{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "![Correlation Plot](/images/Correlations.svg)\n", "\n", "# Uncertainties\n", "\n", "Here we discuss the python [uncertainties](https://pythonhosted.org/uncertainties/) package and demonstrate some of its features.\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The primary purpose of the [uncertainties](https://pythonhosted.org/uncertainties/) package is to represent quantities with correlated errors:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:45.981920Z", "start_time": "2017-09-12T23:18:45.893094Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "1.0+/-0.1" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import mmf_setup;mmf_setup.nbinit(quiet=True)\n", "import numpy as np\n", "import uncertainties\n", "from uncertainties import ufloat\n", "x = ufloat(1.0, 0.1)\n", "x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here $x$=`x` represents a quantity with nominal value `1.0` and error `0.1` in the sense of one standard deviation. I.e. we assume that the parameter $x$ represents a normally distributed [random variable](https://en.wikipedia.org/wiki/Random_variable) with a Gaussian probability distribution function (PDF)\n", "\n", "$$\n", " P(x) = \\frac{\\exp\\left(-\\frac{(x-\\bar{x})^2}{2\\sigma^2}\\right)}\n", " {\\sqrt{2\\pi\\sigma^2}}\n", "$$\n", "\n", "where $\\bar{x} = \\braket{x}$ is the mean of the distribution and $\\sigma^2$ is the variance.\n", "\n", "Base quantities can be combined in such a way that the errors propagate forward using standard error analysis techniques. This propagation of errors assumes that the errors represent 1 standard deviation of normal Gaussian errors and that the errors are small enough for any functional dependence to be well approximated by a linear relationship. For example, we can demonstrate the following simple rules for adding uncorrelated errors:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:45.988047Z", "start_time": "2017-09-12T23:18:45.984158Z" } }, "outputs": [], "source": [ "a = ufloat(1.0, 0.1)\n", "b = ufloat(2.0, 0.3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Addition**: Absolute errors add in quadrature." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:45.995306Z", "start_time": "2017-09-12T23:18:45.989950Z" } }, "outputs": [ { "data": { "text/plain": [ "(3.0+/-0.31622776601683794, 0.31622776601683794)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a+b, np.sqrt(a.s**2 + b.s**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Multiplication/Division**: Relative errors add in quadrature." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:46.002321Z", "start_time": "2017-09-12T23:18:45.997007Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.0+/-0.4 0.36055512754639896\n", "0.50+/-0.09 0.09013878188659974\n" ] } ], "source": [ "print(a*b, np.sqrt((a.s/a.n)**2 + (b.s/b.n)**2)*(a*b).n)\n", "print(a/b, np.sqrt((a.s/a.n)**2 + (b.s/b.n)**2)*(a/b).n)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Powers:** Relative errors add in quadrature weighted by factors of the square of the power." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:46.009985Z", "start_time": "2017-09-12T23:18:46.004385Z" } }, "outputs": [ { "data": { "text/plain": [ "(0.125+/-0.06155536126122565, 0.06155536126122565)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a**2*b**(-3), np.sqrt((2*a.s/a.n)**2 + (3*b.s/b.n)**2)*(a**2/b**3).n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Correlations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One great feature is the ability to track correlations. Thus, if we $c=ab$, then the errors in $b$ and $c$ are correlated." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:46.017236Z", "start_time": "2017-09-12T23:18:46.011898Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cov(a, b, c):\n", "[[0.01 0. 0.02]\n", " [0. 0.09 0.09]\n", " [0.02 0.09 0.13]]\n", "\n", "cov(b, c):\n", "[[0.09 0.09]\n", " [0.09 0.13]]\n", "\n" ] } ], "source": [ "c = a*b\n", "print(\"cov(a, b, c):\\n{}\\n\".format(np.array(uncertainties.covariance_matrix([a, b, c]))))\n", "print(\"cov(b, c):\\n{}\\n\".format(np.array(uncertainties.covariance_matrix([b, c]))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These correlations are described through the [covariance matrix](https://en.wikipedia.org/wiki/Covariance_matrix) $\\mat{\\Sigma}$ which generalizes the variance $\\sigma^2$ of a single variable:\n", "\n", "$$\n", " \\mat{\\Sigma} = \\braket{\\delta\\vect{x}\\cdot\\delta\\vect{x}^T}, \\qquad\n", " [\\mat{\\Sigma}]_{ij} = \\braket{\\delta x_i\\delta x_j}\n", " = \\braket{(x_i - \\braket{x_i})(x_j-\\braket{x_j})}\n", " = \\braket{x_ix_j}-\\braket{x_i}\\braket{x_j}.