2sZxGI/EIkrYdKBGDddYrS8gYR26+c5Jm4rRG5Tm2Gceu5yMhRNSjq8W9c4YK5UjoeLztZeHe\nQyIOh26+HzhTX1Sm3FSOS+CjPOzrWpZFPp5W+WPlTMEM6BOKDpgQ7fr2t9fyj7j5bDMjtCOiFbwt\nxtvQ/vpFxVvvo2iaRxJ6hhocYzF8WiSiQIyAnimeulYhZMZbzL49a2Uy3kMmLDXCrJuPKZUeMYq/\n42NpvFurlPabrde383bGGdAVQcCuMa8AxPt6z2i+IwR0fxKC7ZttgyFTb+fGmUJuPpFk/BODy5ZB\niCvj5Yz6PBI0H+r3fdszGdBzZKofG1ZhfwPvRaQiseet0H0EGSiIN4gQUa+oBGSKoEIZihYjTQXe\nF0p6q33wxH+RmdQIP3Cmvqj4TdsKgiMXiRPXv7CPL6t891ZHzAdAQJ9BpraCYX+vvXsC/DV5phhp\nEIbvX2lN2D5APgRA2ELeH2NIZWkWHkHaAtB/jxJEeiXC8+Jsndm7QtFZCnl5qw21iZJWWmRLRLoc\nayPR5vrxyze6gF4yZEqVnG2TrcwedNznh7N5zxhaovV+TnhBtR/9/fm6WIDBETuBnX92Bu1qH5nb\nxY9B+5tIMg7N83+lx8loP/v+p2tEQKZi+6cBEn/UzecRpLJ/36NI44gyH9bfKwHeA9Gn3yjdd3uZ\ngQLpSe2oXe1b/Q0pKr5M/ZuhQsxVjTwd7IgflkDbK0WMBO8lW1vuQZ5OmUqj+ciBsT6horeslTcl\ncpyAnrr5EnfM6PBhKxQ2R1ArOYst44ANUyM4Cz6Dwx/fzVc/OQHdlvU5ttr3XZ3A2hQxkLtTlkR6\n+H7pnrc7zR4go9YQaJtLbJ8J4o2xqFXYJ4Dy2HrPW42AgmfmuTFaXN/too94bPr3soh893bu2m39\nuKRGGLjG1sUrlMfH9u4+Dkp6bFfbQOkmbF0ieNNkyKBGML8ZzhRa92odGNGYcfOhNWD2sPVrHy1K\n2hlQeYIMW9m2GFiTcUUtT4zxRG30JGwTGOIIkUSIqH9PwfNBUCFKKl858R1xG7EyFQ0/kWhAxOvK\nVcj5l5anPE5Gfe7ozDSRHlZeFnE8DoBMmQsCYfoaZIosMJ5z4qFnkUnOFLAQqrLHy16zoOj3LDWC\nd2UFki5AJR5WmRpxRhzUjgjKkaODFxRWp62riHc/IM5UX69VcBlKkckKN2ierDJa8RLuSyRG2cGs\n317Z8JuYUTL25w369bIu8t0rc2XJ3g97f9qHvT+rV5avf5atrks7TEmfQOnQOoc2TaaYoESTlLxP\nEI2MgL4jhgD9uOUUhkzWRToYGfGQpjKgu3mEz+YzdYJ1gqF8mUfAA30e6bfXe6NC+y3Cz+bzTTMU\nDYEH1xqHXpFFwRFIMgrBPcgd63nHJINMEYlzWRZHDi7B1aHI1MfTCnL1THKmNmyxh2g+idCzXj+S\nAjYNGsJ8pTUhkhPQ1yVuqvHoklb+TPzsjyLUzQd5Czj7Mox+Ae8KcdW0ei0d3Q8+FBwjUw3+b9/N\nClqIWdRq65MpSxR6RYTOW7kcGOzIz2BBTzOgk42htrVQZAoS7MEaEg2Jy/cHDIURFwm55CKHBfex\n/mb7GceqSEOhKpcMK5ro2dRr1OCKW4s/zQEhruz+W5/r57WbKuI2sc0/W8+jkRgV1J4z1dbvhkyR\nqNHEiI3IVOxnlo8ucCMX6T5ZRGhISwLGGwtkYHV7RZahnF5KkR+i+b6kZD53FuUSrGWPTF2UKX/I\ncb1+Lmkn06ojTBxPJd/7NWqDLKIwU27iYmHRfBn5M7j5iu9HP1mY2+JRZI+ynIDH16WP5vPWYSvH\n3lX9TJGp8LyXoOQg3oWH/6/Z/3eFLlj8vLwf69pXKx6ZmjvoOOb/0eeWRZi9rCtFpmxUYWunfoak\nnfC+QnNDoVGiDCFCyBREMvu+ieQRvVoP40yNovnQvPapJqCbjyhpKlnqjUzC+lPAeXcTCEl0UcX8\nVd5tuSw9yoe8ASI1FQVsc8OGEHPzoWjCNs/7MowzlaXO8e8cGfH2b9TPrI9MisSxek/yoFsZl8zn\nDvOvuBxA9YX116mb78MLsLaAlYzETzIVb1nGTfHS94k22GS6Js8UOj9NpYVJA6VwjW48WwxxeFD7\njyINlWGbCV9wOSKTo4g9NF4/G7Lko1Dj5hEWcfNOVPG4xuJHGz+KPNrLhzGC2zyZzQUdQLyu0YCp\n88bWkW/ati0NLplxv8Dwc+bCPrDw7xsLc90FpECCuwe6IhGKSMbhhz01QsKZYghaweiLvWbPgA76\nOULis/GVSeRMISVS0rbrdQgB7fvnu1dzZ1WU72Vd4ngfrPHnAhLXAhcaG5u1X61/IvG4soCwkzkD\nkSmCmjIqhFdkr3Hz3fN28XTKVOZzx3yHfiCVgZvPCzucFrUN3Xwemdr6TfFINN8ycXDobmFfwRtI\nCehwUXHojIPDUfuPIsyCRhupX8iZS+1INJ8+0iKRK+FdT34RtwrXETQFp0bI3Xx+rqE2GyK0ybYh\nJQct0NE9vrv5EkT1pXPzefdLJKAzRWXm/c4IteaBkl77zPP++HVOhHGmfJ3qZt04Zwq4DUXyKF1/\n7iAMCJpw8x3hzfj1ByaxnUBI/LqGjZaolCsyBZ/LfrA0dgmct/jeMzefpxjUOkpf5vIDc7HRNA5L\n5Goxt7Zfo1o/MWAwJP+DZ3tP8nQE9MznfkbuEo9MlQhRqzL140/xcVVkatwvNhAqEmTL+UVwDgK1\nZTwHIXfz+f7wXCs5Ad0hFFuEw6Er5J5NjUSuybMTFvLCn332rsbRfP3vgTOFiNz7Itu+m5XddeSM\ngczNh5AptPmIXKL5tg2nAwAbiS1ljRy0adu6FJmiBPRzvz74Pns090g2+dbvSx0edSCIDCSgk6hl\nrWfvJ9kE9+NkzkXezvmzCShFckyUR34yojzRKw6jExE9BIjohOEa6Qtjo+VlXXYXHlo7R/dcCg7C\nYIEHCOnbj1Zy45ehQkx5X5dE0Xe3diJUiEBlGbh2Wzs/JO38opK9GBRFtSw+OzVApi4XfPPpBNub\nIaCzgeB5Mh4CvQ6ZanXu1wM42NaHLE42qFMCunNPbG4BYBFPj49M9d8zAnrPXyKIwDI6TqZHu2x7\n3s3lNw+UGgHlmTqWtDO3zG2fZrhFPWcqEscRGuytXYvysYOORar7irn55lMjvF+kKjuy47zhuYIU\nS3S/yM3HkEF16WW5kRayLmXIlHebonnANmCVbePRopl49LAI4EwNUDGRuD5DowXUey6XBLTguYwI\n6Hzu+r5dfkvcu9ME9BLzu4lggy+LNBXBKDLmTIXmOvHpX+5NnheZSpSpeFBlK1MkWpSKTH3zESFT\ns6kRonXRru8r6Nw5Aw6BFRQauwBLQvsjgomlo7BkmHzUWL6rLCHRnEfwWO6fRxEGTaMoRa9w74se\n4CPAU9aBxan/K2aRtEZAUOBK3Iyt+5FFGGbC0I6MM9VZ8YnrSkQ388iZ8i5l7X+XAd1sNo3/ESdg\nh0z5ZIqzqRFcf25JjaB9gtY8WD8yQjCM/pxABvX5v56bm+9DiKiMirT9G23EPp/SIQJ6Ofhcg9LD\nEdEMIYkuqoh4hYCKk2Y4J6i+jndCQEdJO7170fbbK3u1Xz0yNTphgyl+MHoUjDdbN0ou6vco1Acv\nxdzPPcrTKVNt8MTfEBoSfd5xQ1Fk6kcfIzKFBjUS7ubLuUaMIIgEhcYypIltnki5U2FHDOh92Hq3\nEjk+9gTxW6z3e5BRNJNHBfw7FkHHyeCw7Mxto8VL8Up0PL4nuBWXCP9f8zYYqZntdbNuPrvpouNk\nfD17u16ZvDSQJZKseaby1Aie0+j7HN24l+8Pjm0U1XkmiAzKMo2UORQwgYwvkUZA75CpROG1MoVM\nXfpwlIB+RJdanQsCuQtn0tD461AOOVRvey5RIx6mRtjAcTJgjKA11SOIHo1Ec3hvk3hSaEJZopwi\nZR+NzbnjZO53v3g+ZYpowyLcEuqKgsmwI1OQMzWftBO7+fLQcv3/e0fzIUhYRPkfpP7E4vZur1HU\ny