covarianceMatrix.ipynb

This notebook shows basic functionalities of the CovarianceMatrix and TaperedCovarianceMatrix classes

To see the notebook, click here: notebook

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import Python modules for scientific computing and plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:13.368246Z",
     "start_time": "2020-03-12T16:03:12.737089Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import os\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import the CosmoBolognaLib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:13.994937Z",
     "start_time": "2020-03-12T16:03:13.817352Z"
    }
   },
   "outputs": [],
   "source": [
    "import CosmoBolognaLib as cbl\n",
    "from CosmoBolognaLib import Data1DPtrVector as dv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Construct the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "in this example case, the dataset consists of the first three even multipole moments of the two-point correlation function, as predicted in the Planck18 cosmology"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:16.044668Z",
     "start_time": "2020-03-12T16:03:14.915672Z"
    }
   },
   "outputs": [],
   "source": [
    "cosmology = cbl.Cosmology(cbl.CosmologicalModel__Planck18_)\n",
    "redshift  = 1.\n",
    "bias = 1.5\n",
    "nObjects = 1.e7\n",
    "Area = 15000\n",
    "Volume = cosmology.Volume(0.9, 1.1, Area)\n",
    "\n",
    "rMin = 40.\n",
    "rMax = 150.\n",
    "nBins = 20\n",
    "binType = cbl.BinType__linear_\n",
    "methodPk = \"CAMB\"\n",
    "sigma_NL = 0.\n",
    "\n",
    "xi_multipoles = cbl.generate_mock_2PCF_multipoles(cosmology, bias, nObjects, Volume, redshift,\\\n",
    "                                                   rMin, rMax, nBins, binType, methodPk, sigma_NL, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Extract correlated mock measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:17.542604Z",
     "start_time": "2020-03-12T16:03:17.518639Z"
    }
   },
   "outputs": [],
   "source": [
    "nExtractions = 200\n",
    "seed = 666\n",
    "corr_data = np.array(cbl.generate_correlated_data (nExtractions, xi_multipoles.data(), xi_multipoles.covariance(), seed))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Convert to a dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "covariance_measured = np.cov(corr_data.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Construct the ${exact}$ covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:18.084074Z",
     "start_time": "2020-03-12T16:03:18.076789Z"
    }
   },
   "outputs": [],
   "source": [
    "covmat = cbl.CovarianceMatrix(xi_multipoles.covariance())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Construct the $measured$ covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:18.547760Z",
     "start_time": "2020-03-12T16:03:18.542000Z"
    }
   },
   "outputs": [],
   "source": [
    "covmat_measured = cbl.CovarianceMatrix(covariance_measured, nExtractions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Construct the $tapered$ covariance matrix, given the $measured$ one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:19.938399Z",
     "start_time": "2020-03-12T16:03:19.932589Z"
    }
   },
   "outputs": [],
   "source": [
    "tapering_factor = 60\n",
    "covmat_tapered = cbl.TaperedCovarianceMatrix(tapering_factor, covmat_measured)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the correlation matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-03-12T16:03:21.193100Z",
     "start_time": "2020-03-12T16:03:20.484909Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f9f740ab780>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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txHMtfXwzd2hGRqsIY41Hnc7PvQ/WdHD/HQzsjb29Y8u5pthG0ZulquNtuBHBcp4+O4A1G6yDKjgMuBn+WL81Wm+OC+F07MH9U9KX5Q7HN9qky+d+vqn0WVfC+q/xh7bIM8l5TVhzm/nasv6vYv1h4dlW0jE2Mu9U6Nzmkk54v6c2PwJs5K6ZkZE1ZpEGraSJ5c8ivf7TQ7IpIs3riLShPLN1Seo570zF0b0fWuFQzCxqwOnezjybNuv1+T5tgU1RaIGxAKQx21/2fbZGIYQQQgghhBAxejkTQgghhBBCiBaglzMhhBBCCCGEaAEHqznLS/jU9mV7D/YxY43ZDaRBe6XToAGRDm1ECbysQctUXssnTHnI3kMFTUbiOtkLi8usGXPLWbM2n/cQAIxYjxV5azhdkn1vZ38ap0Vg3d0M+chhXjTr2gJfNKfJKOVZR8nXM3ilmdXZBy3QpJXqc82ueDmtwNo61rfM64uG0DIuXP+oszFaxu0bL7victaYsT72q5e9Bq0icdNJMhM81bnZlPukb32yb8vDLbonB+TfVYhNrEtjn5/MOjjuv3yf04WvSI8xiy8R6z56ge+jF3BRGzNrQjhWNZcBjOfMa1iHdXElzybTxIrX5zYWfPEGfC0CT7BIa8d6HdbRsadj4bT4699cjuJfGFhKsYlXCTw4j6MUZmO0jI82xKdIg/bVeNptU9OZWibzvZMdG6+G1GGe6ZMGjeNTn+9j1wQk9mGkshumcB2B5psJPUQL63gfMieepzbM93B0voulY4jGa5HH4Qy7mJt5xwDhoGK3DTme6JczIYQQQgghhGgBejkTQgghhBBCiBaglzMhhBBCCCGEaAEHqjnbHnVx7+bzvljuuoR2qx9jjRlr0ErrcB3sezZk37Ng+cZoheorCbxYJETLaRuX/8veGzN4v9gK/UecJ+2a7cyDmtdnq6DapqMDToPm2+Q0ZC5Xm1bfowatRKK1Qp+UOTVofB5CDQa81oP34ZezFoUqdALD5voBn9LujntOTdpRY3vUxd3rl2NTyRdoGtaYsQYNAF6zvNpYR58u3DOnbB0bO9aYanXbBooB6WFL15V1SnxY7NflPHxYn8WWYYPm7UttGp6g/rtM2zjPMT4G0rZQG+udQIM28JHC6bNY38U+kRwvWUfM/m/sc1bwFMuBzo095UKxVXAPu2tTGg2w3JXjW6AB8rGn+byVfPFY35f6vAItn27DMdGxbA27+PTF519xOccr1pixBm28jY1hQ9bnU/n8jo1Pmzv2Ym1uN3vCsq8eUPAm5Xudrr3XZdrlTuI44vuOV/BtYt2b94psvvHcPRHpMn0TPPM+cPfBOy3c5XEbFBwy+uVMCCGEEEIIIVqAXs6EEEIIIYQQogXo5UwIIYQQQgghWoBezoQQQgghhBCiBRzohCC9YQdn16+7vHOnzmSaJwgBYqPqUbZ1ONErqaJ5wo8Ric83C6rHEc3okahOPylE84QNTuTKItnIGBQomEpTnTzDx/KcRtdUdhMJFET3CI7buyfPx26MFmcxy25iFtNds7/CPBPhxCjBhB5+OU0swJNClIw3g8kCoglDjjq9YY3H1q/+YrkKeg8bTJcm/+BJQl61dMGU++R8vDa0kw8NaAaIAcWidZw05bzkFfc8qQQ7ltfbdjGL39OWq7IRniiIxfUAMBrxpBDN5zqaNCI0ng0MW8f7iA1z7T4pXrrZN3gHQRkFk2g+dxwn6DkQTcYSGUKXzqObjIMniHGTIzS3gctu8oXStQmuH/cHc9sckzjVH9Z4bP2qL5Yrupg8IQgbTPPkH4CPT69espOI8GRpF686Ycocj84ObXkHNp5VWz4+ZTcBjL1g9Q6tX/FyniSsGb5nZnl+e1Pq5jbx8zeYW2oxNM/bNPdkHbOMi3g4FxJNUiKTaoN+ORNCCCGEEEKIFqCXMyGEEEIIIYRoAXo5E0IIIYQQQogWcKCas8GowlMbl80QK0psZf2X52H3SWRU/cqlNdriC437dJozKp8r5L1usVbAJcFzkjJv0KwJqihnmfVcTh82C5y370yo92ZSzXnYgDeDxYhzs4PzxPByNnotaauaa4wJTvW8GjSgpEkM3Lgj/Qql9lesjym10ZmB0i6a8u6PQS74cFThwuZlTQXHJi6frNiF3cMaMzaCfV16xpS75GB+hgRhKx0rKnqge4Mpr16yGjQAGKxQiE+2zHrEDvcDJyyg80Im1J1Nu3y4XNDoOi1VYIRNZafhCDSb3ri2YEId3IOJdSVklM1alkhn4sy9AXccXo9FzyYy7x5az/JYc8bnjfRlAFD36DzQcQ6Xmp9ljkjbOoN+ms24nwuas+Gowura7PFpmS4ma+0BrzG7leLTUnqKyvbinyZB2Ept9/ng0nWmvH7JatYAoL9pO3mmhxdrQVmDxqbVLj5Rf+X+PGLDexRMpwOtp9NhRibUwRwDRdxYh5bz+GxOvWloaL8bjsm9d1jolzMhhBBCCCGEaAF6ORNCCCGEEEKIFqCXMyGEEEIIIYRoAQeqORuOKlzaWLnicqf3CjzJxp+RFxppzNjLA7R8iIeu2J5SG3LBMOJJ8vvYHnG7yQeN1mfPHKfzoJx6l3ddSBB2vjuhAQhtT7nYQ0qUZp2b8x/pFZKWA280b/QTa8j2yrz+H4xrU6CpmAl33POdl9AXzdvNILMuzeXN88Wb2r+v7sgxGiVsbV4W8TxDyxOd5FOdm025Xzip7GPGGjOOTd4r7awpsbfRidreQJ9fut614ak1u49NWN1HrugR4Ppr833u9Vy0dUHHxDqQzF5aVGatqvNQjDRJHW6zbxN370gHmvrN8dBXSG3oxUITF4NJUzYkzZnrgtwk2iWvX4oLfC4rF1uatchcdvowKpfiZUWf1UEfMxrtY6CHBYA8SuhvXu4AF4Kge7JjNbE8jgG8jxlrzLwPmo1frGPrkhhriTRoX1i61rXh/EW7j36mTl1xBwyefaw7d7p2NC4ff9Y8doo0Y4fjaxZoPyOvx93cJ5H+fh+81Z5L6JczIYQQQgghhGgBejkTQgghhBBCiBaglzMhhBBCCCGEaAEHqjnLo4Te5uUk84uUYzp0Wi3KuS8ksXr/Dutjxhozn0d9iba3GjSuv9QGbudTsH4hrEFzFjeU+80+GiFFeRdpIqIE4UArwPoHdxpYjFDyXgv2wVoUp1dx/l+0/gw5y4vOa47yqp19SEHXEcIaMz4Pbidz+qIB/msa5/XS4L12HHLFhwnDtcuxaWNoz+FgYE9If2jLz5wibSuAtaHV17KPGWvMIg0a+wzV7OlTuBDd2m7z8NBe6B0+TrrwadDclwZ98jnbjj3FEu0zUV+LNBtO78raKfZYdHow3yaOPaxzS6xziwg0HSUfSNZbOd+ySCMWxNdo+Yj2BwCjQXCuo2sX6HGc/rBwmp02mesMNEHHgmFCWr98snskOHya7ush6drP7/j4dPEqqz/l+MIas3l9Gmu62J3CjV2TiSvr93lM6MZKQXzi/uu8VktjJ9Zm7lGfxdu7Q9qFT63r45H2fd5dlGwYm7xOD4LS/o7jvT5Bv5wJIYQQQgghRAvQy5kQQgghhBBCtAC9nAkhhBBCCCFECzhQzRlGALYv5033KWl1jfKN2VOMfTkA733GZfYxY43ZDaEG7azbZwRr0J6mvNgd2Hxxzqt2qbVU3yw59T4FOdCgze2DZstD53dT8F5jLzTOYSZtAcsy2J+I9Szem8s14cCZKS+bdRzRcQfH6XzznA9aQe8yr1fatMawBed5z4wS6vXLBzkaWAOm7R17kZ7s2/LGjhfsDMgk6ky9TWucNaVIg8b62R55PM7C2g5pVfr2Rh6SRmPUZc1GswaJ9UClb/9YUzuvT5DTcHAbIg1aof/X7KVGGtt6xzbKtZHvl0APxl6X43Y2bzPv+pFGxHtEFfYRaMq8rx3FHlcj+4bapaPCiCTsH3zcu9H1tpw0Ajobly8o36dDui+f6duLv7lDhnIABtQHT5OBKuvt5/Vp7MPGp9L4jdmkOLrao/Fd3x7HiD1fh83xKfH6hWeXk3TPq20PPMUiC9FilUG82au3mosNe6tuV5W4MetxGFfsAf1yJoQQQgghhBAtQC9nQgghhBBCCNECwpezlNLPpJTOpZQ+PfXZdSmlD6WU7pv8f+3+NlMIITyKT0KINqLYJITYLbNozt4N4J8D+Nmpz94O4MM55x9LKb19Uv6hsKZRQrV1+X0wk9ZqQHmza9n6cMziMcZlz+I1aJHujVNnn6Y29tjvjQVdc3pa7Io563RWWqzzWC75+JBGjPw96sCXx+k2WLvC5ZJpzl7zmPd6rktN4uNiTY27S0kHxMZ5UT568bzM6Y3Wnnzwd2MB8SkNge7alKaDbspMAsnhli2vbvtQypqOlY4VVVZ0YdhnKPJo/OrAB63E2sBqzrZ6VsNxibR1oyWKZT2Kt8ETZBYdE5fJHg4V6Wv4vuY2cH9nX6HSPTzq8D1Fy+n6V6ytivRbFOvS0ItEIp8zr/udQTTWAHcX1rYCQNXjdei+oDaH/ku8ONDJAV5TWHM353g3tfyQdSvvxoLGTuP4dPlk1Tt0H26RBo3i0+a2F+KdJW+0ldp2gC51kHl9Gl+3bDVqK4kN6zzrFJ92SBO7RRq0IcVd7q8uPgVa6tJnXIe7zVyAme8eiWxKAXjd2h69/iIPxJme7+EYsXmF4vhMfJHwl7Oc8+8COE8fvxnAeyZ/vwfAdyy2WUIIEaP4JIRoI4pNQojdslvN2c0558cnfz8B4OYFtUcIIfaK4pMQoo0oNgkhQvY8IUjOOaPhR9CU0ttSSneklO4YbmzsdXdCCDEzTfHJxKZNxSYhxMExz9hpoPgkxHOK3fqcPZlSuiXn/HhK6RYA5660Ys75XQDeBQArt96Wp3OlR6wNGNq86CF5VmyMSIwAYDRivRflYlNiLHt3sIYs0qC9ymnQAODBwmdXbhPzVD5tyuz/5ox7nPjA1xmlEEe+Z05DEe1gBq+ZUZAYzX5EnKvNmjTng8aNHhbO+7xpzgsx/JivPnetFq1BK50DMneJvNGm08Vb6EcyU3yajk0nnndb7mxeXsZ+XnzOq4G9KINCX1vHSVN+oHuDKZ+orQajpgvFPmasMePY9ErSqAHe5/Hi0Op41/tW49Ef2Bt3a8ceA+u/qt78N0jk2cPMoktq3qEtlnRyrI8Y0f0wouBT95tjMHswMnweZ8Fp9eg8VP3m5bvy/4quDQfhYAMnpw4ebbPgfdBa7cG4q7HTiefdljtbl5cNWS9I9yHHL/b/AoAd2PHUg0vXmfISadBqOtHsY8YaM9aglcZOw2zHThyfNvpWePkwx90ea0G5vA8GXjNoWBdaPwC2ReQxAftLsiZtEW1gIk1ZNAjl7VmDFvkyHnd2+8vZBwC8ZfL3WwD8+mKaI4QQe0bxSQjRRhSbhBAhs0yl/4sA/hDAl6aUHkkpvRXAjwF4U0rpPgD/9aQshBAHiuKTEKKNKDYJIXZLmNaYc/7uKyz65gW3RQgh5kLxSQjRRhSbhBC7Zbeas92RbW60yxUfct5/7GG2SZ+dC7QyJa80y1lT4jxpzqMurTPMZ6nc/AMlH9cztLyfl+mTA7hsge9Z7Ovjq3R+IYHGzBuCNK+fyafHySEQa0FaQSApnFuDRjU4zU/pM5cvvjdPpSPBtI6ONR1OUxT0XQB5yQpqVi9Z/dbnl663+wgEMuxjxhqzWWJT/9T9tkwmUjtD25ke6tnygHyI0oDFEFQsWK8576xAd7RXjZrzCCoEBqfnQhBrnMcY7ZK92eg8DK293HgdroO91lhjy7oiin8cJ1yfpnK949vEvmbOC43iQvhccPowrs+3obNty/X27L6OpVh3JKGpQ/g6OMso7ksFvWG1ZT9cv2T1Xl9Ysv7YHTqZPK5hH7NZxk7slbad7zVl9orcGdh49JiLT1ajFmk7S/2DtZtRftlexxSzaGqdvivSZ0VysOi+OIDH+9w+Z0dg6LZI9jxboxBCCCGEEEKIvaOXMyGEEEIIIYRoAXo5E0IIIYQQQogWoJczIYQQQgghhGgBhzAhyFSRjRGdES4v9++SI3K13CLR4JOBSbWvj/dhTRJLRoosdGWz2MikmuFJTM67Ns9/2SJTaWdK7QwCafvY5TqERfgsePcTgNid1M7UOm6DE7RHRCLUg5gXY58nCAFiYb6bm2VazHsMhLppBEybUEdmuW5yG3ZIBzDq2s8GK3ajp9Zs3OjWhdkzGmCD6dli03lT3iYT2EsDMoHtWYH9ub7tbP1RswC/JDznyTR4G2dMzLGHJ+/gcx/EuqIJtZusiFZYobJT8dsiTyrgJnAoTNDgJk8J7kk3sUoQ29xyqt9NtAE/SQhPfsAT4zCjyGSadlnzZAwAanqod/kh38QxiE3AOP7WO5cPhvs899cUTL4FAJkmpelv2o3OX7Sxo67mm12FDaZ58g/Ax6fXLVtP7v4Z2yaOT5s9exAXBhyf7PY86VwxPtE4I3fiyZ+alrtzH0yEUbxWXGcw8