\n", "$$\n", "\n", "In the same way that for a single variable the interval $(x - \\bar{x})^2 < (n\\sigma)^2$ describes the $n\\sigma$ deviations of a single parameter with 68.3% of the values lying with $1\\sigma$, 95.4% lying within $2\\sigma$ etc., the distribution of the $N$ correlated parameters is described by the ellipsoid\n", "\n", "$$\n", " \\delta\\vect{x}^T\\cdot\\mat{\\Sigma}^{-1}\\cdot\\delta\\vect{x} \\leq n^2, \\qquad\n", " P(\\vect{x}) = \\frac{\\exp\\left(\n", " -\\frac{1}{2}(\\vect{x} - \\bar{\\vect{x}})^T\n", " \\cdot\\mat{\\Sigma}^{-1}\\cdot\n", " (\\vect{x} - \\bar{\\vect{x}})^T\\right)}{\\sqrt{(2\\pi)^N\\det{\\mat{\\Sigma}}}}\n", "$$\n", "\n", "The matrix $\\mat{Q} = \\mat{\\Sigma}^{-1}$ is sometimes called the [precision matrix](https://en.wikipedia.org/wiki/Multivariate_normal_distribution#Notation_and_parametrization) which is equivalent to the [Fisher information matrix](https://en.wikipedia.org/wiki/Fisher_information) in the special case of Gaussian errors.\n", "\n", "As shown above, for any two variables, one can plot the corresponding covariance region by extracting the corresponding sub-matrix. Here we demonstrate this covariance region to show the meaning of the errors reported by the uncertainty package:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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s3V9Lc2RopaDRLEGCOGVXtY1U0Axi2nHKgxMtHrGuQk9et1rRPHy0+0ijWYJMNEOkgslWCAjKno1lGNwzXCOI026Lp1nCaEtBo1mChImkGcQ4poltZXu7nGPS8CUTzZD1vfmDXOHhsZhcVhO7tvLqCz/BdfIMQM94OFpoS0GjWYK4lkE7TrFMMXMskYq8axImC1NwONtllXdMpIJd1XbXLJN+UedR4oGu3Hs5o5WCRrME6S+6CMCPUpRSxKkkSiRF18a1FubPeqIZ4lgmjmUghMCxDBzLZKIZLsj9DoZCUBGtrtx7OaPdRxrNEsSzTR6xrsI9wzUaviTvmvQXHITIFMZCECaSvLO3q8g2Be2oO5aCMC3e+pgKb71Au42OJlopaDRLlJ68w9mb+46Zj9+1DOJU4VgPuaziVC2YZXJQSuvgka/ozr2XMVopaDRLGM82FyyoPJf+osuuahvILIQ4VURJeszuvw/5Pjjuqd259zJmwVS8EMITQtwohLhdCHGXEOIj85zjCiG+KYS4XwjxWyHEloWSR6PRHBnTCsgQ0I5SDAHre/PdK5iTCey4oTv3XsYspN0XAk9XSj0KOAs4Xwjx+DnnvBGoKqVOBP4Z+MQCyqPRaI6QacVw/GCxuwoBoD0BX3o2RO3uybAMWTCloDKanW/tzmvu8IYLgK90vv428AwhhECj0WgOhtmp3K5u664cy4wFjRAJIUwhxG3AKPATpdRv55yyHtgJ2QQ2oAb0L6RMGo1mmWB52b9j93VXjmXGgioFpVSqlDoL2AA8VghxxpxT5rMK9hkFJ4R4ixDiZiHEzWNjYwshqkazbJguMntgrNnV4rKFYPZaMD7VAGHA6D3dFmtZcUxyyZRSU8C1wPlz3hoCNgIIISygAkzO8/OfV0qdo5Q6Z6WNJtRoDofFVnV8tJm9FgwMroKBU2D37d0Wa1mxYCmpQohBIFZKTQkhcsAz2TeQ/APgL4DrgZcCP1dLbWi0pmuEcUq1Hc3k6PfmHdwV3jp6dtUxMFNTMFxt49rmouhZdLS4c1cNnvfvkNce56PJQloKa4FrhBB3ADeRxRT+WwjxUSHECzrnXAb0CyHuB/4G+MACyqNZRoRxykjNRyrIOQZSwUjNJ1wmO+KHS5hIbHNvr2wqJTsmj8x6WLQuqS1PhlWndVuKZcWCWQpKqTuAs+c5/rezvg6Aly2UDJrlS7UdYVvmzAKYbXpNqu2INZVcV2XrJvNVHY81QwqutY/1cKjdVKcVgmOZ5B2TOFXsqra7n5IKICX8/ttQGIQTntZdWZYJuiGeZkkSJhJrznpkmSxYh9ClQn/RJUpSokSilCJKJK0gYbC0dz8k2xSH/LtabI3wZrPlwqvZ9u0Pce2XL+q2KMsGrRQ0SxLXMkjmeDCSlO714VlADsd1M1/V8ab+Aqax9+/lcHoWzeeSOpBSOdaupp/Ic3iCcRcEtQW9z0ph+f0FaVYEvXmHOEmJU4VCEaeKOEnpXWajKA83m2i+ITjrenL7WA9Rkh5yN9Vpl9Rs9qdUupH9dFX6OFyRwN3fX7B7rCS0UtAsSVzbZE0lhyHAjySGgDWV3JLPPpq7yx6e8vdy3UilmGxF3Lajus9iu78FGTiinkXTLqmGH7N7qs3WPQ2GJlsU3H1Dkt1wNd2uTmCrXMvNV/zrgt1jJaGVgmbJMq0YNvcXlpVCmL2o75hokUo58/5IzccUgjhNGa753LB1nAfGmjMWwtwFWSq4a3iK4SkfgHU9ucMOEHu2SX/RZbQR0IpSco7JQMljohnuYwEcrqvp6CC4PH0GJdoQNhbwPisDrRQ0mkXCfIt6wbMYa2S77GorwjFNIimp+SmWYVD2bCaaIbuqbep+vNeCnCmKgDCSR+zKaYUJG/sKnLiqxLrePOWcPa8FcDiupqPJV9NncX50MbilBb3PSkArBY1mERDEKTsn2wxPtRmp+TML92DRpRUmRIkkTFKCJOGPIw3CJKXaipAowkQy2Y64f7TBzlmLfrUVYYhMsRypK+dQLYD5sp+iJKXgWgsafI6xUBic+YFvQX33Ub32SkMrBY1mgTlYNs70+6YhsI3pQryAIE4xDYPVJZfRhs+28Rb3DtexLYO+vI1S8OB4i7FGiCkEPXmHsKNc/CihFSVIpeiZFXx/uK6cQ7UA5st+6i+6TDTDBQ8+m6Rc7X4ArnrPUb3uSkMrBY1mP0xXTT840XrY1dL7C/5OtaMZRXHX8BRSwaqyRywlqGzxHm0ENPwIKQSrSjmO689TyTuEiaQdpyCgGaZYBggEJc9mY18B1zIYqQV4tsHAnHYWD9eVsz8LYL4MprkzF1phckyCzykmlydPh/uugq0/P6rXXknocZwazTxMKwTbMjEEjNR9to01WdebZ03Z229Qe25KaBin+/QiCuOUu4drbOwrkHdMRqYkE0nA2p48ayo5qq2IKJEEcUqaSFIgTiStSJJzTCbbEfftrrN5oIhUkj31ACEEJ68u4dkmG/vytKOUvoLD3cM19jQC8rZJ0bNnMo8Ol+mFfqIZ0o5SXMs45IB1mGQxjdnYpqAdHf001cvS5/Iy8xeIr7yV86OLCciU1vaLn3fU77Vc0ZaCRjMP0200pFKMN0Isw6DoWlRb4X6thnmzhybbM9lD0zTDGAUzO+eCZ2EIg2orwrNN1vbk6Cu4OGbmSiq5FkGcsm2sSZhIThgosL43z1Q7Io5lJxvIpdqOCeJ0xs0z0QxZVfIoOCZ+lDJcbROlkuEp/2G5bw40de1ALjLXMmgECbunMqtr95RPI0gWJPgc4vDB5M1sMfbwAevrR/36KwGtFDSaeZhuo1H3I2zLwDINbMtAAbaV9Viay7zZQ67F2Bw3STtMyc9aUHvyDlIpWlEy45oZawQMljwKnkWqMv/8QMmlFSSEicIQsKrkMVhyM5eRac64nKIkBaVwLJNSzmZtT571fXlM06AZJBgChqc66ayjjSP27R+sYK3gWgxNtogSiWcZRIncb53D0eAG+QguS57DWjGJySJp3LeE0EpBo5mH6TYaYSKxjCzrJkkVKKi2AraNNxmp+dkC3GG+DJ3BzkI+7Ytv+DETzZApP2b3VJZl5Nlmx/dvzARne/MORc+iJ+/QCGKGpto0g5gwSfHjBICcbTBY8djcX0AIiFNJO0wQwM5qm4lmMLMwT7Uj8k7WOntPPcjSWXM2E53YxpEohoMVrE2ns7q2QZBIXNtgY1+BVpg87HsejH9IXs3/iv83KZny3fKBqxbsXssNHVPQaGYxPaOhEcTU/BilIDYkApHt5AEwKLkWUsGeuk8uny3s83UojVOFZ5sMTbaIU4WUkuNWFWl2FMXuqTb9Ra/TosPt3D+k6Sc0o4SKZyMQOKZBEKV4tsVAwcF1LFDg2saMy6nux4w3AmzLpOzZNIOUoWqNnrxFzU/oy9v4cULB8TKrRymSTszjUDumzvs7O0jMIEwkRc+ilLNn3ldKLUhMYZppZbBBjPF+6+t8KH7Dgt1ruaGVgmZZcSSDd2YHlyt5G9sw2F3zmYwSKjkbx3zIsO4puNimQJrZgtpfzBb0HZNtCq7FYMklThVDky029hUoehY7q23CGEqeTcmzmWpHtALJWDOgknOQUlHzYwwhQECjHTFU9VlTdtnSX2B4ymddbw7HMPDjTKn0FQoolfV+GmsE2e6/GVJtx2wba9JTsAljgUKxs9pmoOBidayZRGaZSIca9J2vr9KBlOF0zOBg7y8k6xjnWcbNrHKmIH4B2Cu3rfqhot1HmmVBGKc8ONHi1gcnGan7GILDHrwze0ZDlCjacYJtZlZBb94