6PnmWJcNogiBSWCLz555KVtv68rcjliYAVqr72T69EU5CJAYdx9e+g59OV0w9kPOnYFFoTGiDuT\n0jzLLFz/tC7ymXCmXtbm7mp9btfZ+3qv1AhaN1KQGCLMoqsw4tPK0ZB2dbOei7wSzhQ9Q3BwGHrt\nQ+k+O+NvpFiUY9F8UZHHSnrWNrrOrt+llHCsk8iYM9W8D5g0hdDezM3n3d21b5cybg1nqNB549zY\nqMS1PsH7CggaVvRZSh7bzg+cqS8oyPWgol91fBYByJS7TpUphEx5ZQgJI+hpf707xvaAafewHbCI\nq7LIjgsIGxnYqPw1kETpuA7ez78sMYRe5DqOzj0JsvRF5hT2AhY9/Ru6p4ESqyhMT0Dv6+pJ0ai9\nCP9fp0zFZ5C5+WJUY9m/t2LzEaEIqNPKUiM4I0I37QQFPa2LfHtBpsLzAaHyMMv0SjhTR918QKlm\nSgRSvBhvz/5W/y+hnIhJ2nlBppYFuGLJBshSOPTX9MjUdW6+Y+gEWmcDKr8re7weGFgzmEPrkkfz\ntfGO2zwDNA55RPDYvPSb9JE97/O2TZ0la9tFe0mtu/8+8IJJMIMXdiTbvciDbmVcssRr6AiVxW90\nEpNr/ubXH0Qk40yN4Unbt/76frEOB2Wu+eLStbNPJmDpsQkArImRmw9NMr+xeoSiboBxU3pUZGq0\nmWQHHXNEBrtksySMWroI4nK0OpB7pONMJQo/E8TnG7n5bFtMqdyRkW2r7q3g4hjnrrH8rGysfXpZ\n5VcXZcpzplBqBITm1PfbrjuDeXiNoDxamZvPDxnI2wNIUjYORerzf9tK4EvVMn0dtp8rUL5sHwJi\niNYrsgadD0Z0eeUDEsWJgWQleA7WyDv03NiXk8kzRRI/i/DUCMjlhvYdnAHdrctqwFz6yMjfWfQo\njKRdUL446drc78cZPr6PTPx19yZPp0ztFli2KRGYtl4XF5ef/9Y3IiLyi+/eQHsx74aXjEMxQhBY\n3hnWDuM2+Meh1V2TZyojl3oLxyMFjKT7qJwpb/GpoDQGPvqMbbbjpJ3Rgi9mkbTVIdciQqYCZ+qA\nm8/3lS14Ic8Q2cy7IzhKdPPBg47DeBODGHAj4MOpKVOez4IJ6K0Pra1eCd7n1sGxzZRF7ObDZWsf\nbbm4DrSzPB0ypW7Wc4HKrL0GcabYffsM6AgxHCHxKE3AjHh0GCK1xPC04hHCfg5l85o/m2Yw4zaR\nYoOCMPCxU/2c8wbMbuAAN9+sMoWiDUX4GPFpWjz/k8lRvtyXkqfjTLHoBPtdFrZ+mQ7ddb/z069E\nROTv/uJzqNOjDkgY4bheH5Exb/mITCJTwNqiPnHiZkOEVpU0IZ9biM7eggObO7JmHkU4PI5RJOTm\nw6TS2Fbutml1ZlGqWwHv2ijOLEw+E+rmI++0oSN937NoslIAegoW9OA6MPf2lvBVPpxW+ZYedHxB\npqybDzwnH+HE3B6zgpTqawjoWPnufxNJOFMmaerrOUZT2muQMUE5c36NAAiaV7i8HHfzIeOiLzOH\nTKHjZOr/GdKqGdBLIVGOBgn0ojysqSAMcOCwV6K9AcNQoTPI7ybC3Hy5WxfN1dHYRIKewz3J0yFT\nmWWDkx8uUqRfYPx4/9lPPtU6wcsOBHYgjHAsIjHhX8GWzYQudfGtRwtGJHHzgfJsUKcEdAfPewsu\nHCdDNodHEZq0k1iHvWKDN9vTiscYS7dg66rRbGJ+j5tH5irI0FMmLJqPVeEVe+ZqVvcaI4Yjq7wU\n6aL5bCBKlgH9ozkiimX5HqVGYFywows/itSiqAZCCgg6Wvtm+gk2X5F4NiJyTWX0AYZMxQzoAEEb\nKFNngCjNSAx+SI4xSlCxWpetd4y0ntZV3s7KmUoOgIYAQOu/FaWnoGTAvn8i7VlTztQsMgX2IpQQ\nWIQ/T6SQonJefkCmvrB4i93KGQzMgEyViCD9oz//Tfm3/rl/UP6lf/znsL0ZX68I1t69C2gDA9O6\nLDKpmnv/Hdv0kX9d//7ujS9kInkWX20mTpho4T9qjikRa03138MjMoJio9/HzTs/Tia2b19rv4jO\nEG65xTojXjlSK5qteB7OZ2iYPruWTNOdC7ewcOvY1nkr9Jwxkf7MuYhMxUWepUaYIXbPCiSVb3zD\nmuFDtvESN1//unZl6oACkCGT7Xle+oncfIliof0/ErQSPRAgVcigbTRvF6P4snn9cnlHRSKfSn8X\nwQR0lGql/t2U45ObhzA1QnBFXurZEXZ/r/g5I0QM5cESiUh0V/cSy422uHtHpp5OmWKJwkSwJYQI\n6MiX/m//xX8ItncNAZ25+YIy59yMyFKF7RCiov5mhSFT6xrziLRrtr1MvI++Xn+siHeFHM1kfC9C\nn2uJix9LCUAX861XNBkPy9a1OVTSK/kIca1uvs31af6daNGmHEnoZ99e/RxFPykS8t2rKlOuHjPH\nLeLCiMzZodqfMmQKKVMllvXo0BHF1IqNEFM5F354MHKj+D6i8coQtEZAr8fJZMaTVwAy9KA9z+3y\nGcc1q9fWf2RDDes82Jhn2haJRkszIPm8ftuVKfAOdwQ0Nsz4ftY1dpJ+nKJ5EA2YpeurH0NvW4Hj\nDRl8TIFm7jv/7GfdfBnqfQ/yvG4+5C6Bi0xMuHfNXF2W/jgaJIXA6SLVqhj68oH1icRvKHqtCIZa\nUZ9OS1QQVNgRAyKRD4HdfAaZIjDyowjj5sE0BkFhJpsYhdyBxbnX1T7jIu/HFVDSnSJ0zRtBJHgR\nPn+Qa7J+35fbkakzQ6aQkoNJrduWu6c/GBeW3zzQ0Sb4lAGXuBEoCdcISv3Azjxkm5tIHA8i0hlK\nSDEUqffzsi7ydsmAjt09Wkccq9TN5xAYpCigdBRd/QfRibjOo3U2bxsZHJ2bj4yzl4vCi3KmiTTj\nIeNLotMLfF/1v0v33vt6gpuPoEJsvDHlHb0SRjEJyBRwQSPxBuO9ydMqUymR12504aDj617YDGcK\nkVbt9d5FAN0/E24+NKgzqBX1CR0XoMKOGNA+ar2lFOgXL91Cft9WxkiYnz9XfHJEhia5Q5tOcKv2\nGcA9mR1FL1n0qhxK2tmPrbJ/n5cvbjNleab2zORE2erdNiJ9frbWRhY5at18nz54ZSoS0JF73Ls+\nWJTcrCA3JlNSVmDMwQzoa99/kRxBq+H89dl9SML5ETLLlClv6EIkhRgUts9H1o2ZdZbxh1QKmLd9\nagT9vb/utC4Xl+lGI+REMDJFPQhu/tf/g7XHzVH/zj1abNtl4813k5alhnxE0VEfvJQrgY4vLU+o\nTNVPSOYjfAdbsrrZrmtv1s3HQox9VmKkEM1G86GcPLYPKmyDQdml9/oT11yzVO2i0/fDRzw9MjJF\niZtAYfcLH4v2YoYATOnhkAG/0Hg3H0r8Z5EpRkbOJFq9uRLhy6PNyf69c6acnw+5Jlh+Nj1g1n5n\nxRLQrctPBBPQ2REofV/6Plwr1dWOrHm8fiB+lW+fRV5qHV5e1lVezzzRJONiZtF8IQO6Pifknk3W\noOMEdFMPmA/DtoHyaecZW+eVM3VmyBRBuUXMvAwu6L5Ptt/Qheae+X42X7KOsbMsZxPKIoVP+9DN\nVYdwM/HuwXuTp1OmstQI6IwzSyAUickPR3IdZ4pYlm4hRq66CV0KLrgZ1CoCJmmCtLEjBup9tHYQ\nNO15IJkF+wjC8nfhjezym3dvkQWSRQj2aFc/zr0yFbl4WNGeddEh8VYvU4729tzcZMiIuj2yaD57\nvfYBKbCbHY8jZOqlP+HgdGp12HZ8n/2zvjk1whKNJ4SkiGCXIMpCDiMvk35qosnKmeI8H+zCIcqU\nU04Rh5WhszP1Z+KNC3i80rDtSzmCuLN1/rQuewLUTDF9A2TV9i777zPlGHGmbJBIrwzidawau6E7\ndR0fIE2t7f4eVNjZfCPA4N69GU9HQM/CLHEGdAnup2s3lFHSzmyT8UoGdNUtc9F83rUmkkOtqE8r\nCc+vdeAjBkT6SYuzgEdeyT1bGSPZ4XHg5hBhEUr17xEiEyPVYnn9r5asgRNt9VvdocnMrcG4FLOy\