HCGzW7SnGCSsFL1TWMAlCYtaV4/ujdnMZ3eqzF1m+c10y9nQgghhBBCCNEC9HImhBBCCCGEEC1AL2dCCCGEEEII0QIOVHOWss17z86QknJ7oxx8AImScUcjm4O8TXU+hdN2fUo69ZozCxtMA15jdgPlUXOudZ2sESwzCvKJ+zjZuHwhRLm8nE/Mi0vbB/m9rE9wsg6nMaOcZ8rVrgsJya6OvTJvzvMidr9gDRpQMKqmey/SLB510gjobl4+KqeVoXM6XIq1C94F2F6ITVj9xMNDu/7ajjV8XiMD6ItDuz0bTANeY8Yaj9cuP2HK21fZ+Lnat/voDchY2934ZFI9LOkbm8+d15RRmQ2iA40aw/qy4j74HitoxJr26Y4p0M0BXlfCJtF82zqzXII1ZnwtOF6WNGusTXHG2HQu+bj5Foh0waX7iD+bRze8V01KWxhrzi6XWRfF59Fdl6K4hu4j2E7Zp3uZ9fubO1Zvuh7EJzaYBrzG7JaOHZ99zcpjprxxtd0nx8TPUhvXYONdIqFdVYhPbl6CKJ4UNGJ2OX8w5/rxJn5MEGjGQ/Fn4ZjnHbpE5tyRLs7Fhlnu5V3MfbBowvkZZkS/nAkhhBBCCCFEC9DLmRBCCCGEEEK0AL2cCSGEEEIIIUQLOHifs6k8eefdwHn6nHNfSN50OeqkZ2AfNNagPR154tA+h0VNWrOfB+s82I+I/UAi7sON9oM25tWWcpbnzMWd2wfNmXHFfiEHzix503MndzfvItag+UqcF1qDBq3FViGzk4G6d/mgEvsIOU2SPT+jjj8L9bYtj5w3kb0QO+TB83SfPBzJ02e9b/UWfSeU8z5mrDG7lTQef+LEw3b76+w+T5AR1WeXbrZtSLZc6hzeB8ivMw3JiP32dNjOL2wG/RjHokjf4Nan5WT/VtDFzfIsC5ZHXoQD9g2l6ikO8HkeN5P6LOu93HkLfNACbV4Jvt7czUPtynGA9frBPeTk2QWdHnvYOb/Ayp7oIV3L1Z7d6Q7Fq42+vQkGBZ9a9jFjjRnHpzecPGu3p/HdEgkS7+naeJTTDVSewVMs0E265ylvz9ciiE8zPVAjbdV81mqFsVJBr7/o+2rO+krjRXfvzzkYWZQ+bD/2cdhDVSGEEEIIIYQQ0MuZEEIIIYQQQrQCvZwJIYQQQgghRAs4XJ+zSHMW5ZajlNPOOe92J2xrsQOr23h6AUmn7GPGGjPWoEU+aOx7dl/60rnbNO9hsXaAvYX8Dmj70ipz+lpEWpEhLye/kZKWpeR9ZnY5p9ZkX9irV8ecGjQg9kJr0qAdB4lHgtW/JPYRCry5Sp5T3F877IdD12FAPkPDgV3/0g75EJHn2M7Qh/NLA/IaIh8z1pi9kDQe33jCatZWkj3QZdJ4fKQmzdkMN0ykO+K+yT5lkV7M+yWWGhFsE/icOR8zbhPvcxmOyM+LH3WRrqjuNbcJpIsrSBbdt7fuOIOvd1lfU1Gb3A6KfoG0Cuk7+Vk1zYHE6xbg/OXolFSDgoaIfUFJgwaOV+wp27exZIs0aA8PSJM2iOMT+5ixxozj0xtP2rHSCgVi1sjeWZHmbIafJyKtp4tPkbdfuMMZ1plzjOB8FwNdXFWq0Glgg0Ff4GG4iLHWvFrhw0A+Z0IIIYQQQghxhNHLmRBCCCGEEEK0AL2cCSGEEEIIIUQLOASfs8tJoU4jxF5ClK/OWoNn6zSwNiRIkmfvjh6t/lS2Oc7sezYL7GMW+aC9snvRVnDqPlN8P74p3OdB59o7nUdppcCXh5c7KUGgA3E2KkVtCWmp+vMlKR+KJi30KJlveam62Ast0KAdcTLstSv530zjtDQsZgWQtqjsjfpsiTRmoy6Vl+xF2to5acoP9XyA3OhZDcdqnzRo5GPGGrOXdG386yarUbum3jTlj6Svtg2Ywecs0nSw9MXd504YRfVHcQcFjVlQZyjBZQ+xmnzxur4C1pjVq7QC6dScJnvH7oPrY0akQ6rYfwlxPHM6EvZDRPM+ZvFOmsULzdQ5fe8eI81Z07VwyyKPPAA19ZeUeexEdXB8Io3acNt2+gFp0B4rxKdN8m5cG5B3I91IrDHz8ekhUz5T2SB8Z3qNbUApPkU6psirbxaN6xz1l4g0Y6G3VuQtWVjunnnsk+fGGdSf3ACvuQ37wl71/LtAPmdCCCGEEEIIcYTRy5kQQgghhBBCtAC9nAkhhBBCCCFECzh4zZnxOSMvLedzRpq0os8ZlV0+MOW9upx4y5BynPuUIPqMbwIyrcO+ZAz7mLHG7Bby8qiT9Ulz+z+MvPpd6KBc7m2Uu827jLyG6KuG4VJhHfbz6Dcvn9c3Yzc+G3u+fvPmUZfy7HmVeTRox0DXMfZgnDoL0TG5jjLLXijeOR8hW6z6FP96pPsjDchg4M2zzvXtheyRNxr7ALGPGWvMbqXYtJTO2x3OoLdwMZv8ckYc94OnlNM60PqL8L4JdU9hPGzWVwPAkDVk7CPkRR3NTVrAfem0LawXdNpLroA0Z9ynuf5SjA/im+sv1ZXXPcpM90F3HQJd5Qz2cXDxiXW3vA8yGmUPu4p8zgYD/0C+QOt8lsROSyScZB8z1phxfKpxjhpti8X4xMfZb45PTko1px6Vx73FeBXp3pp3Gc8JEGlu4Y/L+eIdRYLzuJAYKp8zIYQQQgghhDi66OVMCCGEEEIIIVqAXs6EEEIIIYQQogUcqOYsgXLUOdeW889HrNHwdbLvWMXJ1V00E+bx2yT4fva6jvNzJpU6TRr5mLHGjH3QDkVjNidFL6Hwg2B51F9myJseFXRojU3YowZtFnbrg3FFduPlEeTiOxudqchxFPpjCOlh2bdsRFoY9scbDeKTwBqxinymBqzHYR8/itYVadDSwHf4PnX4VWrmZ5duNuVl0niwjxlrzDg2JfLWKmm15r6ngjhQRf19Fh8h3oY9N7kK1vwE9bHPWUlH53w+K+4vaCzX21Qm007ni8a+e4Vr5awjZ9HHmBWa74tSjPZ12CLfi06nNu1XOEP1R4JsPVtZ6xfhPRY9rBd0WtDBnPHJxTvfhj5ttAYbT+7p2vjEGln2MWONGev3FxGfnHcu+3kFvmd+h837K24SjH0cwX3mYk/RI5bKG1wJrU79x833wHNMBHF7Fn/KkEPwOdst+uVMCCGEEEIIIVqAXs6EEEIIIYQQogWEL2cppdtSSr+VUvpsSukzKaXvn3x+XUrpQyml+yb/X7v/zRVCiDGKTUKItqL4JITYLbNozgYAfiDn/LGU0hkAd6aUPgTg+wB8OOf8YymltwN4O4Afaqwpw+R8Or8Hl/caJ4Q6nxXScUReDC6PNTKAKJ4y8kbDSVO+DzfacvpSU34/vqmxjZxX+7Ef/ilT/mSPxAYAfnP9lab8kdWXmPIDF6435dVV0rVdtFqVet2+x3e2mj1OaioDhTz5wOcszEmeM5e7xPIlu9LSmm1kZ9OW06C5UufNR+VRp+AuM+c2Lte/yeenWC60wYlL3CpXZD90eDOysNg06gIbz7t8Evqn6BqQVpHPF/vlAf4e6GxSDj717872DOZETRSumdN5kGa2n6ym4yM1ldNXN+6DNRx/9KM2Nt254wPB722+wu5j9aWmfPbidaZ8Yc3G094lewzVhr0hqm3byHqHYlXhWvGzaNQN9Fqsn6DzzMu769QmH7LR2bL7PPOIbehw2Xa6lfP23Kae7TCjZdvowSlbXlqLYxM/T/m4BifsNsMlOg/UpZcv2TZyfaNuyYSx2R+QtS31lB6U23/ALCw+5drGJD7PbiwV+NGVPmONIscn1tkmHlvtQs/DXmkp20kCcrrBlO+sqJxe07jPKD59dMcHg9/Z+DJTvv2CHTt9ftXGpw2KT0MeO23Yi1HvJj4Fz3R33IG+y42b6VqynnXcLhorrTfrsl1/4scbx1we51AbSvrUcAg477gm8t7dhX5/t+Oj8JeznPPjOeePTf5eA3A3gBcAeDOA90xWew+A79hdE4QQYn4Um4QQbUXxSQixW+bSnKWUXgzgqwDcDuDmnPPjk0VPALj5StsJIcR+otgkhGgrik9CiHmY+eUspXQawK8A+Hs5ZzPXe86ZEhbNdm9LKd2RUrpjsM1zbwohxN5YSGzaUmwSQiwexSchxLzM5HOWUupiHFz+Xc75VycfP5lSuiXn/HhK6RaADCYm5JzfBeBdAHDq+ttyZ+dyHOpT7niYH1rK93QeUZTD7FYotbJhH4tIWZ/TSyHybmCN2Vcurbh1uqc/bcrLlMi8VL3MlD+XbjJl62YEDEGiGzIZ67A+sKh/oVUo75ntQ6Jc3d34a3EO8WCF+mCqqWyXswat6rOGgvOsOY/fN9ppxjqcYE7FQCfpNGxue39i3TrB9WyLt9nCYtMNt+Xu1PhnSN19FPglFj31KLoOl9mXjI6FtDNcZXTOi7oSpzXgmyzYSeR/R/WzxuyPL3tjwZPps6bcpYYvVaSPJZ3JU3QP9St7cUYr9syNtm2ZNWkAkDvNGjOnMWSPuU6zvgL8rGNvLvjYsHWD7UDchnrbLl/ZsJ5PvM80tDtln8iS5sxpwFg3QvfFgPo4e2fxPrjPl3TmnUA3zvtoEwuLTzfelqcf4aHX2wz6L+5P0bWJfKciz7qSp5jTtQ2b+0M0RoziE2vMXr/sA/upZMdOKxSolyqrkb2f4tMzdB8PE8UnukdGWxSfSv19Tl+zijwznYaswRsQKMcn3ulgpXGxuy8r1qCx3rDiGByPKUPmnacg2r7EvD6dMzLLbI0JwE8DuDvn/BNTiz4A4C2Tv98C4Nd31wQhhJgfxSYhRFtRfBJC7JZZfjn7egDfC+BTKaW7Jp/9IwA/BuCXUkpvBfAQgO/clxYKIUQZxSYhRFtRfBJC7Irw5Szn/Pu48o9737zY5gghxGwoNgkh2orikxBit8w1W6MQQgghhBBCiP1hpglBFkXKQD01IQiLOwckYB6lWCwcCfYyrcAThMw7P8h+MO/kCmwwzZN/AMCXL1ljxDrdY8vkcFuRcvZuPM+Uz1MbByTCz5VVkNYFQWnNIno3IUJzeV5hZWlCEWfg7O4A28Ze8P1FhzX4ZAQLniCkIIp2Ez/kZvftzB0mmDDECb9ZaFuoI/G954TYLZkRZEGkkTWB7pBJ8JAnjuHJPk74zjYiYTj3NRZMO4E0T5jDRsgspi8Yv/NEFzzpRCTid2a2gTE8G0zz5B+Aj00j3GvKOzTLxHrfmk5fWLfb9yt24LVFF2dKcYEOhCdD4OOunWlr87VjY9mSCTWbtg5prgLugzvXUszdsecpEvlzmSdjAAqG9RRc+LgrrpNNrIMYPlwufBbGfTYynioflziVbR/k85rZwNdN9jHDLlx84XuC6pxzQpCyuTIZGfOzLopPgeEvL2eDaZ78AwC+YumEKQ/xOVPepuC/PrCd9uK63b7XoRPb50GILZbukcI8YnYbZxhOyzkeBfGpdK1cnwv62DB6nkUTyPB5KIydwrHzoj3oS/uL2rDLEKRfzoQQQgghhBCiBejlTAghhBBCCCFagF7OhBBCCCGEEKIFHKzmbJRNXj3nnHJ+u5PWLCDfM9KgMbOkrEZ59K7OPabBf2TVmrSywTTgNWav6J6yy0/ZPOqKDqKm8t3Vzab8dHXalIeVNZvNtX/vZ50OG7lGedLuPEemmK4FhQ/pWrC5J8gw0mnQaHuWc9V9TtT3TUqUy80GkRUfV5CL7bQlfJeXNDfBvdioSVt0XvchkEYZnc3LJ7LbJSNjMuPt8fkqaGVy3SyAyKyFCjRlkdEs632AghaK6ww0Zb7crCH6yKo1aGWDacBrzFjjcfLMJ22ZXFlH1OiHutea8sVV0rQNWR/rmoS8FAQP7v99vj9IixUE+UhvAfj7NjLGHpwkk2lqU1GzPb1+ITbxcbn+w8bp3IfZtDowli2ZvUfap1B0e0yYvpXYVDj3A/PmQmxwfTB4NrpYwdc2Gk2W7js2Pg90bC4eufuyOT7dfsGOndhgGvAas69csm7LZ858wpRPktiXdXNnu9eZ8sYFG+9GQ74n/H3K2mEWobnzwpoy3pzq59NQjE9Bf/DjdzaVpvXnHQcXbuuwiuB5N2+FpTaH4//9MqEWQgghhBBCCLH/6OVMCCGEEEIIIVqAXs6EEEIIIYQQogUcqOYM2epratIYseeFy5EvJHe6HPY5XzdZg8ZEmrRxHQfLAxeuN+Wl6mVuHfYxY43Zy7pWM1adtDqQJUpC7rAPGmnQnqptfb2O1aABQN5kLzR7sZwmjXQdToPGvhmBBm28UuEzs5Ethhq0ZI+hy+tvkq6OfdAAJPZC4zJrRzjxmb2rKLHaSTCKmjP2l2n2NJlef17NZSvJQD11bTrb5FG2zueDfc/iBHqnqZzT529opQ+ekn1d4G0VEmmGiLMXrb5iqXqJW4d9zFhj9hKKTW88ZWPT5sgK/D5S233cn24w5dVk9baj7cJJcJoOv8o0Q9YP0nnJrCNlDVDhOcXaKvatc/oblvM5jTb7Skaei7HPGWsOnTaV4cWkKXPeWqy/gfd/c55zbvm0HvY4BCdMfM4uHwufJy87Z0FqQcfEw6u9arx5FzNoiubWAAVt4vjEz87Pr3J8shpZwPuYscaM49ObTll9//r1NlAvVS825fvSjXb9RBrZnVJwoCLfJ+68VE1FN7ZiiteFLjD7njk5fhBDGe9rS/d16fkW+RjO2b9ctIhfQeIxZaDlvBL65UwIIYQQQgghWoBezoQQQgghhBCiBejlTAghhBBCCCFawMFqzmDzpjmnnr21XG5mKb902W4zcjo1riMoO7ubOEF0Fl3aIlldtRqKz6Wb3DoVJfCyjxlrzDiPGnjQrk8ijGUyWrm7YzVoT3TOuDZtdWwu9qBjBQfVtv2ugD1zOK++orxrp8HwFktza86cBi3QdeTEud52eWezoKnYsQ1lXQfrX7i/ObuabDdg35WqkAseaZOcpua4aDkmpAxUU550nS3WLtAGToRX0HRE/bc/3zlkzzKnGSn6VDW3iX2l2KvI2d0FnnkX1qx+4oHK6r8AYL1vNWPsY8YaM/Zo/PYznzLl0/W2KZ/qWA3uA8ukQdvy4r3RyF7PwYB87oa23KeTP6p5/WafqVTQDw5Jz3rmLD3bSKPY3aIYT3rWUXduAbaDdSVpYPfB9wVrWTj+1Z3m81L1fZs723afXKe7j6YWHws9bAG+153mzB33DHpC1jrPqRlyD0cXn2bQ71ObOB5x2euUuEZb3wbFp/tL8WnA8ckOVFljxvHpz111lylfXW/a+jovt22g+HRxw/qgAcCQ4smwb2+cEZWHHPdpbJW7pB3dYQ21a4J7Vpw4R/sgX0/WglY0HnO+eMHwv9R7WFPol1MdrM9nnVzgrVzUCkfaS2bGmKRfzoQQQgghhBCiBejlTAghhBBCCCFagF7OhBBCCCGEEKIFHLzmbDrf0vmVsLiG8mRn8DnIlADK/kNhPmjka1DyiHKJqsEu9qjXyReth9j5wjp343mmzHo+9jFjjRlr0Op0lra3CcQdSijukg8aADxWX2XKG7UVXoxq2x1zXVOZriVpDZwvWik/uKRDm65zzv7B5YHzC4v9jfizeoe0JKTziDRozuKGFxfueu6Srkz7NFqR46A/G2XUW3xPXCbSNqSRv7Cco+90IqTncbGM8+HZ786JDV0TvHYQzfvgvlE4LFrBFnuXrF7jKdahALiwTr4+1Aj2MWONGWs8uqSfvaraMuWPL7/IlB/dusa1abVndR6Xdmxs2ujZi3mJAgXrZ0HaqUGXNYz+vCTSnDkfUPcsI30OacxGS81eWKNu/NxinVCHr+eQdSYcKGj15UCTWzCYq3e43zfHm+njCuP5EcKOndgLk9cNNLMonEcX06IGuRqDDUptCFZw/prNbYh0uEMaOz1TiE8X120sYM02+5ixxszFJ/KYZY3tzcsvNOWHNq0XGwBc2LExk3Wzm9s2Zm7DloekB8u9Zh+0YeHaO800PS6jZ0Uk0+YrEXlqlnC6RndfNN83zrdxhia4eysYI84ak/TLmRBCCCGEEEK0AL2cCSGEEEIIIUQL0MuZEEIIIYQQQrSAg9WcZZhc6ULWvSlV5JNQTEENvNCGgQYtyikNbDPGH82Zaj2Ld1oT9bp9px5iya1znnZxN2nAOuyDRrn+rDF7Ycdq0KoTD5tyl8Rc7IMGAB0y2Hqsshq0S7XN9eY86VHNZkF0kKzRYe8XAJXTKPp1Gonyh1mSYVO/kSv/fUhUR7Yp6t57yOVRN/ukoSStcvqD5nM7vfy4eAlN55tzvrvLj6dzXLGxDGbQq/J1Zg8yLu8iWjudZuRnx30x0Alwt6k2bIX9ioR3APqVPZCHutea8kfql5gy+5ixxoz1saeqR0z5xs4lU75n+fmuTWe3rdcQ69Ie37Sxqjewx7BFMXhU8XOHNB4DH3hY7zBYIe8i0pBxmTVk7lrStRqssFdbHAxH9PzsbNrg0l2zQdd5OA7teRstUQcrxEf2VgOfy0CHdFyYvp5OGxNu7D+KPcJoMZ/nSA82A5EmO3w2zqkRrzdo7JR8fOqRfvRs12rAlqoXmzL7mLHGjOPTCo2tbuqsmfJnl1/g2vTg1o2m/AWKmY8nG58G5Hs2IDEx68P4OZH6hRPLHnSBRybHihDSi7ln0wz9i71AI+8+fkaPan6gzfC+MK8/mzRnQgghhBBCCHF00MuZEEIIIYQQQrQAvZwJIYQQQgghRAs4WM1Zgs/hnIa1M+RJVfeuUOd0Fa7cnIfPvj5RjnPRLyRIMp1bkxOs39niRvl37AFpPZ6ubN4za9BYI8Y+Zqwxu5U0aFh5zBTrgkkK69KWKuvF9kh9jSmvVlaD1q+srmNI+oS8bctVKbk38MiZV68Q9RcuF2xV0OfrR322w9o68hKq+rbMXh8u77rgS5bpQJzPGed/Ty8/DpqzBHPeWSPEX2NV5LHHXkzFXbj8dlt2OhKWWAa+Q0X9RaB74xgb6eScRx5r0LZJl7BSMvazxYur1sPn/mT1X6c6LzNl9jFjjdlNtfUZetWS1ZzVM3TYHRJQsA8a62fruvni8H2fZ/hedHCiWS84JF80vu8jXdKAtuf9AV5XMqTruUxalcijkdvoPBztpR3XSf6DmXRqQ/J3m/bHPC56WCS6nnM+p0LPMsTnyvfh+bYv4h40rBmas7pgRFtzfFouPZDtjbZxwd779yWr/zrZebktk48Za8xu6bCHrHWq7ToPWs/WkHwX2ZdxiTSwQzpuqm+WeMTbeM9CqpP1W7xPfnaQXsxprr080MW4OvC+dc/paKzOvmmlmTKc/2ik12+q7cqbCSGEEEIIIYQ4BPRyJoQQQgghhBAtQC9nQgghhBBCCNECDlZzxrA2hnM1Od+zkH9ckZcVW7X4/E9b55B9NijPdSZfjcjnYMGatIq0d06TBCBX5JFDeq2natKgdcgHrbInm/VirDFjDVqNJ1ybvJeaLbOO4+HqGlO+QNeuR8fk9FwFzxzszOdzx8zri+Y0jty/inWyTpI1ac37dBq0GTQ2rAWJtErmPjoOuo5RRrVzOde/djqWZv8U1qABpZx68u1znovs+UM5+JG+MZZ3eYL4xrEp0qTVdH+Ntn2jWFIxIv3EarKasQeWrQbt48svMmX2MWONGWvQqiXrKzTmUVPq0426NrCajs2+95acZqdvH60DikXDygeCEd3n7tyzFMVpGJs9o8A+aeTBOCAZMQDQYWNIujTWhVR03CV9q1nOGrSef8hXffsZ3wfsXTkqeA4eebI9l6yl92MKGlvNsItY0xp4Pwb1z+0pOkOlfI/kwLvNxaetQtCkOlivtZ5II0vx6eblF5oy+5ixxozj06spfgHAMFvNP8enjaGNR9vkw8g19uiwh+zLWJjHoDS3gVkc6APdWIiqY5801g+yxhYoaOHpmVrTcSW6lvxMZmINWmn83qxTM+ehYff65UwIIYQQQgghWoBezoQQQgghhBCiBYQvZymllZTSR1NKn0gpfSal9I8nn78kpXR7Sun+lNL7UkrNeR5CCLFAFJuEEG1F8UkIsVtm0ZztAHhjznk9pdQF8Psppf8I4B8A+Mmc83tTSv8KwFsB/FRU2XS+pdOYET7f06/DOaPO96DHydic/0nbU15rpEErfebS7CNNWlAfnwfn91ZoU825uLV9D+917PPgic4ZU+4GPmisF2ONGXt5AMDXpqdM2Xmp0Zno0D4qOhGsQdtOrEHz3dvnUjf3wbnz5HeRV8+515Q+7vUFqdlfhHWXrIeqhrHpjdOKuE12IyBYOAuMTcnEhuj4nXdcKXedpYLO44nWDzx/nGce5+gX4mmUx+9y9mfwdbQb2CJrgNn3rFSn0x5s20atblnh06Nb15jyPcvPN2X2MWON2Q2k8QCAP0br9LLVoK0PbRt2hqStooNa37GCrm3SYvUKt8+I9RHUp9y14P5APkDOd4g1HCukQSv4CI2W+ALbbfqnqbxOz1+6lnwP1D3WxxbasGwbPiI9KGs3WR96iCwuPqXCc4CWGw5Bdhd5fjoNJHzMcutEOttAE8tlF5+sJVlxGx4zjnZsIy9uWB+0hzavM+XPLr/AlNnHjDVmpfj0muVV2wZ8wZTXKD71hnTf0UGtOf0+aWRLYyf2+hzMl3gXegrzc6AbjMVR8D7j5xcJVEddiqnBUCjUXGN+b+VZCc9uHrM+KXYn/zKANwL495PP3wPgO3bXBCGEmB/FJiFEW1F8EkLslplefVNKdUrpLgDnAHwIwAMAVnPOz34F8AiAF1xhcyGE2BcUm4QQbUXxSQixG2Z6Ocs5D3POrwFwK4DXA/iyWXeQUnpbSumOlNId/d7G7lophBAFFhabBopNQojFsqj4NNhWfBLiucRcSaM551UAvwXg6wBck9IXE1NvBRvFXN7mXTnn1+acX9td8rm0QgixV/YcmzqKTUKI/WGv8amzovgkxHOJcEKQlNKNAPo559WU0gkAbwLw4xgHmr8I4L0A3gLg12fa45RYLiMQPDMlQ0sS/Dkz2FCkyoJUMoplMegsU6gEovpwwpDAD5jN/tzEAgBqUpw7MeamVVdudayg9LH6KlNmg2g2pWaDaZ78AyiZLT7TWAdPOsLUdKKeofJWQYiZE6tKmy+ouxah0yZXEKxfWMdNkEAThPTnNanmg+AJZeCF+s7EtGGCjMOS3y88Nk1DXY/NLcETaZTE7mwKzHXyxC10X9cUy9zEByw8LhmczzkBSGRK7eD13QQkBXNuqjTzpBO0zWhkT+5qzwrwz25bE1iPHfvy5B+AF+G/aumCbQM+b8o8edE1S1um/MSWnWDpwo41ruUJQwCgN7AXp+qfcOtM4yalGfKDxxb52eXE9CWCZzJf7wGZVPdP22vHfZonW0gDH/M5ZLt7kdcvGMUeBosfO13+M74v53SIBsrjq6Zd8KXi5xZPSFOY0MRNWrPXh0nUXzlOlzyoXUxrHlMO6b7je/3BrRsb28QG0zz5BxCPnXqnHjBlHjud7tqZT55csuO7C9s21qxv+fjU79EkSMNg7ETPMzcXG93XbGjP5Vn6MPcfroOff/xMdX16AbHEvdfMWOUsrxq3AHhPSqnGuCv/Us75gymlzwJ4b0rpnwD4OICfnr25QgixZxSbhBBtRfFJCLErwpeznPMnAXxV4fMHMc6hFkKIA0exSQjRVhSfhBC7ZT6jAiGEEEIIIYQQ+8IsaY0LxZhQs3Ym0KAVNWnOqJoMSMl0kHNS6ygvmk2qC0avJa1H0z5DjVmUo8rbU24vAJDPISrSoNV04IOOPYiNmjRolc1RXqqeZ+ujZF02mAZ8njQbVddplbawedRO50YnjstPF3KUt8ioet5b4FA0aJxHTYcwcLn8ZFJNjS55tLIZLDhfvEmDNqdW4Uji7jk6H6WTytuwro9OuTMLp3x41qSNqL5c6FyRpiPqzyUtnYFz+MnksxQbnSbIxXBbHJDZ6aWdZlPqHRJX9akRbDANeI0ZxybAxi42kr2he7MpP9C5yZQf79r4+bSr3x9Xn7WhrFGkGM/36JDEM07jyM/G0rXe4Q6BxjJrPIbLgUE0CTHrQkANNWS8fPq4j1FoMqdmTi3oTMw5TuHlrKl1GqPCc6IUs5r24fbp9tG8fFcaN7qPWNs57NtOv7pl7+MvdK815S1ye+f4xAbTQDx2eh3OmfJKsjf3DZ3nm/J9XRufHuleY8rnaquZBYC1batDq0n76zXUzeP5IZlM8zDGPe8K18oN1wNT6ag/+O7ImrQ4oHAcdn18xpikX86EEEIIIYQQogXo5UwIIYQQQgghWoBezoQQQgghhBCiBRys5izBenXw4kD/UNacsY6jeSPOY82Ud+9S4p0Pmm8C79L5MzBRbneQN8vLS5Ifr2ehbejKV9v2wEa1XeFSbfOLH6mvMWX2QWMfoPFn7GO2asrs5eH9Ps66Oqfp0sVNhQ7zdCIzz7zi1rGVBIsjX5XgWs+yD1cn+8mQX9HAGe1xDfF3MlWfridr0FriJbQwEjDqXj4vw2W6H7pc5rgQX8RUNeevpwFpA3fsNRjVfI/GsQnUvUN9LC8PYpOThMzg/+biWyQpGtpKNnq2wz++afVc7IO2NrAnYX3o73n2MWONGWs8uumSKZ9KViBWc6yj8qDwkBiSMdQa+9zRJqzpcD56rK8YkIaRNW2l50hBz2yWR/pp6vND0stWfWpT6T5i3TdrU1jrdNxi04RQ/znNLOu6ARjFJyfgotX5vPOlC3wdiwS+i5Ee2z1uo/pKTXD9iSu1xRFpzjZJm/V4svGJtaUbdFOsFeIT+5ixxszHp1VTPlVZn7MqGGQOCg+KIZ9Mik+8ifM5i+IT27VSfKtKF29OXaQj6k/BWLy0T//e0qCJbUC/nAkhhBBCCCFEC9DLmRBCCCGEEEK0AL2cCSGEEEIIIUQLOHCfs8acX05aZr+AWVI1g/xO5/8V5TQ7H4RSYn6zn4xL320+TE+U6z2D5ozzf12uP2tFavvBsLY7Wa2sruPh6hpT7hSSddkLjX3MWGMWadCWkt0+yqMer0PHgaubN5hXvjCnj1RxHwvWoPWD/jneJyd80/Ieawqn192NqU67yHXC4PTlE8eashF7jlEccf6IKPidUB2p39y5nG6UNWl0D+dOob4gaIYxNbIhcjoBW2Z/RQCorfwBiY6DtQ19Kl+icm9gH2Osf93sW03HztA/9lgjyz5mrDG7gWJTjU1bX3rY7SOiQ8LOS3xu6fJyf2C8DpI9O5vrBwoabrcCFdl7jXVxdfN95XzQ4PWeTqtyPCVmFtbrz/ucKV1bXoXHOk6/HzQx8j2L5YT+Wu5R8+3WD8ZB48+at+ETRV0c27CaswFp0jaWbDzapvjVG3q9F4+d2MeMNWYcn4ANKj/k9jENj5MAoEMn4rHqRrtCFJ+CsbV7hvK4pnCjV26wTStwF55XBzffLVBml+M7/XImhBBCCCGEEC1AL2dCCCGEEEII0QL0ciaEEEIIIYQQLeDANWfTefDsR+LzO+cVZ3lc6iztk7UjvEuXAl9InM4VHwfl1c+rQePlu/ELCfwffO41t4GOgTRo/crmTV+gc1DKWWa6Lpn7rClFGjQsrZnikLavi15r9rNP5BdEzTSE5z447F1curkrcdoBussHK3ErMmnQOrzJlF5qpv54BJiOTSUNWeO2Bf+wTBeKu3u4j3k9XIo+kEGdvHhe/SstTuSllQo6uGrQHNd97LF9cdCxJ3sLNhbVdbP2tOR/eM3Slinf0L3ZlL2PmdWYXVufNOWXksZjtPyo3X4GfezddJ/yJp0t1kGypydfrOb6ZunzLmSzTISfK1RmOc2IYtNoqfB8Dbz5vC/V8ROhZTTH2dATtmQRFXk6BR5QCyHyyYt8FqPjZl2l0/H6JrmxkfPuozJ5xLI+f0CmsqMhaWh5/4X4dLprhbo3dJ5vyuxjxhqzeTVo7MtY4gsUn/hexw75eLLei88zHTfrUWd5W3GeYtF8DYHmzOvkSjdS8/if22TiU0Oo0i9nQgghhBBCCNEC9HImhBBCCCGEEC1AL2dCCCGEEEII0QIOVHOWE+V0UsIw59r6tOkZkp4j0YTLQW3Oi+UUU5eTCqDmXH0n8CIfn0hjRrAF1a5ywSPNGTUqswcTH0NlG9ULNGgAUNN5iXRp7GPGGjPWoL16yWZv16RBK/EJvCpcZ5pISrcrTdpePWvm1KDlrl9n4BrB+yAN2nRO+jHQnOUKGE7l0HNuuTuHvLx0Dwf57u7C8j7Ye9BpRFg/O4NnD7VhZG9b79EYPSEiH5mSv5LTdNC5JO0UazTQtydqVIg10+z07UGs7yy7dZ7YOmPKD3RuMmXWYLCPGWvMIh804HHXhm0yKBzStWF/OO4fo+BGjPQ2Ja2W24b7E23S2SYvvt58z+MSTnsSaKVM/zoGsemLzHEsu1Ldcf1zfnUfPftKMkvf5wJfRm4Tx8zmJnjNZCFus3aKm83eaLlL49Yex6fm+mh1rBXi2ZNLV5nyfV0bn7zHK/uYzatB8z6NfXoY/C6NIyI9IJ9rN0zmWMMa7ZIMLvMzkJdTnRS/nC43iqGF9wun1XVjp8Yqr4h+ORNCCCGEEEKIFqCXMyGEEEIIIYRoAXo5E0IIIYQQQogWcOA+Zyb/MvAQcD5opepcymiUM0r7jLRYrIMr+GJEx5G5DlrOOclO37KAvPm5j7sf6GHI24O93LYTCSYAPBNozrqUZMx51OxjxhozzqN+JWnUxnU+aMq/4NbYG7vSpM3pjbZXDVppOcldMAg9jy5f/6L3xxEjZb4Hmr1L2FNqVDpfoQCCAwcvD9bnxayngM/BdzYwrAOgXYxqDhTsQUb38DrHjVgH56B9cBsHXVreaY5FA9LHbvf9Y+/CjvUpe7xrNR6R74/zMZvTBw0AhqTzcM8R8ozrn7DHxX0yigNDuuezMzOE65OZNULOu4g13Ozxw89Gqr/wdfGIfe+6zcunxw3HITYdGNFzhRcvQFvjdWjN8SYcCwV6fmcHVqjP6SpLY77pfewE+mTqn5kGU0PSmPWqQnzaPmHKj3SvaW6UYz4N2qgYn2wdUXwaBPEp6j8j54k4Q3yqON7QLoI5JlLgWVzC69GpzqY6GhbplzMhhBBCCCGEaAF6ORNCCCGEEEKIFqCXMyGEEEIIIYRoAQevOZvC5WZy/vEstma8ybwGH5zizKIM8tgpprDTZ+zn5fKmA98y9rdx689wjE5jFix32gG+NuwPwY2uWPfhu9YWbfI020MEF6+mo2AfM9aYsQ8aAFSUS+28o3ZlEDM7s9Qfacr2qkEr5lFzvrfLH+fc/2lPMF/dkSMDaSonnnUGibULfRusEntxTeo025D+purZOrzm1p7YNCSvLfI1Yw0RUPBKY18f7jxkATZifRfXR7d5vR3sr7ROlLO/QmXnixZpOmwjeoVLxd5nT3dOm/KABRBE7R5e1seMNWazxKbwq9NAr1XUaEwvZ+3WDKOB6Bk9XGreJz/bnO9e4aHv/NxYw+M2OWaxaZ9wz6Lo2RRJGkPNbKkRURsoZtIG8+r1nQa35HNGY50oPnEMHLLOifX7RKbB1qAwdlrfsvHpXG19GQd0IKzn95pZq29ljVkpPjkvtD364PGzhZklPrlxbhCfnP6PxvsuZnJ/ZEFzaR/B+H7WZQpdQgghhBBCCNEC9HImhBBCCCGEEC1AL2dCCCGEEEII0QL0ciaEEEIIIYQQLeCAJwRJZiKBxEavbuILEsjPMBNG6Ps6p+jViWDZhBMFkWkwAUg4YQgLJ72fM7XJf+aF//OVvRk3K2tpAzZi5BlFAGSaVWGLjKqfTlaEyqLWKri6bDDtBPbwZou+jba83xOElHAi171OEOLq9wfl+ywJr7lRU5M0LMIk/dBJMCeSzXPd/DdsqMnrY37BfSg8D75KK/VVvo+jSZi4zLFtGEww0tlqNh0GgLrXfCJ4m+EyPQeWm/sqM6JYNOLYBaA3sAdyacfOQjKkmQc6VcHxe4ptUrOzwfQssSkyaB5YX1okniBmpVncPnKTv7gmwc0jENzsVY/axPskQX4U0wEv0h+uXGHFwvqaEGRx7Mu5jJ5lbkIGWp/jWzAJSdWPHq4zmLnTNnzf8IQiPIucG65RfCqd537PDtXXtu3NO6Q2dfjEcH00iwkbTLvJP+AnCdlzfFoO4jaNe4sTgswZnxJfW55cisd/XH3h2njTcSo3rN/UXIUuIYQQQgghhGgBM7+cpZTqlNLHU0ofnJRfklK6PaV0f0rpfSml4PcdIYRYPIpNQoi2ovgkhJiXeX45+34Ad0+VfxzAT+acvwTABQBvXWTDhBBiRhSbhBBtRfFJCDEXM2nOUkq3AvgzAH4UwD9IKSUAbwTwVyarvAfAjwD4qaZ6Rh1g67qp98FZTAqnKOVnRpqgo6CH4Txol7NMLF8ig2DWFqCQn7vH8xCexwYj0Mtwo6icrZhgFVeb8ifyC2wZrzLlX6DaZ7n2d/6I7bLvXbvWlH/+8a815Xseu9mUR0/ZNnfX7E5rct4uSVU4PTzSATmDZNYHUl61kzgW2pALOhy73JaNJ+8h3mOLi00JWzd0psp2Od+TrD0tGWpyHVzOrKXh788Dc3qmKINiDRmvE2jM6lVqEh03673OPGJP1PQ5fRY2y2YTV9YtnTlLhqp0LQYrNsmfDdNd/2fdAYCqbwUSfWrDGsXoS3Q/3L3SfC2dLq6kXaBV7nrHvzTlf7d2vSn/7CNfZ8r3PniLKS+dsyd26WKzaXkuaM6S6/e23Nls1udEGkfWoBWkyk7/uXyxeR/T91lJj32QLCo+jSu7/GeojZ4hJpf8dJvqmHcMwDrm4iYF/XPj+hR/qh27vKYyS6eW1nns5PcRaX35+XriHC+3ZdakDZebfxOpBn55Gtp7ue6RoIvi02PVjab8BYpPv8v3/j7Ep3c/8idM+f4HnmfKUXzyz0vfJjcW4vi0Nd+4JtT7l95B6Jna4TkoGvpT0/vLrL+cvRPAD+Lyo/x6AKs552eb8QiAFxS2E0KI/eSdUGwSQrSTd0LxSQgxJ+HLWUrp2wGcyznfuZsdpJTellK6I6V0x2DbzwAjhBC7QbFJCNFWFJ+EELtllrTGrwfwZ1NK34bxBNpXAfhnAK5JKXUm3wDdCuDR0sY553cBeBcAnLzxtkOYmFwIcUxZWGw6dYNikxBioWjsJITYFeHLWc75HQDeAQAppTcA+Ic55+9JKf0ygL8I4L0A3gLg16O6UrY5oaFvRgs8p/aDverkltZskiv7h032YkojXiXIpZ1fY9Y+SueZj4s1Zt915oIpn6x+x5R/vmN1Hp/sPN+Ud5ZsLni9bk98ve3bVPdId0E5y5zDzrcN51mzzwbrRor33ZyaBbPPQ7ovFxqbRkBn6/JBDVYqWk5aqzq4vwB3Xjiv3+mSSnWYRjSvX9SQBNfVaYC4DvLC4hvI+aCRnqLU19h/y/nCsIaIc/idVq+5PqdLmKW/stck1+n8L22ZtS+5M4NHJx03azi+58wzptx/wUdN+f/uf4MpP7Z8jSkPV2yHY98hvpYAkNj/kGIJay1ZQ1Q5byOqn/QapT7MHpvz6pQOi0XGJ2besVBbtfez6NIM845TnM9evL3TOgV6rFyT/rhBAzmuz5YDS7IizmMs8LVlrbEbM+xLfLrdlP8NxafHg/jEsYO1yICPTyOOT/SscL6KHH9Yd8ua1Vm6q/Nem2GbAnvxOfshjAWu92OcR/3Te6hLCCEWhWKTEKKtKD4JIRqZabbGZ8k5/zaA3578/SCA1y++SUIIMR+KTUKItqL4JISYh738ciaEEEIIIYQQYkHM9cvZouE82Mhf4lB0TrPsc8Ep8JHXQmeTNWe+kT1+716eU4O2R3bjSefasA/SAm4D+5ixxuzPnto05ZXn/a4p/2LHbn/Xsp0VefX8KVMerftbbrRhr1W9QzoPzrXm80J50lWPNTjke7aLHHenTZo+jJbqGeYhV0Dv9OXrMHKeYnROd+F/MiK9DetvIu0V6wKc/07fN4Lz9J2HImun5tUykE5p5bzdYb3t+/vOtbbSSIPR3bKdj+Mda86Gy3wQ1IDitWKtlF1eueW23Nnie85u3z/BB+nbMCDrIvYxY43Z911lDZbOvPQ3Tfm3rv9yU/7o9S805QsXbWzqbXijs7RpD4T1gnytWD/b2aTlW7bc2Sa9TmFE0j9D55Y1QMS0bsRpSI4w+64bW7Sv2S7GTqztDfcZ7ITrq3t0HxeehcMhx3p6frK+tNfcZtY98fN4FpyX6bD5mc7xCTv07KDTNuD4VIDjE/uYscYsik8fvv6Vpnz7EzY+rVJ86q/7m7mmsRPHpz49E3ls1KF4xFphvrYlbXlmDTWfSqc9n6qv4bTrlzMhhBBCCCGEaAF6ORNCCCGEEEKIFqCXMyGEEEIIIYRoAQeqOcvJ5ltynizn8rrtZ3mV3Gte9gHoZzjfN9JiOU8d1jtsxiKiUIMWaWiC8zJLPvy8x73o7Uvc89jNpsw+Zqwx+5aTVrRz6iarUfvlrp2E645lm0f95PmrXBsGXStwyuv2WnWcpjC6GLQ2n6fCeXPrRN5pLfA5WySjDrBz3eXzGuWNu6+1CueA9V2hr1l0mdljjOpnPy+g7F1ltnGxhco7zReXfftSz3aclQ1K6gdQ71ix3eAkdy5brKjOUbeiMumgRqwToFhX0CEl0pmwl1YOnk2s8RjRQfDy0rOMfcfuffAWU2YfM9Zw/IXTl0z5tu7vm3I//0lT/mRlPRqfSaddm/qVPVkD8rGrtsnXjkcU/GCh89ih/lPqr3y9auqTfP2n64jGFMeWQ9DK76b+eT3r+HqmYCdujMma2YJejLeJ/CejuRMinGdZYVSeWLIa+Cw6P0seItIxufhU0uVSfLr/geeZMvuYxfHp90y5P3qDKX+C4tP5ymrQAGBI8Wm01ByfaHWkzHHfLq9Zs13SKPK5pD7FnqjT16ppDKtfzoQQQgghhBCiBejlTAghhBBCCCFagF7OhBBCCCGEEKIFHLjP2XT+Lufxu3ziGfyYovzeyDNsIRyAP1cTVd8n1rN/A7exR0nMkUeJy4tewHncDw3ZvIyeWjHlT3ZsnjP7mLHG7OtX7HnsXveHpnyajDNu777YteHhzjWmvFPZNiHZpGa+aaO86RHpPgq2eN4XhWVAB3EfHTLT8cf198CDrKTxmNe30e0ziG3OH2yGr9pY08P6VZdjT+tzG50PzDIn4JfEC1RkfRd1UKcxI18zf96afWeK55XqGI6iOkjnNAyCF0uvOv68sEfP0jl7pz+2fI0ps48Za8xev2wFFv0b/osp/1rnj5vyJ5esRyMAPHbJamS3tqxwkjUffKM4v8DNIHAUNGKs4XDjhKZ+fwz0sPvGgmN4dB8X9WVz6qNn0U+b9Zv8OeG1pkDhXo+6LNUZrR/F+eL2FFaH3fliXKS9432yjhPw/pEcnx6n+MQ+Zqwxc/HpRrv8VzuvNeW7lm91bXp8ycan7U2KTx3bxrTWHJ8yaWAdJb0+e845/d/ugpB+ORNCCCGEEEKIFqCXMyGEEEIIIYRoAXo5E0IIIYQQQogWcLCaM/I5c3mxkXfDbjRoR0AbM6/2yvkmFPQO7A1Em6DLGhpK3B+wVmROq63i8nlTbwMt3yI0a901W8nO0glTvmvZ6jDYx4w1ZpxHvXT1Haa8wuZUAP6geqkpn62uM+Ut2Da5BHQmSHqvev4z58tEfcqd2nSFv48oaWTPS+Icf8pNn0WD57Qx7B0XeNOE2gXWBRbio9OYcX78HrWE3IbBKftBYhOYwjZOm8L6R8LdQtF9zxq1wlMv0o3kQRCM+Bh2469FVS5dtHUOV2wn/Oj11kORfcxYY8b62JVrbzflqztf6Zr0se5tpnxu84wpP9O13kPbtfWw63cCsSZr96xEd7wJVdHZpD5Mfdp4ET1XNWezHHdwr4fjkKj6OT3MZqp03uoCrWeq5t+hu7c5FPAG5LtYUSzh2FP6yWTEsT7UrdF9lSJdlN9nRBSfbn+C4hP5mLHGzMWn6z5iyld1XuPacGfX7uPchvVqPE/xqV/ZNo6C+MTa4roUn+jcd7aDc52v8DehX86EEEIIIYQQogXo5UwIIYQQQgghWoBezoQQQgghhBCiBRyCz9nlHM5MubicohxpNmbaH+vaePkR1Ms4zVkpt5vy8Gv2QiO/Ge8NRPnEVkowtz6mtM1+aMjmpd6inOJ1m4O8et7mLN+xbHOc2ceMNWavWbYnrkp3uTZ0SSxUpS8x5c8nq0HbTCepBttmfy2afaEA7281chqaII/6qJOBeufyMQ5Jp1RRavpoF95Zrr877RVtzvEw0NxWpeWsc6sCvQNp60aB/iuRH9jSGms6/DZ83L7O5uXswTMgf7DBcnPsYj+xcZ22zLo21mm65wq1mbV+Q6qf9wcAI24nrZNIq3Lhoo1Nn6ysRyP7mLHG7I8v24td4xOuTVfX1jDzY0s2/g2p057bth0qb9uLPSQLxwH12brQX2ryHuJYxUxfu8PwznyuEGrSZhgTuDrm9AgL4ZjLvo0sxi+1ydVJz0JaPKI6Od6xfow1sCWPMd6GY72bd4DuI9ba8fZcfzE+8bOB2s1aulWKT5+g+MQ+Zqwxc/Hpqo+7Nl3d2TTlO8hH9nP0oH46ik8neJwTzL0Ar0NLA7/ONNPPhqa+pl/OhBBCCCGEEKIF6OVMCCGEEEIIIVqAXs6EEEIIIYQQogUcrs8Z5946fQRtXtAizKt9ifQOzndgN5q0QGuyV5xXB+fFonBeWBNBPmgdp0EDle0HvMvwvJaYV4PG2y9As8a516xvGK3bW+TJ81eZ8u2U48w+Zqwx+8olEl0AqM98kraha0MatPvTDaa8kdgHjW5rOi98rUuwZobzyYsaq6POVH9xGrsh5exz3ypEUqcZc3oHW+acfu7PfE2YkgdLTZ4rXAdrCyJtg4PiCscmLo/rjPSLfGM3L2aNx+AEla31jdNylXD9m6+liz3NGs3szovfJ1+LzDo4una9DbvCM8ke6CeXrEcj+5ixxoz1sQBwpvqMKS9TfNuik3lp08a3zR3boUZ0rfuJ44rvL/7c8sPHFqe1mccyTi2KvfqORqsH9+0s2+x1TgBX3yw+uJGPWXP3c/A++T4fkka2OJZivzZ+NtAKI56HgH0cw7jtm+C8IFlzRlrQ/ro90POV1aDdtXyrKbOPGWvMSvHpJMWnlWTj0/bQNnJt09ax07MXZ8gPQIJjEQB3baL4NJp6NjTFJ4UuIYQQQgghhGgBejkTQgghhBBCiBaglzMhhBBCCCGEaAF6ORNCCCGEEEKIFnCgE4Jk0IQgbHxcW+Ucaaq9CB8F0f285riBEexhEE1swcaJLIgH/Ft3GvAEB2RSvWOV/25CENpFn9xleflMprzR8khpu4CJV9jYt+7Rud2wBzLo2lkbHu5cY8p/UL3UlNlgmif/AICvWLITelSnP2W3oQPjCUPuxU2mzBOE5Cq+zWsW4tPkEm5ynmnRfQvumb2Ssp38gkXZ3E+cIXSh7/EEDnWP4htPCMKTrvDkHGy+y/GxYBjtDDJ5ogoSOLt5MIL7mtfnNpQMVd2kDyRe5+VcJx8Dw4L7Ac3BM1oqbM8f7dAkFHz9C5Mw2eVB/SVoG9K2I/HEGJu2g/Qre+CPXbKTF32se5sps8E0T/4BAC/r2klGeifuN+X1q+3JXd2xsefzA2pjx7Zx2OEHsBfku4l05pms5RjEptawD4be0aRde50gJJxUbBfbuAlqePKNqH437rXLSwbQjJuXwo2VIzfv5kmXSteFYxrflxyfaho7DSk+Pb5k49OdXWtwzwbTPPkHALyiaycZGZ68z5QvDk/acs/Gp7OD6015QO8gmeNT4fcsN1kYjx3cxDizdWL9ciaEEEIIIYQQLUAvZ0IIIYQQQgjRAvRyJoQQQgghhBAt4GBNqAGTwOuNjmnVYDlQ0pyx41tzfqfLL+Z9uh02Vldmj9oop/sgjVnu+BOT2WXQaWiadRz1DicY0w5c0rMtD8lQF5jRALJhufMHD85jKbU30ihyHnVN2pO8bg9ip7Kai7PVdaZckYE068UArzH78iWbJ12fscu5jooO6t7qRlNeq2x9rE0BSvci5Y+T3sl40R4DXUdO1mRzXrP6klmzu8doHdbQOp0bG8cXNGV2eaENdF9zOzPreaJ7imM03z8zaPF4J64ONgAfkCk7xXQ2UB2ukNaBTKlRMDr2bYxXmcZdW9KLZT6mkjaaAhavk6nO4QqZbS/b497askH43OYZU/7YktV4sME04DVmUWzqUyfuVDb+PXrxalNe61oNCOsuAWBERrFsMs79PhXM2MURwT3kqbgPurdF42Iu9em632xQX3qeunEqx8zA8Jt1cXzPZHoY8fCx1AhuwyiIT6Mlex9vb1J82rD61ju6LzZlNpgGvMbMxaer7jJljk81HQTHp41Ldnw3LAxsKxojjsgr281rML3LhkeRfjkTQgghhBBCiBYw0y9nKaWzANYADAEMcs6vTSldB+B9AF4M4CyA78w5X9ifZgohhEexSQjRVhSfhBC7YZ5fzr4p5/yanPNrJ+W3A/hwzvnlAD48KQshxEGj2CSEaCuKT0KIudiL5uzNAN4w+fs9AH4bwA81bpFIsxD5d3GebMmeJvAQcB4Uo+Z89RGdkVCDBsyvudmjBo01FmVdBx1nkIPMHjsV6Twy5fF3SHOWne9ZQTtA6bp79ccKPUxK/SXI3Xa52KS14uNGsjnMWyCfn2Q1aB3SoAHex4x1HOzlUZ/+tCmzlxpr0O6vbjDl1WRzuwFgQF5ouWJxEV3v6cXt05zNH5sqmyPPccAxgy8Ma5uG5K8V+d04zVGgCywJxtiPyx1X4GMWacr4uFkPVPLsYQ0G67H4uNy5JS1fZ9M2ctn5QNrN+6cL3mt8XqLr2yy5LbQ52L5AZ7PZM87p3LabfYWeYU8gCoZbQ3+x2Mcsik3fTj6OrI+9vX6JKT9U2/j49I4Xew7IR4ifVawLnqalHozzx6fnCvt8vWbSvfO9y/orjpGR3oviVdUnDRoNzkoeihzDHFF8itrIxzhLfNqi+ETj0j4dp4tPHRt0z1Ms+dyINGpD/1BmHzPWmHF8+nNXfdyUeez0h7X1qeXx26VSfGLNK3WyijWwU6etKT7N+stZBvCfU0p3ppTeNvns5pzz45O/nwBw84x1CSHEolBsEkK0FcUnIcTczPrL2TfknB9NKd0E4EMppXumF+acc0rleXQmAeltANA9c+2eGiuEEIRikxCirSwmPp1WfBLiucRMv5zlnB+d/H8OwPsBvB7AkymlWwBg8v+5K2z7rpzza3POr61PniqtIoQQu2JRsalzQrFJCLFYFhafVhSfhHguEf5yllI6BaDKOa9N/v4WAP8LgA8AeAuAH5v8/+sz7XE6x5I1FPz9EWsyCqIzl0Ps8oXZm4HyewMjs0iDVtrlvudNU9pryZsoUzIrr8PLEx9F5LHUi3zQ/Inq87llDVr0VUGQRx1q0ArbsK+Za0Jwcf0NZC/OZrI50fcnq/8CSr5ltswas5d1rWbsTafMl7Euj7qTvtSUP1f4ona1Jj1KRRenunIedXjd9olFxqacgMG0vCaIKy5Hv+QLw1AsCr1rBlGsipZ7vD9O80ZO11Twc5tmuMTeW/4urOrmslufNRoUe7pr1v+GPRqrvr1L++u+TU4rx/q/KG7Qeelss8edLfN5AoCK9K1ex0ba1B77XdL29KDYrq0Bz7ltu8GlTasvA4DVHauhZZ8g1ph9xZJdnz0cz1TbpvwHnZeZ8j2l2HTS1tlbtu3srNHFWrt8Xg4rNgH7MHYSnijmzakVLVYR9KHMY8zAx7He4djAOt3COJfHfEGbnDaYx3N9Xk6639qfGH4eMRWd7IriE9urJrpv+zTmeJri09omGYgBuNhrjk+sMXPx6cwnTPl0bePT73Vebsr3Vv5Bf+mUHePtnLfH0SFvXFyaOi8N/W+WtMabAbw/jScE6AD4hZzzf0op/RGAX0opvRXAQwC+c4a6hBBiUSg2CSHaiuKTEGJXhC9nOecHAby68PkzAL55PxolhBARik1CiLai+CSE2C2H+KO/EEIIIYQQQohn2YvP2a4wOovIK4Y1aQVtgvc5ozrm9H+ohs0blPyPQi+0KK95Tt+zEecDF33OeCMuUz6waxLrWdiro1lkU8qJZi+0QeJc67gOaiRtwPuLN4lys1HwaTLrh0Y6ttNupBNujXtxkymzTxlryFhj5nzQTt5LLbAH1SkIh+6p7GzO50mDNqhtHnU9lUd9mLqOhZFsfHH9INKclXSfkVaBu04g44ziQqkrOu2U8zFr9s5yWlQOuIn1FnZxSaPG+tUoRns/N1usd8jnjzwanVZr2z9I+qfJg4e0cs57jb2L6DjrXrPmrASfB+4/7A/X2aQK2NOOZKP9jj3uTOdhs+Dh8/mB/axTWZ9Gp5cljdmXL1k9xgj3mzLHtlHhpjlLXmhPkP/RcGS1KPXW9I3sqhMtInp8hjraaOy0H9c/8oaMxqAcIzkeFoZW7CEW+bU5bTFrzoYcn6iJxYkMgjaw7naL2pCb49MoiE87vUJsGFxvyjUdqPOAJY2Zj0/NY6cSZzs2Pp0bXmXKAzrQemtKE7sAnzMhhBBCCCGEEPuIXs6EEEIIIYQQogXo5UwIIYQQQgghWsCBa84MnG8Z+Z4VEjSd91nkAcb+Xs4AjJoUaNCA2Att0Ro0zvUteVK4w3LnpaIy5da6vGnOi27WoBWaVDhu0qCxvm/BGjTAdyHO9+bzxF4doaaR87LdMftbjnVo91Y32jYEGjTWmLEPWnXS6jxKdClX+57a6uDOgfKo09TFqWcw2Go5aWRz5KtecEyRLgqxLoD7t9caNAcK52tVSo+PfH043pHXFmup2HOMWb5kG8FaCcDfM05DS+elpjqGy/bEpqE9ERyb3P4Ly+t+s8/PkD0ZeXng1cbaPq4P8OeB+8OQbH5q0nS467/ZLI4Zkq3ZqNB/+h17MR69eLUp316/xJTZx4w1ZuwzdDLZ5exTBABVsl5oF7dsw9fXbRtzZ+o4pTk70oSSbiJcfTePqkDin4JnwYiej7P4Ubom8L3J+wx0cH7sRLGGxtGluO18OTmOc9zesWWnqbWhwsenE+QNyQJqAAM6txyf/rB+qSmzjxlrzHx8+pwp991D1/u7sV/k1qbdJk+fW2nOhBBCCCGEEKLd6OVMCCGEEEIIIVqAXs6EEEIIIYQQogUcqubM5RMHGrRSvjDn6VekjXK5toFmKPIv4vzSyVa2TfusQXP5xDN4LHGqLG8zynweqUL2zWCfDDqqql9oFJ3s7E6+LfY5mZuPYV4NWmkVbkKf9hHki49Gc168wuq5sge2VlnvjfurG0y5k77UlNmLgzVmLyEN2hsLGrSVyh44e6F9htZ/unPZBy0dA81ZJp8zp+OMPMYKmiOOA9xfOUef9V1ON8pNYg+zkuYskMy6bYLYEmkZvG/gDH0jOC5XZk3Hkm2E8zmjNtS9wolywhG6p/oc4wP/y+Dala4VP1ucBo19hLYzlX2ddge2vgHV5+ItgCF5D611rSbjIfIg+4OO1YexPpY1Zi42nbIaEMBrbld7Nj4+SCd3s3+5ztJ9KY4voW9aoN2aiUDv5cexLDZuHlMUNWkujjbrU8M2EdnFP7+OkysHPp3s9ViTntm1gb0kw7EVkCk+bVyyeq/PJxuffq/zctsmajRrzDg+/anTn3Vt6KaBKa/2bIz8PJ2onan41RSf9MuZEEIIIYQQQrQAvZwJIYQQQgghRAvQy5kQQgghhBBCtICD15