nXKGQ+cgilhpBn91n5UxNPCc/b6yym50D+elKZArx3ZbFK1z4vmYFcSRZFBtCxvd3ucbxgojyaIN/\nWRd53XjSTma0ZlxIr5yiuXIabKxbOfZcA80AHq+UIyTwuJbFKip9PSr6PosMEh4jZIqMpV0J2kBZ\np+jX31oZhFyh48ZYnilfdiN5prjCTQyfwRZ3VJH+UvJ8yhRBDESaVh64PF2Z6918I3gys1R93g5K\nFJ5x8wHSoE9Z0PrU/961xRaTwgnoPWeq1dXq7Z/Tw7v56GaCN1tbdkS85pGXpn238KMFym+cfh2q\nLiLp6rk27NxuUu2947IofYa9FxWfZyogamCOe0TXKrtbcm85ZyoiFSxiCikpRxd+NAfZRoLKssjN\n+puts//Nysu6yvni5oN5pvaNsv/eBwLAa7wyfbWbD9efySJRkQxuPnJPKkiRtsYwRVrXSzRfwdF8\nL3uSVKBMEc6UT4dg/+8TBtd74uuE/d3WxVx3CDlH74RF1vtnvwCXJZLtyr35S8vzKVNgkKmgfBh+\nkqHUCHl7YxdcZql6JQOhS/PRfMCVQ6BWtsFkitt54wR0G13CLKTOFXLnVsZIsuy+IpivMlIiaCLQ\nlAPT2u0WqMUr6ai9MSl+JNYyHykRkTOVK5XfveEz8zwPROvsEAOLlALOmYpVpj6eiDJldted5+NR\nV4d6sPZmBLn10boggpFxbJDVT4/m1TpwH14vGdA/AH9PGs3H3r+Llpvldllhm/xI4mHUOO9a3rbA\n/pYie9CNvQeVHZkqOTKVeVO4QREVfXQ2Kzt2ioEPb+dEmYIK9HFkaibzfCnx3u5Nnk6ZymBilCjS\nHyq6bXKV+uszmCMZufk8twVZlbNuvlnXEbV4AMFQJVsoG6rCo4m6xezRkSlixSLET/8Xidq4zsiX\niUfv7GjXpooJD9muv+NxNULLRtIdljwYolEB7L9XadF8G/wdbbgVUY4LtBJ/RcYE9BevTO1ISvuu\nHSbevluWfn6dyfudlXXBSAG2/rGbjynqfg7W9pCSWSPQXt9KUDLtNWiszkT8imBul0+f4IUplSNZ\nFo/Oc/SOuxixkShS60ZjQ+SC8l2MTOZStfVbYYaAd5lrH0Ryo4shuMHNR5FQgDQRysYK+qhtZa5I\nJNkeei/ydAR0NMhUUDTassRBfM0L8wgAkmyjipseXghn3XwBuqZQa/976w/ngKV8CIOAYc6GyzNV\njkc73YPsVixTUtFBnr7MFcgUGre2zlL8cTK9kYBQWavIjyLxmHSL62DB8wogUyo9ZwoddFyvb9/x\nBbpAZVQFhf3v/Tjpxm6RqaiY1aCNXnG1fbhWWC4fxktBZX1ReJwMWQP0u/NW5LvzJh9e4jZBo/kS\nxFndt0q0bnPFKlMC6+3rhz+lEjhTicKZtS0SjRb9jW34+ixH/DNEQNc6wxxxaLftXz8P+t+8m5Qh\ngRtx7/rnKMLXcmtgd3W7MbK4PiI5aux9SXk6ZcpnfLWygZe+SMx/dM37uo4zFWv2oc1osaho0bgv\n0M1HlEuW+8ord/194Dwptp26qMS6/Xlq522764kxErYIwcg7v6CRTcwfSmrrRIf92jqLxEV05Naw\nhsRRy+8adMv3mbkFAzIV7l3vqb+/PvljW8gzRNWTzq0gDg1LfTGrpMwITMRJzqRDxhwyyGo/546T\nEanuz9fzJq9vm3xM8kzBfFgDN59Fpth6laFDR9yncT4kyBRZa9EcsYo9OzxeOVM1q3iidGTI1MQc\nwHxNP+fi2K3X9u2+MbQJIqEcNUX3tW2RtyySHyeDDPR7k6dTphA3QOUMkJt1EXfQ8XUbSkbYVskG\ngg9t3oqE1Q2hZ6yd93DzcQL6ODXCZtwqHk72Ex+FXD+KDPlNaLEIySr7Oj1yowIR1cunNl/RiH4R\n9W6+cCzLAsK6/Y0OZBHrtotIgxWfTgK5Jezf3144Ux49wqkReiPIIhzZOZCIDxT72yttItGFjUnq\ntOpU1pWFn4OyYMycN7y5+bUqQ9AUTXk9b50r1P6u/bJy3sbvX+/tDKLAxgT0Y4hfDMgAnCky/9o1\n8b1aQ4kZB/o+GbVhR6au4UyBdR2NzXC4dPHcyv7e7L3SvIiTbj7mJfLKV7Zn22tsf+9RHnc3I5Kf\nwB0HSFVU+jLXvLAZAjoj2up3I4sJ5Z1BgvrOkDrkrhDpI7y8zKRGqNyA+l1w83UL/n1bGSNhVixS\nKLwVSY+TIRsJcq/6YyCqEWD7F8c1IiW/BzLVFLL6yWrwCzdTOpZlkdO6yLeXDOhe6UYbSRFs7W6F\nH+Mh0jhT2LK+bHIGFkZzeVni0T0ix8d3NfB6YUYeUywZIbhD2RLE/OW0yutW5DMhoLPIN6S02/ZF\n2uZa+5mX8YKSz84IOtIJeQBEEkUOKdIGVWHzuiJTG4+M3FFUsGeRd4SOgWnjzpTbjVy5lC/Orbrs\n31thCCNy8zHFi/GX/VjOkDl7jYiEc2vvSZ5PmSLuFxE8QFa3EPpFeSQzqBEj2up3M5yp2Wi+mSge\n+3cW4eUlhfDNIog2nMhZ4IvuIwizYhEyhaD2WgdRpiZg9MCFKCLijpO5V3+SWwAAIABJREFULs/U\nMcuvcxXqoS6DMRLzUuEN5tuLmy9E84GNhHKmLu4VNm5VUWAJdUUmUiMENx9XUmZkBcbTGSgeIr2b\nSYUpXssSI4e1/15q1u7q5rsqmg+sQSotOrIp0wyZYsYjSj47I3qJHXszgQ1WEMHczsNsXp/V3Zwo\nHTA1AqkTu7rR2lM/7eHiSBmMRiE2BhAN5LzxOVx/B+uZGVIscaiVdtwVL/N9ywNvZ1jaJhd/QwME\nWSzXrIGec4Ukg/1D+yTKZMrNB2BzhtQx63ldsmg+zgNpixXjlcRN6Wjo+D0IR5EyZEo/8XjIIqTi\nc+/fK1ImRoirDavfkakrV6saDTuHbnl+Rlb+xSBTfjNHBkJ127QyVjHdNu7m+/rDKdSloghZT0C/\n9MG9325Te5fUCEihxgqS/t6XHde7K7NgF3hZF3k9F/l8LtDNx8YqCnTY23eoE0q1MiaBH1NS24kB\nl3qSpJ1srUXj1Qc61O/661QxfSPUBpZY2X6HXPT+GpQaoRkeVom09cj+vRV60DHwxDDDOEPvkYs1\n4x5ngMS9yBMqU3xCoAGif9oN4ZrXhTT10G5iqa5LvyB5cp7IdciUb4JGaxCrtLoCmDLFCejIzedD\nnmdcEY8iIyW1J6BfFjTpkSn0nkUwD4tZplqyOGXCI6YY8ey5FLbeWcERgbisJ6RmbZ7WZT+bLxwn\nA549P6ICE51V/szPfsRurbblXGPoCBYfRHJragREKmdKBJrfTPHyG2GmzH76cJLPb5t8fjvD1Aie\n/2bbpgbXunTZ4lHZEQEd8V5nBCFTvp5xWgY1lNp3FlVRJTrO61XeLlxSZjjUdhEyhfcOhkja+xCJ\nQS2eK7aQ583mDPLEsKAAhl6itSjbd2wdd6xL/f9LmTqDl+4jCdhCRNtbx8hUtmhBJcMrROtsNB/Y\nMBe8QGSH7bL7ydIZ2HOtcC6eeH7ZIyNTNJoPoBJhjCXPvtaBYHE2bi9GgEs2i553hngetfww7wqX\nnXV3iqibDyNTvh6ti4WsnxPS8p/+rW/Yre39GKZGWN35nqDMNYKsdMTxEcERoP5ZqPiNkEX0itQE\npt+9bfJ6LjB9hHcf7XUO5vXJIN+orCoWyOUlcoObzykf3vgQ4dFnKgxx135RZOpUFYXP500+vOCx\nbuu3writXjm0ZTPkiXHFglJMFD+0P1QFF9xXtp6BPS518x04iP1Ly9MpU8xiEhEI93uYvMh12i/S\n1EO7wKJp10dr0ZPsTmBxZe0EQie1DrRPEa04hEyZzR1ZU36DyLKpP4KwNAaYBNr/xhZIlpeFcf1s\nWe/mWhfpSEVIIesTbh61/OZzVSHDhbVp3XyeM+WfPUzFYZHSjfPzNFHn3/MbX8Hfle+iwjZUOwzO\nNy78zJUy6+ZjihfiLbJ+fvqwyndvZx7N55T5Vide5/Y+mOcJjYQEpdnrP+LmC+s8OA1j6OaL49sa\nQMxoXpeaGuH1vMmnDOVL3HzMJTni83nkaRSIstdFlFZUthAjm6P36H5Gbr77R6aGGdCXZflrIvKX\nReT/KqX82ct3/5GI/BUR+YNLsX+/lPLf/bo6eY0gPoUKzmtSP7U0giDz9iY4U8kmYy0MDTv9gHhM\nk24+vulGC9L+vpcHfA17zZCAvhkX4tovOp7D88ipEdAmJpKnRrBQu/1ehSUsRFy1sDmUEhZ5r6Rn\nC9jRRJO1Wx6ZYmMk9lmEJ/z75WcWzVc/9Vlru9YIsUgpQqSt/M//wV8M2c9tP7y7tPbBP2uAEBwc\n3mjDQu5/24+y9WUZpaCLgEze16eXVb79fJa3rWACOllXtq3IS5K7S/lDIgMCerIGHbHBoiKfofhc\nkbPlRHrEK8szpedMZpGRmICOjV5vTNl7Q9F6W3Lf2K3Mo/kQT5Qp7/YebN2+6hEvuJhy9yoz0/2/\nFpF/Hnz/n5ZSfv/y7y4UKRGuDdfv8ECy5WeI3l17E8jUvmkki6G17pGCM6dMXcHDAQuD9odHs2Ru\nvku9W8sz5ZEST5Z86AzoAyW1uzdVIrZ+jPnhwCxjhDjqtdYIsNX5cQmh9Q6Z6u9rVmrkWWtDhHMO\nvRszQ3Be1tW4+TB6kXGvrBs0I6CLiPzmNx/lx5+wXXlaa1i7CuNMeUOB3deMeA6W1ok3rPp5Hrxr\n7U9PlI/3ovLp5SR//N2biEhKQPf0g4yfJtJz0JCRMDps+FoaRutvu14/o5uvX4tR27Yu+3+GyNt6\nRcizdFwyK/xA+r5PIthtO3PfVynvyCVI3glPn4GRNvbObf/vecsYKlOllL8uIn/3C/TlXeRqAvo+\nGS5fHECmxm6+vm/99fVzt7IFKEQTbYjg+2MRFc3N13/vw7ytvE0Q0LdSIOLgo0rOJVpbjyQZAXdZ\nsCtAheaZShQ0zvXD8D3a4DN4f6QIMYGcKZZnKFjJfIG0PA6PGiEXp61fpF/IRxt8JtNuPqikHGwT\noN2M2M0Si85shOheVD69rPJHqkwlqRFmz2nr+2DG7CQtQeVaz8FebzCakWF9aZshU4BgbtfXLM+U\nClKmROo7z5Gp/H7s/3Falvo3en4oj+GZuMaRO44GPLAjt6Bhl4MSIwrBPcgtfpZ/Y1mW/2VZlr+2\nLMufeLce3Sgnt9BaQWgI4nFc876mzuZLLMBoZcdy10Tz0WMHZt18C4e5MwK6TR6IlMeAwG1FkmPR\n7l6QZSjCFJ++LHfz9cjNXmfJuH71s0g/bsIGDzZYm0j1KDKFeFcjN99Mnim7AXm3N4sK7NpySOnh\nNAXLTGoEcpzMwTbxkR34uSI0swAlpfYT55lCRs2nl3VfEzM3X0TQcuK9Xcugm2/gamP5tkYSlYok\naSdD5gfID53XZqFjGffrkWEYAIB1AmOuBf70ir79bYRQq3DOVDTsR2cOQqQdeF8yzlTmkr4XOapM\n/VUR+QdE5PdF5P8Ukf+EFVyW5V9bluVvLMvyN/7gD/6AFXs30WeNBiZKKKd/WQL6NUas3yCQ5Jyp\nXpnzId4ickU0X4yqoMc+APRI29J+hPtIkKnFLIIoUtArFI/u5mOJ5vJz9C5liHKNSKUiqnjOGAF+\ng+/RkmwR3cm1V64I62qVo0FZYCXb763YseGRKXZMha3HB0S8FzKFnyNGCK59lirwyA5i5PlxoGVZ\nJNYMUV2kP7MwzTPlx/+A06RkbBE8V8ZZyI+5+fSKLGknyiZvBY1Xq8wyo/nTy2n/P0Wm1mVPZmqF\nrdPNmIrKsY80teUYIhfdfHPpNfY6ieJl78GWj3mmclDiKdx8SEopf7uUci6lbCLyX4rIn0/K/hel\nlD9XSvlzP/vZz472c1pYenz9jkVF9D7l+TfGFpW+3b5v/fUS23dl5qP5kg3adZBtZKx8/Y5bBnbS\nIoQCcdPu2cqYkXUBEDZQfPzCp4lhqeKLovkY4mhcbLY6RPjP3HxHLb9F7AadI1P+OYzcfCosms8j\nXJ3yblCGt/OtylSfGgEdwVRK7M9hZAq4+Zh7y9MEavus7HhMqHz60BSAazKgj+b1y2rQUDhXljRC\n+ribr11f28ZIrfYLCXK5WWVWL/P1WsWUHaxtU0ZYGUXz+TMZ62+gXGd09W2goCNmgEDFiyjljFeK\nlPixm6+1f69ySJlaluVPmT//RRH5m+/TndulKQPxN7Qp6cvZt4Ny3Qtj7h4r2aYRlDkwyVEEBWwH\nWBOMQ8bQkTTnycbPOLMcFbQxe57LoyNTIjHSSwSTaiO/Kd8YkYsnKvj9ey2lj2bzix5yv9j+H7X8\n1qXNnZGr0C+uWXmrQH0gZ/O1DaJ+emVSRJPIHlfcTw4VPgNjy6NDt6dGYIlbQVnImcIo1rL4zZf3\n0W76KM9UFoAxdPMZdJoRl3l6loPRfAGhyZJ25soUy2fGzmDtnyVRpk74npkhjox41D9kyEHOFBxv\n+L37rWEr2I3Oj5NB6Nggmi/x7tyLzKRG+G9E5C+IyJ9cluV/E5H/UET+wrIsvy91Hf1bIvKv/xr7\neJVkBEZEet6zU5sjLq45THGUm6T+1peF19vcK8ByOMqZyojS9ve9LeA2UMkI6Pa5oxBhz3NBEP+j\nCQsp9rfVFjReRgRvjPp3PE6i/xsdJ+NdP3749Xyndt01si6IM4XLxjBtHSdoIW43HM7mc2gMIv5a\npPQWxT0m5Mwjq1aD1B1PjTB/nAyarxzFAm4+0sePAzSF5Vkbzet17ZVp6B4i/KF6zbF1AxOx+zLs\nnlrbl/4hI9EgU75/FuVDZH5tOztOJu4J2qd+bIo4N583YIACfV3GfWSY470ty8WHnj3iOascRc6/\npAyVqVLKvwK+/q9+DX15FxlF83kja4d/NVeOXEdAz5SPvd3MnQHQiBnLAbeDUK36GawDQFbMymv9\n/Gy+NmmRmy8icI+dAV2ELSxZtvL6N0aa+FhKk3YatKtHZuJCi9x8kQyO75WJRcBatBMuG1zaZKMQ\n6QnoHg1FQRu1XYAYbLdFjtYoqz41AjJ2bD9ujeZbwcZSmOIB1g+mrPtM16mbb4CmeMSj62dy3zZq\nDRkJWoYfdHyrm6+t80GpGEYSxvFqnwPLKD/in4lglFuER1yifQ6nRogGTHDzmXVgr2vj5+0hfhUq\ny57ntuGz+Y56d+5FHjdrIhEWXi6CkRvkMrjmhU25+ZLFFcHPIV3BFcgUX+jdZCE+8Sxp3kxqhHMH\nd7ey3jK8JVz9XgSGFAPIO/Kb8pxBEJVg41YRVbc5BAI6GhtLJKAfQabsBiXCofhrj5MRqS4m5lZr\nhzRf2gVl9Hijo5GjKDUCIvCKxPs6zpli4eeo7OU+N/+uY2Hk+uXK1An+v9WFuU3nwbP2bj7mHmI5\nh25N2tmv89Fo1TaQZMhUlmdqVpl6AwR0XV/4GYa2f2jd7X9D941oJAwBpAk+0V5CnidSiEdR8UeR\n8y8pT6dMtUU0/obOEEI+5WvcfDME9H1xJYPTloHo0poPtNbOfITKVvBi792O3TUJx8IiU4gz4i3D\nrK5HERSBUsAiNEu+Z+R/tOmgRdIWWRy6MSKg3+TmMy7yrI6I0HE0TNEolCXfu4xbu7aMHY/vR0BH\nCFHgTB1E+Wx92DWSGWPtO+Z28a7f7NBgqwD85CuS0BSgFKNjoqzblG3YGUrBNu6RBFQUIDSjpJ04\nGXG7hhkkVhm9OjUC2TvQOYLIaPdKL3LtwrP56BoFUKxCzuYzBnas29UL0oH4a+r90CLfuzydMqXQ\nIop+Q0S5xS2ERa5Dphjc7du1Za0EJaPgaL4pNx9QUBghfyMLKXI7qrxtGyWgt8XKWEgg6qXLMfPg\no49b5oPNlh73gRdztEHp5Vq0OCXcL3oseqkUb1WTmyXSufkAQmRlhuukogux50tpv0XaIo24V3Zj\nRGjSrAQCOnLz6X055PEoWZblmRodR6WSIZ+eM8UUk48TylRFNPrvGBm5v2YGmeLo0JHn6g0ajI5I\nV8YLOsnCjumNBB58+jARzUfumbkO2WHfWpcVq0QjJWl2HdO6ogGJDXNGW0BcOeQ+9G3Uvt6vNvXg\n21mULFcIjOa7fBYzya5Rfz2BHUm2aaxuY0CTfDqaj2j8ItHtyaz1lVgT9RrOPfEHy2q/fb1P5eYD\nPAcczVc/e2Qq1kezSkPX4dKVLU4J94seJrG3xQ7xjmZkWZYYzccyoAeErv/eim462VlmPr9Vf//1\nc3fzvRMylVMFmpJwC+oK80wR9xaL6mIJF2dSKIj0aMpPvvoAy9gcY6O2VeycYSgWQ2m0/iOvsq3z\nvJ5pN9+K1rVmkPhHOuvmgzxVQhGBnClGVl/6OQdzPJm2q3GF13qEGvKz+fp+7fcEAAMUJWiFRUre\nkzydMsWQGBGuEYtUC//IC9stQ+EjIQuV9hEPjPfECJlWsCsHK5fMzWfddah+ikx1i0r9rjtOxlnQ\no2MnHkFo1BU5R8/yk65Jcpel9NjrlH58eXSDufn29oDbY0YsAjYKX0ZkWNsPK19dIqDQePNzHHG1\nOrfzDYq7j7LagEtjX0PM8Ta3jG10pBNXkOqnV5KYm69zByaKyY8+WWWKI1PImMgU8nrWYTMqKPpB\nFZpjgSvIxRwoEQlf1H5vnxkySA65+YjBDM/6FMsNbt+x/HX+lAKkbNmWM86fz6mmfWRKsb2H1k/U\nx5F3R/t6v3vG8ylTSUQGG0j6W7Nw51/YHGdKJ0T8bd8Ud9dHHDAsoVtsB+cSEsF+a+x25Pfzdk4I\n6EZpyxadZ0KmFuDmwPymiKRc5ebLjACzSNoq49l8mIun1x5VANZuoe77Fso65A1Z+iqqTM0kjCyg\n3fdMjdApKlueGqH259iRJ7Y+ZPzkY8YrzqBehyQVoBiq/O5vfLX//6sPkYCubUM3X3Lv4TgZhkyR\nBRXxXmfEj5lbknYO80y5+//qww3IFPFqIJckHyO95wUZ3B7ZrH2K/USuO5S7qvYRBymwYJhsiztK\nQ/iS8nzKVDIhciLvbcjUHGeKL4b9phg3vexEbduOb4Jt0DQCQ880g8poslEatAAdn+Of062ukHuQ\nE3BzzBwnwyOz6qevE3Fg/GLqF0mEGKEFTK896j6xGz+KqkPt7Vwn4sIQEflakamJhJGZ8n7z2Xxu\nk0Nojo+YfRc3H3KNJMZPv7lxxasnLPOIw5/9+NOwn8zlkz1rS1pnKSvWxHhk9zbua/+OCnmemYsR\nKe12bs8gUzTP1EiZGriWRTjSaN87mude4WlEe6yYoXbZO6foPTBIZvZQvrp8//J0ylSWeA0TeRtq\n0Hgj8+3NJO3Un1C1yMr27Z8GkQ62HebKQZyp1NIFD/Bt2+Dm5u8DETXt2X1a/6MjU3ChgAT0+mkR\nmUyxntmgFD3tAhecMjHiJnlU9iix17oaUTuxvdau/d6KWvPIzeejrgqYt1bBGUWYZeIJ6BtQllFE\n7i051JCVThUkFNVFNtWIVnIF2p+HCPu5xsNp0fPx13RrAFFoUjffOxx0XA1D0PYSXay2bZH+OmvU\n0DxTFpm6MppPjehwILSbA9oHrkS3MshNXdz4sW10ZWG7WCnWfnsgoEh8Rv2xVFGaIkuLfO/ydMqU\njhM0MAtY5Bbz2yhPDhIWsWCFQbX2OxuZhIiRMwR0RATkKf1z3g50k2Zn8xllCUW1nNxzegY3H3Jz\n4HP03EI+IBOjOqNlWj/1LZXSu6ftAjo6WFlR2UPEXoOAZUk4bXvBzZchU8Bftro5jpBfe7zRUZ6N\nCCCgAyMkKsvH+Ge2vhnXiEiMbGztY1TBIwq3REchBGnEhbRrGXPzvRhelZejqJ9/Ryhpp8gFpaGK\nnNYVkalScH49kZ6A/vVH7DIdRvORExB6pHGcXwwpkZWjZtpUnhapC7cLbytwN+tzYpwpXEe9rvX1\nXmWYAf3RZFmWzsVhpbpg+u+sMoQs3JHMufn6tnD7VpmKlu8MMoUUJHpECYH4s1wr55KczWeRgH1z\ns/1odWj79zwxZoRFM4X3Z37TT0i8TQ6PpRnQd65dv6D1Cyg2EuzCyKzakVgUpSG7DJnqx+IGxomK\nHsGBAjv8nMHuF+3Te3Cm2t+Il4jcuLcYCug4lewcOxGXBoOgLh5JLSVu0lb+6r/6j8lrssN5ro3I\n2Eh6OS3y3Rtf60QEHrzb9/nYOK1tyv7JciONz+bD9TKj2aJRlDNFDGaE8tc+RCMZjU3tjz7Oyufr\n++DdfLsxnBjb9vVk490nNmZK0TRn6o7hn6dTpkQUMUDICrAqO/dU/f97E9BLsmnMTPIM9u7bwYO0\n1usWZ2rpXn537ZWBu8SSN/cFwJT1G+D5IFx/T4KjmVDknVciRvy5cZ143PS/twW0ftJzGDfdgI9Z\n/IEzNUCmfOZy1G5KQHcbyb7J2TKeXH9UmVp6ZOoMUKf35gMiJYUpEWj9QRumSDz/bITY/aV/5E/R\n32rbEcUZGUkVzar/pwT0BIm/hdun14twJDZz86HxamkULM+UzvV/+Hd/QvtHkSnCK9TnZpcKloQ1\nIlNxHYAEdLhf9WW03YxL61FTW89eDhimVjLe8b3IcypTK54QyGpSxWkrZbeCr5msi5lMTDLEK07y\n2H5GirQC3XzEdbQRxahNUo+O9PUh0X4iJM5yFlQxe/yz+Xo+jQiLvLv8p7MOcX0iUTGHyoAfN+E4\nmYgARXi/1XHUNWVRU+02W1h3Rf0KN9/XIJKMcaa6g7WNwjU64iQTv8kVoIAgZfmWQ7wRsj4KWrDr\nD1OMAwJxUIFWgXnWBkaSNQzZochZwM3xBKzgHU08IyujdS1DWv/7f+eflt/56Vfxh4uc1kU+v8Wb\n3pUpsqZ4F9oImYJBSk6Raa7FTHmfG0c+rc/+DIFhd9S7cy/ynMoUmRDIEtM/i1g3xTVtRQvBS1PS\n0OSN1jq0HCaj+Xg+org4s4knEjlnetgrI6CLNLIh4uj0G/el/D1jthMCuS1g4w4H4TL3BkEFkTLg\nX91WpINmfASPfof6db6gskeWqfoMtA+5MeIV9RkCOgrL9wYMuj/7zG8moJv3gaxwvwZkHJIZQcgU\nGzOcM4Xr7dM83MrtIvmwBsjUnmeKGFQs4Eb5Nrdxplo/ITKVuPmydU37JoKVkN/72Y/T/vHjZCLK\nX9ttxkIri59Nb1gxZKofF7YNK57Ir31kCrS/L6Zwjs7mG0UK34M89m5GhJ06nuUWyQiEmWR5rfZ2\nE63aWxhoITytmFCP2kEuQpGInJ3pxIuTtF7P70FlWTQqMlo2Ng9VS0Q3vKW7Fh8FI8JccvVzZBWv\nTtmwdQ5Do32dnZJz+SpxAY+isJjYZzAyRhARf1kwdK/h5EiZitwr1FZr42YCeufSGKMEt7Sn9UXj\nh3N8RDyHhY0vjyjcmsJBHB8Gk4v7/kqHTF3j5tuVlUPKVFR42fPkyFRc16xBMjImMuGpES6/E0Oo\nc/MRBbGLuAVlvCKj4z1LEhuSdiZuvt4F3b7v+iD5Hqq/3DMy9eDbGRYUZSKiG50vWz9LwYvyTFsi\nI2WKw78+6y5aCGej+dBEYakiMsus1tV/r8+TEdD12vOGT0+3CBxalB5REDcPuSHQQccMOai/999n\niKpFhWyJdVk6t2L9DrdXyvH8PYtR2sYZ0Ftfte+sTUVCbcJDlZiINo43W+ZWArrPMs2O5dHncGuU\nnM8ynUVJMncPLrsEZeoWorxXPFi2bisv6zoMQmEEdJZ6YEZQChqGvGTk99q+UaY6N1/8fVZGGdCD\na46+d6wAZQFOXnnPovkwR4+v5Z5XN6IcMBlFCt+DPKcyteLIAGQJdYPjwGRAsKcX7cvMBoo2Wp9B\nmwneyNtvVlgYLXU1nccKkGZqbyhWrLdDpu7YypgRxM1D+bP0r97FwJ/9jEvWW9pF/CLf6mEkVs+Z\nOrRJGWRqhBzEXD+8zV99PosI5kxp9e15xnYtwnqTMrUsu2Inks+xbqO+KQN6fE7aFy/M7cIUhT5n\n1m2EXs8ZzBCN/RrLmQLGrUg12K5JYDkjswbNiPwukqxridE8ktHZfNTNN4EQdS5/4J2xnCqR6zi+\n2ofMte+PY7L9R31EwtD1e5LnVKaWqAyIYM1d/9INReRYaoRM0Wn+XrTAtfZrWYBMqZU9QKeQgqSp\nIq496BgRS0VwhIe9tiJ8ccJYBG9m0X0EsRafSqawK3eOpaVA4c717zytgX7aIj1n6vJdYkgc3Vj9\nuV+1XlzWut60Xdbmn/mTPxIRkX/y934b1NMbF2je2jI3nc136snQOWeq9ecWQ+HkUBT2/mrbl7Id\nF4q4BN14vZ3b5ZER/T4zuNpaQt18K84zNVM/72uvdBbB4/QEDCSVTGm3NJEj736UZ4qmRnHKMePB\nZgYMRaZAXShJdRZMFKP5+nq6Pia84Ec46PhJCegEJibKhogm7WzXX9OWyACZ2svy6+3RH8FVZ1wW\n2Qtj0DXiAXCyIlam1Do/JUQnVWIhZ2ptzykjOD6SIDcfTup4uff9IFx+lIVIdLEigmccN/0C5XkS\n9Zq+jl0h2wp1DY2kdyFc6iU0Ue/Sztr8J37vt+V/+Hf/Gfn5b30D2nQb477JxbY0IOLoWPOpEQrY\nsIKb74b2RDCKUr8H/QPGD4/8i26+W/rpOYMsOWx3zbrI21mNCtz+y7rKLz+/he9n6ud9rZ+Zu0tk\nlLSTK+3bdtu6xgnol3YIT88rx6jpZbFzLvbPuzZzzlS/Ro1c+6fVo158LfoBmbpDoakRkAvGWPhH\nkCmLbDHJJllzR2g9GAKt9eR9YYvossSJWgnHsSzlWJFjDbpr1z41Qn+cTGt3hlvxCFItuv47mH4j\noEhsLPTl9jqB5dfGHY50sYst43LYhfHoxmqt3lGeKezm420iRaq22a63n+gsyOp2fr+DjlH6Ed+f\n6ua7TUnReuxnbvy075hRtTjrf3uHfvpzC0VGnCl7Nt91Bx2zyLbZvtY6ZP+kSTvJWo4ClPr9Q8Lv\ns5K5+TIj3LvQZlIjoGzqHcKV7letHts+eyfeS5StRckWeiht0ZeW51SmiHWRKSqlGF/xFW0tbuFD\n0rRq0NcA6ZfQgezwYSssbwuKbmTQLOVMXdrOCOjrpR3MLVCF0Jxhdc8zY0IQUfYMSLURSbkyz9TG\no/nsuOXEWLwQ2bHHFLyRWBfBaDOJ6MAxl0jLDaf16femzNJOQrjJzeeVKaAA+vQmSOG6RpiyiA2l\nvuzeRzi+5hCs6X46o3UGmbHPkyF47DiZW9AJb/QeSdqZufnsPFsO7KqZmy9DiOwlLEJ7WfqxND6b\nr/Vp1G5WVkRCNn82ln9Apu5U7MnkVrC7pH4WKUPIEglDE6zoLzOH2yKrElkhSNiGiHgAG1G8ds6U\nV6ZmCOgX5UKv7c5K69x8l+/ueGLMCLKmKgriyl3+nnEx6O9W0KnsCFHtldf4O0uNoGHdx17HPDLl\nxzrL2Dxs0T1PhtwocnLL0UUeqcB54OrnNni/sxLchgARCWUdQsHK2qF1ez9jiLzIgIBu1maGoL2c\ncjL2EQXQG71srZxx83XzzIzFDEEcCSO+00AhNwe0f9BgX/rTEDD90BrlAAAgAElEQVT5u/2duVP3\ndWdrY91+78Ub8tlalO1uIz7mPchTKlPIrSXCOFP1cytW6Zlvy0PySGaOk+lg2IBMaZlcmWLW1rJE\nRSxbcOvv/fezyNR5w9ZK5+bb4fr0du5ePIQtMsqyr2UYQZgostA93cYEQj4t72Z0zMWtyRDb4bG4\nHXHfq0u7EIV+3GacMyIS3RcXReiWo4t8aoTsaJ9+Dh9f9fVSHVslyfGGztJk73J1+eqqknm4m8HN\n15Abfo0ll/NovpUgU2Nljfe1fvYGDe4fj+arn707OSJTR54pVSCHyFSv6LPDibfkvj0qxCLuULtZ\npKmWnwlSGCFTR3JAfml58O0Miye9qSA0xm8oIte9sJmknVm9M1btLDJFD0NdY3JJftDxpa7gvqor\nerb5aVLA1M1nkKt7nhgzggIdMAG9fqrfvy56uD4R4OZjKOJSFRitFy3yJVnkT24jOPI6PB8DtbOX\nBVFqRxW4vh5s7Z4ufbvl6CKfGgHxjNB93Zq/SSRGK2LuTN+2/p/xbN6VgO7dfLtSOzK4LsoUGdej\nBJZHXD02I36WXBTNaRVEnu4R4FbH1f0jyBSiDdg2RpGmWjZD5ELSzgRhbGO9L0sNqNUfFI7HskfH\nvMwkjf6+5SmVKYQYiOBFFfq8r2gLhYp6yTkPvaJUBECglwtHnClGKF0BUocObNWyts97+RkC+mVB\naInmgAW3zbkDHkGQmw8T0HslaeTmi4os47fVhb/sm4z9rbXFLHpb5jAytfZKRO1HjkyN0IFhm+55\n7ohyKCd75Ngtx8noBlzbxBmkRUzI/82cqTheRPA9oPVn1s139J23+vp2Z/LHvazN7cOOk6mcqRht\ncwvy48d6/e46ZQopDh0CPHB5ZZIdJwMVY2DE8/Xfc6bi70fP5tuVHPJS/NFAnICee15uebZfSp5T\nmQLEYBE82PSvUsqvLTXCvskANc2Gwzd3iytjFBEmWR4Odb91fQLuCi2rv1u5hg+hj96WtblznibP\nFDjmByvs9bOYBQgrU4ssYFFhi2SFxnMCek1V0er37Wl/jiJT3UHHgwUPkVeP5bbS6/t2wwK9LvL5\nXJN/Zu7pTHyOt8wg6xSuG8Z2RN7q3zOcSxGheaaC8lMwUX1WPDeVHcrbXWOUhjSaz58gLmOXUiaz\nSs+Mm687TsYiwDcg7uyeaT5AN+ZEFBWPdY94alHJ5s8ZjfValtyXR0M3/OyzzPMixyg4X1qeU5ki\n7pf6WywrUl/W1rSeK9qqn2nSTuGTF1lMXumaiebLIObTijZov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c6tP1bOE1FRelgndPMZ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C9f4AZL8yugjYQsddqODEwvEqUvlgbJ+Z6xGhYKh8SRwHOu88Z4rnFt2TxNA0l2DTKsxySHps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\nN9845SPSWFvP50GFWHTo5rvokny+r6LNMh7kYpJQhm6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L+1n9kdBwTAD9YbPkluWsQvzz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\nFEAwBQAAUADBFAAAQAEEUwAAAAX8P1B2U1AiUyRSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118141e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.polynomial import Polynomial as P\n",
    "\n",
    "plt.subplots(figsize=(10, 10))\n",
    "\n",
    "p = P(interpolator_2.coeffs)\n",
    "roots = p.roots()\n",
    "print 1 / np.absolute(interpolator_2.coeffs[-1])\n",
    "\n",
    "ts = np.linspace(0.0, 1.0, 1000)\n",
    "zs = np.exp(2 * np.pi * 1j * ts)\n",
    "magnitudes = np.array([np.prod(np.absolute(roots - z)) for z in zs])\n",
    "plt.plot(ts, magnitudes)\n",
    "\n",
    "# plt.scatter(np.real(roots), np.imag(roots))\n",
    "# xs = np.linspace(0, 2 * np.pi, 1000)\n",
    "# plt.plot(np.cos(xs), np.sin(xs), color='red')\n",
    "# plt.gca().set_aspect(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.015\n",
      "0.0150675087206\n"
     ]
    }
   ],
   "source": [