xNp19GFmKB1gooeCc4DzDagNd3Qo4gH3gGrcB+a9A4NzcXRGfOO8j5cdlixTnL3DNsWq33hyOqYeFEUc6x90Ij7zVaPlih4ybNjs8FL3ks0fVlnU+goXGaRfZNo2PkY+iw91CBfmUPbDXZvOfPUadkfRjDGjPOox7zUGMd7IP26eqWL/79eN28/6PC9LUKfWICz7LSNmGsYj1jpLGcwdevJg1lUZdmdtq8ONLwjLrs81fQMZFfl/N7G5L+tW8PvMONrOjEkP9X1bP9s2jBSDq1mjW4HHMpeI2WAk861hvOIHbh5wRLMLh/VBSj3Wki36Ha9fGSINZe8NHArvP0jl1+D3XyER04+5ixxuwV3VNg2Mexf6Otg3Ukn8qXY1PVPR6xSSyIWTRmgaYsiuPxPufToBWrjLwcqez0XMH4zQUbzPD84cNiz9hgLMW+aLOM53jMOCQDyUsUn+7lgS7BPmasMSvFJ1AM277JPtB+v/MlpvwZXI5PqXvl9uiXMyGEEEIIIYRoAXo5E0IIIYQQQogWoJczIYQQQgghhGgBejkTQgghhBBCiBZwqCbUEU6IWdIrB4Z/brKMyMCZK2SxZsm/lIXX+zxByCwm1G7ik0D87YxeuU5ypeaJVGYxm53JDNZs0PzdwYDPazBBCOBFpZndtoPDYLFuNSABPO00Ml4EgJqvBR32gEyqV2srSr2nutmUefIONpguTf7Bk4R000NUtrMNVFP7uKfD9R9NmoTdTgROy91kDIiNQHkeC75MHFdYYM2UTIjrreb4FYm8XbyLJnGiwNFhkTeAIU+qM+J7hs2VabKOHTomnsxji/pq3yrRR8v+sZecoXezM+yoS5MX0fbOpLpujrelbRKdqIpiV/9Mc/yr6DzyPmvqL8UJlKhfj3r2uAc0ecvqSWvAepZMqqv0MirTM+GkN6F+GcWmbz11tymfoplOpp+/T3aPR2wS+0TpeR9MAOImBYtMpN3y5glAIiPtEuEkIrRPPw7iCgtVRJOl8fo0gduQYyzFN64/miBkXAdN3LRjywOKX5dOWQP7sx2KT3SxeNzDk38AfpKQ+vSnTflMVXgwTzjXEJ/0y5kQQgghhBBCtAC9nAkhhBBCCCFEC9DLmRBCCCGEEEK0gMPVnAU+yZF3HzCD0StXGmmrovzhUj4wb0O5uHvWoEXm3CWtQOJ83matVag5o0bE580nQbvP+Dz1SeDijpMvti0OEp9X34ai0WpDnQ7W4DijRdKmUJtK2iRQbrW/VmS0WFmjxfOsQatvMuXIpBrwGrNbO1bn8brlR0156erLdf6nmlx/nwOwFiuVUsfZRJg1P9yXuE4qR17f9bbv713SnHH/4zax7skRGI2G91epyuC4o9iFDum/lmzZmTd3/XeSOThujsHzGs+yHow1aAAwXLHl5YtUJetG6Lw4LR6dx84ma36p/hmMZwcn+MBssbdsD+KJka3g4pZdvtqzGhA2mAa8xow1aN30IJUv3yi3d557sekoM4sB8952sPgqo/FZZAjNg6ey2TLV6TRkzeu7OqN5DArxjceIncD0nutgDayLT/T8YrlXKT5V/Pxapm2oETvn7djp3PAqU760yfHJamjZYBrwGjOOT9XJ++36N14+8I91Nl19X9zuikuEEEIIIYQQQhwYejkTQgghhBBCiBaglzMhhBBCCCGEaAEHrzmbTiudM/+3lFfLqbQuV9aJBZq9FZw/WLA9MIPPxV41aG6PjZsDmOG4OMeYfXhYD+PWb67fabNQ8vcgPQxrasgHzclCIh801kcAGDktXmMVXv/CXh2B/xX7JVWDWNfhvNG4k5MGbVBTHjVsHvVnqDr2QRt/ZhO8WWPmfdCe+OLfJ4uCqyNGAvLUfZc5n57vcd6+0I+czojKLqc+0C64NkQeZDPgY1dzJZFfl+vvRZ1c84Gxz1nVb24T3z9D0pSxP1ioqwOcv2XFcSC4Ft6jjs7bDE0IdW3EqEs+ac6XKOggM/hlsmaxJl+hzprtEEMSgayv25vgQToRv9d5uWsC+5ixxuyFpI/92pXL+tnTqWC0J1qL87YNPMDm9QiLPMjGKwXrRHE2mEvBPyvi2ODHGXSvc0CK4rrzEA6Ecr7KcIzpxpyss6WDKnkIN9bvq/DzPdDt31mnsdPIjp22Nu3g+/N0MX6/8yWuDexjxhozHjuNcDl+neEGTtdzxSVCCCGEEEIIIQ4MvZwJIYQQQgghRAvQy5kQQgghhBBCtIDD9TmLUuDjNNiCFxYtDzRozjMn8kkrJAQ7zwm3nD7YowaNKeZZUw5x6HvGx+A0ZYHPGZ/H0tViXQZr0FjnwduT9qTjhG3kd1TyCyEvIfZpcloR1v+x9iTyOAm8P4BCnjRJuJxfCKUp15xHnayu4+mO9UH7dHWLa0NFDZ32MQOsxgywPmhL6YKr70gy1b0ivY/XFvp1nIcYe+K5+4H2wX2T+gnfL2HOfokwBnO8pBWov9eBPgwAUqDj5ePynmGBZ09tT9xoyLGtEMN5n+Sp45YH20fXqhQfWQsXxX3WMBY9FKeXB3GG2wwUNB2RhGuNvNe27LXI5Em32bd6jE/lQmyiTtqlhk5rzADrM7R8XGLTc5TYv+tg2mEINGnRmCBcv0Ske2MPMDcO2buB3CxeaE3L59WUOU/O0jHQyXPeobzJJY5P9HyjGLxDPoyfgY9PzLSPGWA1ZsDs8Um/nAkhhBBCCCFEC9DLmRBCCCGEEEK0AL2cCSGEEEIIIUQLSKw12tedpfQUgIcA3ADg6QPb8e5QGxeD2rgY2tzGF+WcbzzsRuwFxaaFozYuBrVxbxz52AQoPu0DauNiUBv3xhXj04G+nH1xpyndkXN+7YHveA7UxsWgNi6Go9DG48BROM9q42JQGxfDUWjjceEonGu1cTGojYvhKLSxhNIahRBCCCGEEKIF6OVMCCGEEEIIIVrAYb2cveuQ9jsPauNiUBsXw1Fo43HgKJxntXExqI2L4Si08bhwFM612rgY1MbFcBTa6DgUzZkQQgghhBBCCIvSGoUQQgghhBCiBRzoy1lK6VtTSp9LKd2fUnr7Qe67iZTSz6SUzqWUPj312XUppQ+llO6b/H/tIbbvtpTSb6WUPptS+kxK6ftb2MaVlNJHU0qfmLTxH08+f0lK6fbJNX9fSmnpsNo41dY6pfTxlNIHW9zGsymlT6WU7kop3TH5rDXX+zjSxvjU9tg0aY/i02Lb2ur4pNh08LQxNgHtj0+KTQtvq2LTAXFgL2cppRrAvwDwpwG8EsB3p5ReeVD7D3g3gG+lz94O4MM555cD+PCkfFgMAPxAzvmVAL4WwN+anLs2tXEHwBtzzq8G8BoA35pS+loAPw7gJ3POXwLgAoC3Hl4Tv8j3A7h7qtzGNgLAN+WcXzM1DWybrvexosXx6d1od2wCFJ8WzVGIT4pNB0SLYxPQ/vik2LRYFJsOipzzgfwD8HUAfmOq/A4A7zio/c/QvhcD+PRU+XMAbpn8fQuAzx12G6fa9usA3tTWNgI4CeBjAL4GY/O/TqkPHFLbbsX4Bn0jgA8CSG1r46QdZwHcQJ+18nofh39tjk9HKTZN2qT4tPu2tT4+KTYd+PlubWyatOfIxCfFpj21TbHpAP8dZFrjCwA8PFV+ZPJZW7k55/z45O8nANx8mI15lpTSiwF8FYDb0bI2Tn7yvgvAOQAfAvAAgNWc82CyShuu+TsB/CCA0aR8PdrXRgDIAP5zSunOlNLbJp+16nofM45SfGptP1B82jPvRPvjk2LTwXKUYhPQ0r6g2LRn3gnFpgOjc9gNOArknHNK6dCntUwpnQbwKwD+Xs75Ukrpi8va0Mac8xDAa1JK1wB4P4AvO8z2MCmlbwdwLud8Z0rpDYfcnIhvyDk/mlK6CcCHUkr3TC9sw/UWh0+b+oHi0944QvFJsUnMRFv6gmLT3lBsOngO8pezRwHcNlW+dfJZW3kypXQLAEz+P3eYjUkpdTEOLv8u5/yrk49b1cZnyTmvAvgtjH/mvial9OyXAId9zb8ewJ9NKZ0F8F6Mf57/Z2hXGwEAOedHJ/+fwzhYvx4tvd7HhKMUn1rXDxSfFsKRiE+KTQfOUYpNQMv6gmLTQlBsOmAO8uXsjwC8fDK7yxKA7wLwgQPc/7x8AMBbJn+/BeNc5UMhjb/m+WkAd+ecf2JqUZvaeOPkWx+klE5gnNd9N8aB5i9OVjvUNuac35FzvjXn/GKM+9//l3P+HrSojQCQUjqVUjrz7N8AvgXAp9Gi630MOUrxqVX9QPFpMRyF+KTYdCgcpdgEtKgvKDYtBsWmQ+AgBW4Avg3AvRjn0/5PhyGyu0K7fhHA4wD6GOfNvhXjfNoPA7gPwG8CuO4Q2/cNGOfSfhLAXZN/39ayNn4lgI9P2vhpAD88+fylAD4K4H4Avwxg+bCv96RdbwDwwTa2cdKeT0z+febZe6VN1/s4/mtjfGp7bJq0UfFp8e1tZXxSbDq089662DRpV6vjk2LTvrRXsekA/qVJ44UQQgghhBBCHCIHakIthBBCCCGEEKKMXs6EEEIIIYQQogXo5UwIIYQQQgghWoBezoQQQgghhBCiBejlTAghhBBCCCFagF7OhBBCCCGEEKIF6OVMCCGEEEIIIVqAXs6EEEIIIYQQogX8/5M4RkzMvoDaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "vmin, vmax = -0.5, 1\n",
    "\n",
    "ax[0].set_title(\"Exact\")\n",
    "ax[0].imshow(covmat.correlation(), vmax=vmax, vmin=vmin)\n",
    "\n",
    "ax[1].set_title(\"Measured\")\n",
    "ax[1].imshow(covmat_measured.correlation(), vmax=vmax, vmin=vmin)\n",
    "\n",
    "ax[2].set_title(\"Tapered\")\n",
    "ax[2].imshow(covmat_tapered.correlation(), vmax=vmax, vmin=vmin)"
   ]
  }
 ],
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