    "print min_separation\n",
    "print min(\n",
    "            np.min(support[1:] - support[:-1]),\n",
    "            support[0] - support[-1] + 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 40\n",
    "m = 20\n",
    "fc = 50\n",
    "min_separation = 0.54 / fc\n",
    "\n",
    "kernel = trig_poly.TrigPoly.dirichlet(fc)\n",
    "\n",
    "support = test_data.jittered_supports(N, min_separation=min_separation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Tbb97WOA9lhGU9mur/tyssUSB91W5WeNUX7ss8F5EfhC8b2aXS4/P3f08dnBIhty4+3NJ\nryWNNJ8K3w2HHIb2RowEAZSVHwRfuftxxvGX+tM5wgeSnoa2RR8jSRcNr5PEOUEAhXWdGDGzE0nH\n4afc/UrSp+HxS3e/Cm2LTPJk8bgJI0EAeyVMe5+vtK1Nl1NT6GUEQQBl9fyKEYIggHL24LK5vCBo\nkn2w/pKcjPFSV406yxpLxQu8J4t6D6DAeyo7S4H39+VmjaWebtVfwqCCIADkIggCqJVpaNNhAMhF\nEARQrcElRgAg17CCoDVmY6OZ3l1mjaXiu1SnsnUUeH9frQXekysIYu27zBqXMKwgCAB5mA4DqBtB\nEEC1/ryNUm8FQRBAUUyHAdSNIAigZpa6gLoHsoKgmckalp3EAn1ye/3M5TMUeG/f1xCWzkjDKPCe\n+rPoZYH3rnFOEEDNTNvthHSbCIIAymIkCKBmZIcB1I0gCKBqgwuCDRnUpoyxlP7uXW26sNMC7zvM\nGkvlt+pPZ0Ip8L5s8AXet8VWWgCqRxAEUDNGggDqRhAEUDNGggDqNcjL5g4a8k2z5rxVLGss5V9v\n3MsC76kC1hR4b2XoBd53mTWWtrveuHODC4IA0NI+1B2+1f8QAFTIM28tmNnRyuMTMxub2eNUWxOC\nIICizD3rtrE/s7GkZ0uPjyTJ3S8kTczsqKkt1h9BEEA5uaPAFiPBENiul5oeSZqE+9eSxpG2RpwT\nBFDULZwTPJR0s/T4XqStUTdBsCljLEWzxlL+9cZ7lTWWBlHgfZdZY2koBd7j37uPBd6LyA+C983s\ncunxubufd/eB3sdIEEBRW4wEX7n7ccbxE0l3w/1DSa/D/aa2NQRBAGWVnw5/KWkRNEeSLsL9prY1\nJEYAlBO20sq5bWJmJ5KOw0+5+1VoH0uauPtVU1usP0aCAMrqeCTo7s8lPV9pWztn2PY8IkEQQDH7\ncMUIQRBAWS0WQO9SfhBsWvYSWyITa4/1o+6WzkjlC7wnl5Ds0Vb9uUtnJAq8t/1Maf0r8K4CK2cY\nCQKo1yC30gKADJba66sHCIIAymIkCKBmnBMEUC/XwLLD7tJ02v74VHY4c9OFPhZ4j2WNU68ZQtY4\n1RcF3tt9prTdbdVPdhgAukYQBFArrhgBUDd32azfUZAgCKCsfsdAgiCAsgY1HXZJPl3PGW6zDXv2\n9cY9LPCevG55AAXeU1uw79NW/bss8J7KTPexwPt7VTm64JKYDgOoWr9jIEEQQFmDmg4DQLZBXTEC\nAJkYCQKo1+D2E3SXZ1w7vMussUSB97Zys8YSBd5X5WaNU++xywLvXZtfMdLvKMhIEEBZbKoKoGaM\nBAHUa3DnBAEgi7NEBkDdhrdEZraeHd7mO2ZnBXtY23inWWOp+C7VsayxRG3jVblZ49Rr+rpL9dYY\nCQKollNyE0Dtej4SzK/iAwA5PPO2gZmdhZ+nS20nZjY2s8e5H48gCKAoc8+6tXBqZi8lXUuSmR1J\nkrtfSJosHrdFEARQlnvebbPP3P1BCHqS9EjSJNy/ljTO+XgEQQDluOZLA3Jum41Wpr6Hen9P7Hs5\nHzE/MXLQkFxvWDYj7XjpTOq5wktnJAq8r6q1wHtqA4U+Fnjvmqn1FHfZfTO7XHp87u7niwfu/kSS\nzOyhmWWN+pqQHQZQVn4QfOXux01PhGTIjbs/l/Ra0kjzqfDdcMhhaG+NIAigrG6XyFwqJEQkPZD0\nNLQtguZI0kXD66IIggDKWZwT7Ko79yszOzWzG0kv3f1KkszsOEyNJ4u2tgiCAIrqeiut5fODqba2\nCIIAyur5FSN5QdCsMYMa/YqRrHHyNbG3zjxeUvEC76nvMIgC7zvMGkv7tVV/btZY6muB966xlRaA\nmrkIggAqxy4yAGpGjREAdSMIAqiWS5oNKAiaJMvIGCa/ekfXG/cxayzt2Vb9uVljiQLvLaWys/tV\n4H1bZIcB1C4yiOgLgiCAcoY2HQaAPC45I0EANeOcIIBqDW46bNaYQd0m+5Z7vXEvC7wnTvgOosB7\nIvtNgfdVwyjwXgQjQQBVIwgCqBfrBAHUzMU6QQCVYyQIoGoEQQD18oEtkYmJLCGpdumMNIgC78nf\n0x5t1b/bAu+7WzojbbHpwtP0Z8vmknPFCICqVTESBIAYzgkCqJY7S2QAVI6RIICaedUjwUT2NDf7\n1ssC76ns8AAKvMeyxqnX7FPWWCq/VX9iCwr1scB7+vNug8vmANRscFtpAUAu1gkCqJVLckaCAKrl\n1BgBULm+jwTNMzI3ZvZ7Sb8r93EA7NjfuPtPu+rMzP5d0v3Ml71y91929Rk2yQqCADA0+Yu0AGBA\nCIIAqkYQBFA1giCAqhEEAVSNIAigagRBAFUjCAKoGkEQQNX+H8tFnNXPDiGaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120f353d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import rc\n",
    "\n",
    "rc('text', usetex=True)\n",
    "rc('text.latex', preamble='\\\\usepackage{bm}')\n",
    "\n",
    "plt.imshow(np.absolute(kernel.derivative().inners_of_shifts(support)))\n",
    "plt.colorbar()\n",
    "plt.gca().set_title('$\\\\bm G(K^\\\\prime, K^\\\\prime, T)$')\n",
    "\n",
    "plt.gca().set_xticks([])\n",
    "plt.gca().set_yticks([])\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.savefig('./img/kernel-derivative-gram.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cuaXiC6hmZTfDILmT+kl6m9n3VI1vwnQGIhVSJ+Vk7LlvbOQqmGIuptdH4lHu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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1165485d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_util.plot_trig_poly_magnitude(interpolator_3, points=1000)\n",
    "plt_util.plot_support_magnitude_lines(support)\n",
    "plt_util.plot_magnitude_bounds()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'status': False, 'max_deviation': 4.7203185361632732e-14, 'values_achieved': True, 'bound_achieved': False}\n"
     ]
    }
   ],
   "source": [
    "print dual_certificates.validate(support, sign_pattern, interpolator_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Phase Transition: Real vs. Complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'test_data' from 'test_data.pyc'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reload(phase_transition)\n",
    "reload(dual_certificates)\n",
    "reload(test_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fc = 50\n",
    "sizes = range(1, 41)\n",
    "separation_ratios = np.linspace(0.05, 1.0, 40)\n",
    "separations = separation_ratios / fc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0\n",
      "0 1\n",
      "0 2\n",
      "0 3\n",
      "0 4\n",
      "0 5\n",
      "0 6\n",
      "0 7\n",
      "0 8\n",
      "0 9\n",
      "0 10\n",
      "0 11\n",
      "0 12\n",
      "0 13\n",
      "0 14\n",
      "0 15\n",
      "0 16\n",
      "0 17\n",
      "0 18\n",
      "0 19\n",
      "0 20\n",
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    }
   ],
   "source": [
    "probs_complex = phase_transition.grid_probabilities(\n",
    "    test_data.jittered_supports,\n",
    "    test_data.uniform_sign_pattern_1d,\n",
    "    trig_poly.TrigPoly.dirichlet(fc),\n",
    "    dual_certificates.interpolate_with_derivative,\n",
    "    sizes,\n",
    "    separations,\n",
    "    num_experiments=10,\n",
    "    verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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    }
   ],
   "source": [
    "probs_real = phase_transition.grid_probabilities(\n",
    "    test_data.jittered_supports,\n",
    "    test_data.uniform_sign_pattern_1d_real,\n",
    "    trig_poly.TrigPoly.dirichlet(fc),\n",
    "    dual_certificates.interpolate_with_derivative,\n",
    "    sizes,\n",
    "    separations,\n",
    "    num_experiments=10,\n",
    "    verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAAoIAC9/Ccc/exxewrLM89tphJxLzLbl/Ou8FIZLxJGdE0AAAAACC/Em+1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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fdd4ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import rc\n",
    "\n",
    "rc('text', usetex=True)\n",
    "\n",
    "imshow_kwargs = {\n",
    "    'cmap': 'Greys_r', \n",
    "    'extent': [separation_ratios[0], separation_ratios[-1], sizes[0], sizes[-1]], \n",
    "    'aspect': 'auto'}\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
    "\n",
    "axes[0].imshow(np.flip(probs_real, axis=0), **imshow_kwargs)\n",
    "axes[0].set_title('Real Amplitudes')\n",
    "axes[0].set_ylabel('Number of Support Points')\n",
    "axes[0].set_xlabel('$\\\\Delta_{\\\\min} / \\\\lambda_c$')\n",
    "\n",
    "axes[1].imshow(np.flip(probs_complex, axis=0), **imshow_kwargs)\n",
    "axes[1].set_title('Complex Amplitudes')\n",
    "axes[1].set_yticklabels([])\n",
    "axes[1].set_xlabel('$\\\\Delta_{\\\\min} / \\\\lambda_c$')\n",
    "\n",
    "im = axes[2].imshow(np.flip(probs_complex - probs_real, axis=0), **imshow_kwargs)\n",
    "axes[2].set_title('Difference')\n",
    "axes[2].set_yticklabels([])\n",
    "axes[2].set_xlabel('$\\\\Delta_{\\\\min} / \\\\lambda_c$')\n",
    "\n",
    "cbar_ax = fig.add_axes([0.82, 0.15, 0.01, 0.75])\n",
    "fig.colorbar(im, cax=cbar_ax)\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "fig.subplots_adjust(right=0.8)\n",
    "\n",
    "plt.savefig('./img/real-vs-complex.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Timing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%load_ext line_profiler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "reload(dual_certificates)\n",
    "reload(trig_poly)\n",
    "fc = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0\n"
     ]
    }
   ],
   "source": [
    "%lprun -f dual_certificates.interpolate_with_derivative phase_transition.grid_probabilities(test_data.uniform_supports, test_data.uniform_sign_pattern_1d, trig_poly.TrigPoly.dirichlet(fc), dual_certificates.interpolate_with_derivative,[20],[0.5 / float(fc)],num_experiments=10,verbose=True)"
   ]
  }
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