hSFJsUzBY9mYWNMsU1IOEXdU2tmWyZaAAAraPt5hoBGzsK1DK2QghUArytjUTUF5TyXH8qiIGgrJn04oSXNsk71qUPYdizkEoxUQzO/+M9RVytkksJaZhcPbmPnKOOeNyyrsWzSCzbgD6Sy5+lDLZilhVdOkvugSJJE4kcSqJEklP3jmkBfpAcYODpaseTjrr0eZGdRrvjd/KY8R9/Pyj53PSB3TTvIOhlYJmyTO9w6+2QoquhWUYjDdCpFL7DQrPe51OcDlMJGP1AKmg4GahyiDN6geGqm3+MFJnaLJNmEiSVNGO4hmfes6x2NRX4IRVJRCCoveQMe5mBQVE6UPZSHGqUEphm4JGEDPZDBmqtplshUSJZHN/gYJrIQRM+TEA/QWXjX15evLOXtlAqZQYIguIR+m0S0cQJlnQeUNvjoJrUg9iEilZXXYxhDikBfpAcYP5CtZmZycd7P2F5kr5RP5P8gaebt7GZ+1PQdL9ORCLGe0+0ix5pnf4WWaQASJzU9T9iIGSix/tW8E7r5upE1weawTUOjtuISBvGYzVA8YafmcRjxlrhgxPtUH5tGSZyXLE5v4ClU71sG1m9Qg7q22UyhRCzjYZbYS4HX9+nCqiJGV1JUcjSJhqx1iGgWcbBLEkiCPyTo6JZoBlZIv3sJ+QSsWTTh7c55nytkUtiYnTbEe+a8rHMgwqnernXZNt8q5NJe/QjmL8KKWcO7R6g4PFDaYX/v1xsPcXmq+nz8BE8mrz5xC1wFp4K2WpopWCZskTJpKcY+CYBkmqsCyBZQj8OJ138M7s2EHOyRTBSM0n55psG2ly32idvryDbRo0w4QgSbGAWCk29BXxw4TxZsjW0QZnrrNYW/bwY8nvd9U5Y32ZSt6hGSSEiaQ62cYyst27bRr05i0qeXevAjCAWx+cpCeXZRoFiUQqRTlns7Pa5rjBIiNTAQoo5Wxsy8jiBXlnr8W8nLOxTYNWlBBEElMY5F2TME7ZNt5ktBFyyuoiWwYKWIZgrBHM/Gz/nMrnuXQzLnC0+Fp6Ht9Mn0b80etxiSgQMEl55n1d4JaxdD5RjWY/TO/wK3mHOJUkHZ95kiqGp9o0gniv2MLs2IEgm1Gwpxly09ZJ6mFM3rZoBAk7qz6lnE3esRlphMSpwjIEfUUXhMKzTMabEbFShHFCPYi44YEJdky22DbWxDQFa3py5ByTKJXU/BjPtjh+sMi6nizgOTzlM9EMyTsmRS+rK7AMQTlnUfIs8raJgWBdT54tA0VWV3L05h2UYp82Ef1FFyGgr+Cyrtdj80CeqVaCaRqkSrG24jHlx9SDmMlWVpAXJukBexFNxxLqfszOyRZ1Pz7mcYGjSdzZB19sf4ErnA9zkhjqskSLD60UNEue6SlshhAMlFwSKZlsRSSpZKDgUsnbewWdw0SSyqxAbNt4k3t316m1QmxbYBoiyzyyDPqLDmmqsA1BlEgqnkMjjIkTyZ5aiNPJ4plohNw/1qTmh9T9CBSMt7K6gKJrs7qS47iBIpv789T8eN6gbTtKKbo2J60uceaGHk5aXaa/6NFXdGjH6UzGEGRZQ3nX3Kex3WzfvZSKVpRy+oYyJ68uU/JsCo5F3rF4cKKFY5odZaX224totpy9BYdVJY/xRkC1HR/zuMDR5ivJs/FEzHedi3iGcUu3xVlUaPeRZskzPWyn2o6IVTaBrTfvzFgDYSKp+xHtMKUWRORsi2o7Ju+YNMOYuh+zuxawpuLRV3DJMk8TPMukHaf05mzW9eZIZEoQQppILFMgyVJH/TilL+8QpZJyzmFV2ct21+2EkjdrPKjK8vNnB20h64c0WPIYawS4dibzdLzhhMESdw/X8DvDbRKZ7dL7C868rptpxdBfdLlh6ziOkcUvDATtOGFdT46haps1ZTGTkgrz9yKaK2cpZ+Pa5sPun9Rt9nEP1V4C33g1l+2+BJ76PpDng7E0ldzRZMEsBSHERiHENUKIe4QQdwkh3jXPOecKIWpCiNs6r79dKHk0y5u5U9gQYt5MojBRjNdDoiTtvBdiCAPPMkhTRZwkhEmCYUDONenJ2QgBG3ryJFIRxCmtKOX4wSKxlISRYutog61jTYZrPv0Fhz/sqaOU4sGJJo0gc7fEiaQdJ6yu5OatfC55Fj0FlziVbOv0DxJki/wj1lVIpaThxwgUBddktBFQ9+P9un0822RTf4FUKfw4pZLPqqOlzKwTP0pnUlJh/vhAd6aoHUMqG+ANP4KzXgM3fRFaY92WaFGwkJZCArxHKXWrEKIE3CKE+IlS6u455/1KKfVnCyiHZhlxqMVp03GG2b02XwhsAAAgAElEQVSLkkSSt018BZ4BjTDGFAaGAZsHCky2ImzLIkkSSo7JyFSAVJKSZyM7vYQKjkXJs8k5WR+hassHBaYhKDomu6ptBksea3pyJEoxNNHCsgSGMKh4Fn0Fh8lWxM7JdtYUzzToLTgYQsxkJW3oK2TurWbIjsk2m/oLnLauQitMqAcJU62s0V3Rs4hTxa5qe15XzrqeHKojt20KmkHCWCNgVSmHHyUMlrJ6i+n4wNzd/3IILh8UOwcXXAr1D0JpDUgJQzfCpsd3W7KusWBKQSm1G9jd+bohhLgHWA/MVQoazSGxv6yh+eYz9+YdRmo+7TCl4JozwefBsgeEtONssc/bJg9O+kw2IyxLkKQprVhx+voyuUmfKT9hpJEVw5UcC9OEHZMtwjilFSYMFh0Ge3rY2Wn4tqvm005SEIK+gstkZ/rZ5v48RddmuNomSOVMiqeUip2TLQpu1oICCZYlCGKJYxmEseTOoSnKOZs1JZcpP8aysmymrF6gE9eYp03F3HbXOcfk7M19eLY5U518oDbY/UWXXdU2wF4uraXoOoL5+x9tv/h5Wd5xZUN24LavwQ/+Gh7zJjjv78FZms96JByTmIIQYgtwNvDbed5+ghDidmAYeK9S6q5jIZNm6TE7awggW8Oy4rQ1lb3bF0y7k2pBRDPKupJOVyIXHBs/Dkmk6hS8mTQjyJlZ8HZN2aPejmn4CX6csLrk4lgGtXbMHQ9OsabHo+jaxIlk+0QL22tlbSzGW0y0IhrtmCiRtMKUsmdy+toe1vZki8uOySwQvbEva30dJpIoUYxMNUAoenIOQVsSxBK7k1pbbYbsnmqzbdxkc1+BXttkpBMD8ToxiHaU7rcNxXyL+KHUDRzJDIUly5kvh7H74PpLYes18MLPrjirYcGVghCiCHwHeLdSqj7n7VuBzUqpphDiucAVwEnzXOMtwFsANm3atMASaxYr0/UIs7FM5i1Og0wxnLK6MmNdpFKya6qNH2ZtqLPYApRyFmsqHqmEXVWfRjtk20Sb+0ebBHHCaWsrbOwvUG1HBKmkFqaUgMEeD/DY3Uroy3m4rokXmTTDlDiR5CyTup9w6/YJip6FY5sMTWaxgrAzRMcQMDTZzhrdFV2iRDHeDDENQRADCMI0pb/g0opSdk35FFwL1zaZ6ijDOFWgMjeSY5nkHXMft9L+FMbB6HbR2VxmrwVmed8CviPG9uDZH4eTz4fvvx2+dD6c91F40juP/r0WKQuqFIQQNplC+E+l1Hfnvj9bSSilfiiE+KwQYkApNT7nvM8Dnwc455xzFJoViWsZtIKUdpQQpRLHNMg7FjnnAEVXHYthpOYzPOWTc0w29OUxDYNxEXLauhJhImmGCSO1gJofcveuBiBIkgQ/TLl+2ySjzZCGH9FTcMjZBiXPxg9TGkGEYxkMlGyGa1lMoLfgZCmsOYsggUaUzU0+aU2JyXZEnEiEIfBsk7F6QCtMMEwDzzEJk6z19Y6xJqmC3qJD0bURhqCYszCEYLwZsq6SI5ByJh4gRNZJdXZGEzDTrO9ACmMpMXstcNeedMRrwYFaahe4iA9al3Plf0f89sqrEEjUrNyc5VrstmBKQQghgMuAe5RS/7Sfc9YAe5RSSgjxWLJsqImFkkmzNKn7Edsnmow1InZMtujLu5S8LL/fNAz+ZHPvAX/etU1c22TzQHGvbJqcY9IIEwaKHmEssQ2DHRM+sZQEUUqtHdGKYlIFdw1H9OY8yvksFmkZBrYpCRKJaUOUwmDRQcrsOrFUFFyLZhhlWU+pZLIZU7QNhtoh2ydSNvbmCZKUFEXJswgiSSVvsaeWDdxxXZO+vMNkp3fT6oqHZ5k4liBVCqWYSQ/dNt6i1o6IpZoJXrtWNp9hvhRYmD8OoXmIFjk+lLxx5vsLrcvpEw0+Fv851VmV0MuNhbQUngS8FrhTCHFb59iFwCYApdS/AS8F3iaESAAfeKVSSlsCmhnqfsTvh6bIORYChYFi52Sb3nyWM++aBnsaAeWcc8DrzOd66i+6DE22GSfAMgVRKmkEMWGcZou9YWAIAylTmu0YxzB5YDQlDFMQimaY4Ecxa0oWG3o9+go2U0FMmirWVDwMA4JY4VqgpKIVxXiuRV/BxQ8T/EgSJCm9OQfbMPA7dQL9RY+zNlmZG0pmcYYwSUhTRS6fZVL1dZrhTbuGplohpmFktQypYqTm01dwZwbrHKsZycuV7Rc/D665HX51CS8p3pW5lKQEYxllYnVYyOyjXwPiIOdcCly6UDJolj7bJ5rkHIuca7FtvEXJc4lliATW9+Tw45Q/7G6wqbcwk4E0bVm0OplHW/qLREnK1tFG1j3UttjQm8NzLNb15hlvBCgBZlaLxmQrwrNMEpXt9qcCME1B3jUZLDgM1wMSFKuLLut684zUA3585wiPWF9ibdFjx1Sbph8TmilBnBBEEFWyltWek6WRKiBnm7h2jjBKM0shTplshni2wVkd6+ePIw2UVMTKorfgEMaS1SWPdbNcPxPNkMGSx0QrIpEKyxTEadbb6NGb+5hohss/tfRY8LQL4fQXwZXvhh+8A373tSyddWCfMOiS5rCVghDiBUqpHyyEMBrN3DqEqXaW9gkghKAVxuQskzDN0j4tQ2Abgmo7ojfvsGOiye+H63iWgWsbTLUzSyORCoEg55jUWzH37qmzquRw0qoSqtPSuREmDBQcHpxoMuWnRGmKgSBB0pezEcIgSgWVnEXZtQlSSZTGpFJRDUPGGg4nrCpjmoJ79zQYa4Ss63HZ0JNHCLhp2wR516ToOvTmLfw4IYwlqyoepiHY0Junr5hQ9hzKnSllZ2zoYbQekErFxr78vAHi6clmtpU9rx+nOJagZGUN85ZbamlXWXUavP5quP1y+PnHOMi+d0lyQKUghHjx3EPAZ4QQFsB8wWPNyuNIpp3Nvc7cOoQwSqgFBj15h568xVgjwDHBtUySVBKmksGyy0QzYNtYk98P1YiVzGYQexYDJZdd1QAh4BHrKgxVfabaIVKqrF8SBkGSMtGIWF3xyLlZAzw/jhAIgjil4NoIw6S/4NCKU9JEsXvKBxSrK+CZJlGiGKr6CCGwTcGWgQJb+vMoDAyh8KOUVGYN9db2ZMVjCEEpZ2GbgkfPqh/YVW0TdaqJDSHoKzgHDApPF5lND+4BiBJJZ7T0ykwtPcrsG5DuxeYTxJ+8D7iPj1mXcaM8jX/5+MdmWrcvVQ5mKfwX8D/AKA+pxALwfEABWimscA6noOxgzFeHsGmgwP0jTQwESimCOKHaTDl5bRmpoOw55F2Lu3fXCUPJlB8hkBhm1qMnSrM+RWmiuH9Pg3qU4AcJUklG6yHjjYg1lawO4cGJJo0wwbNNBvIGZthi58QYYZpgeB64a9nQv4qRWkDVjxkoOkgZcf9ki4JrEETQDBOO6ysiLJEFnhVMtiNcM+uu2o5SHMugN5/DMg0quayV9uyBNP1Fl3t319lVbeNaJicMFg74ezsUS2CxpZYuB6Y7rhbweaTxAK+xfgZfvg2e98nMoliiHEwpPAG4GLgJ+LdOltC5SqnXL7xo86NURKv1h27dfkXh+9uwrAMvJGONoNPoTRDHnYNSsacKgyXvsO7XbPt4liCKH9ppFUzFmmLARDPrenrygCCOU0xqFE2XsuswPhXQbrcouyaDuZhqK8ISApWY+Al4QtKQKVPNlB7PIlQBDT+h4tkULYex0RaNkW2M7dhKdc+DVHcP0WpM4eXLGG4ew7Jpq4Rf/rRBmsQMnHAGg2c9g3x5I0kYULZDSo6JYwjqfopnlohiSRplGUBp4OMDvTmbwbzASCeZrKVU8g7lchEPk1ZreoefsqPaIgpjNpVNEDBWk0SRyaa+Io5lEiUpU+2IKMmqnnvyDn0uTLUj2p1jfXmHNDJpHdrQOc0R0CLHC6O/55XmNfzD6Hfhc0+Cx70VnvZBcEvdFu+wOaBSUErdJIQ4D/hr4OdCiPeTWQhdQymJZRW7KcKKwTTzmOaBd6mJEni2gZjlW7VNRRBLTPPwdqaGgLFWNvHMMbNaACEEpm1y6tr+GQsiSiSTrRCpIOd6xA1BnKbUQgNl2EwFklimQNqxJByUUECCL02CSDK5czsjQ/ewZ+ud1MZGGNh0Ir0bTmDDGc/g9Gesxyz2USl49ORdxlsh47WsqZ4KqkzcdxO3feNS5AveTHnjFpTI0Y4FbQXCBMMo0lM08GOFn0AkFSXPxXOyWc851yRKY2p+StW3GSyXsKwsbjLe8jsuqzxWJxBsmJIgldRDh17TYazpY1tF8jmySXHNlDWVHOv6tDvoWLJvncLzof0h+NlH4I5vwlPf2xW5jpSDBpqVUhL4tBDiW8CnFl4kzVIim3Y23XIiI0mz4wcjjFNqfjwzs3iyHTHRyIa/mGbWVqKUM/HDlPE0wDaNmQCsaQiCMMl2za2IopNV+E74CUEsaUUJiVQUHRvTEPTmYOvWu7jhpuvYfd+t5Mv9bDj1bM5+3uvIr95CpeBhG4JWJKm1IzwlaIcpzaBFK0qwLcGqoofjFjj9+C1sPvFU/vtLn+IJb7mIySDAMAwKrsVxAwUmmiFb+guctKHI/aNNplqgkPTnHSoFh11VHz+KcCyTZpBww9bxmXbXjTBBKfaan2AZgjjJAsqH0+pD0wXyffD8T8MzPwK5HpApXP3/wWPfAoOndFu6Q+KQs4+UUsPAyxdQFs0SpJKzO2MdTSwzUwhJmu7lOpq9+DumQaWzsI81AizTxLMNdk76jDdC+go2fqclgx/HlHMOa8s5TFOggOGaj+h0/iy6FuPNiFaU4IeS0WZMlCQYQpG3LFxHEE7s4Nof/oIH77iBgVVr2XDG4zjnWS8hVxkkTFJc26DgmCipaMYSA0Vf0cEUUPUzN1TZtbAsk0AqCsKgGUbk1p6E7Xo0xnYjy2spOxaVnMNEK6LkOtSCmFYY05dz6M07OFY25W3HRIuyZ5F3cziWgVQKIQS7p9rkHYt6O0IqRZIaWJ0U0kQqhJEFlA+31YemS+R6sn/H/wB3fhtu+UrWKuMp7130TfYedp2CEOItnZJzzRLhaGUJzca1TQZLXmeiWLboD5a8meuGcTqz+BsCxpoBOydaOHY2q2B6x9sKE3KuSTNMaIYphiFIJYxMZZO/ojgl75hU/QhTGKypeKwpe0y2QvrzLkORT94xaPgpKvEZuv06dv3ul8RxyPFnPYXz3nYRZ5x4POWcza5qm5GpgJxlUMrbeKZJKFMGXJu8azDeiJhsBqzryVHJOQxNtLE6qTyxlGAI4iQFYQCSTX0FTATNMEEI2NxvcdraCs0gob/skrMNhqo+rSAhSlNGGwmD5RyWYWAZgpwtaIcJ7Sihv+Cyu+bTJiGnsphC3Y8xhKDRKZZT0qHgPfSnO98cas3Cc6AWGbPp5x+50L6cl/zqkkxB/Nk/w4nPWGDpHj5HUry2tPOuVhhHM0toLq5tsmo/16j5MZZpopTK2lObBnlXsKvaptoKKeUc8rZJnEoskTWk6y+6GAJqrYgUiOMUpWC0HuLHCVJmQ+3vHWmQsyw8z6TgmjT2DHP3D7/Pjt/fyLpTz+ZRz30ta48/Dcc2qbZC7httsqHikirFmp4cFhAjSRSsLnuM1kOiSJF3TNqWRdwZyFMPExphTJiAI8BxBDIKCaYmWLd+A6FUCEMgBJRzNn6UEiuJVNmM6DSFkXpAKlOSRCIRDBQ9klTiWRapAq8zx3nQMxmQLo5lMt4IOqmlgjWVHAXPxBKC4ak263ry5D2TJIU4SbXraBEzQYX3xG/jJW94P/z3u+Hq98PbbwBzcQ6+fNhSKaX+39EURLOwLLQvem58AKVACPZM+VkRmZ9gGIKevE2cpIzUQ4qdFgxrKjlUqhhuBjSjBCcwaAdZcZprQqJAougpOrSnEizLZKoVE0lJU8TccP1NXP+jK6hP7OG4xzyTp7z1Ynr6ejNFWA8puCa2ZeIaMNoIOX6wNFMrsG2sSaoS/FBQ8Wx2T/mU8y5rezzuH20w0YoZKNrYpokfx+xpx+Qik6l7rqNn0ylIYVH3Y1BZ2qdUCj9STDQiojSl6ad4jkDJrBDOEII0Vfx+Vw3HMtjQm6dSsBksejPxmZJnz0yRG6n5SMXM51b0LNb25KmHEcJwcS3jqCh2zTHguKfAW38DjeFMIYRN2P4rOOU53ZZsLw6qFIQQzwZeSDYgR5HNPfi+Uup/Flg2zVFkIX3Rc11Ee+oBIOjN29SDGOULTBNs02S0HjDZjMg5JqGUjE+02DHZwhCCXZNtevIOE4QEoaTgmliGIExSDGBPO2KyEVPJWUxGMff89lp+d80PcHN5Hn/eBfSf/GhakaLajhit+RgGSMPAVQb9nkUQyywYnQuQqOwenoVhQDuQ+HFmmfhRnM1ejhRlz6bhp0QqwTGy6WkySXnguqs5+wVvICFrq5Eq2JjLEcQpnmNz3+46GIKenE3UVuTcrI1FLUwZKNokqeq0tYgwDUHZS+nNO/vs+uf73AqeiWG4bO4/cGaYZnGxt7vpHt5m/oD329/g++kT+XD8euo89Hl2swPrwSqaPwWcDHwVGOoc3gC8UwjxHKXUPnOXNYuT6fGUc7OEjtQXHcYpW8cbRIkiZ5nEUpKzs/9WI7WA/pJHtRUSxBLXMmlFKXU/or/koZKsqVzONgmiBMfKZgcrwDLAFAIhDGQKiZI0gpSKq7jrNz/itp99n/Kq9ZzxnNdx3GlncsKqEltHmwRJkjWxIyFKIScUUaKoBTFBmGKbEMaSiUZAM5CsKbuESpAikQpQirF6iDAg7xkkiUIqqDgWec9md91n+MarqaxaR2XjKSQyKxozDfBDxaoeh5IjqAcp9UbEcf15dk62SZUiSVNKjknFcynmLBp+xEDJI0hSUFnX1rlxnoX63DTd5wvpc7FIeJf1Xc5x7+NvorfzW9X9oreDWQrPVUqdPPegEOKbwB8ArRSWCNPjKWdnCR2pL3raQohjhW0KJtoRw1M+ayoevfksi2ig6GKWXPZMZS0W0iTFNgwMoOnHrO3JkbNN7t3dIFUS17YRQE/eZaIZknMMVpU8Jpoht/z8SrZe90MGN53Iua99D6J3HVLCaCOiEUxRzlkgIWcLHNNleMqn1gopODZxYmOZBlIJ9jQCHNPANATbJxIAHMsgSRW2ZWKaYCiD3XUfYQgsw8S1BamU+Ht2sOPmn/Knb/47TNOgx3MYbZu4pklv0SJnm1nsweq0nBCKwZKLH0uKnk0QJ5gGSKnY1F9kbcXDj1L6iu68n8VCfG6axUGCxb+mL+YX8lF8yv4Mlzsf4wPJm/lWem5X5TqYUgiEEI9VSt045/hjgGCBZNIsANPDZqrtCD+SR+yLnrYQ4ljRCLPMo7JnU3Itau2sfbRlCBKpMIXBhr4cJc9m61iTIGmDACGyhXm8GTJWD8i7Bp5tMt7K4g8l18CPEn7yw+9z20+voG/9cZzxknfSs3YzMdD2E1wrGy7jRxKlYtpRlqXUjhJsC4JY0AxjGmHM8YMlhCHwwxRcsJXBlB8jyNrVeKaJ46SYQtCKYxKZYkgTZcTsmAxRScBdV/4/tpz7MtxiP44pMCzBmnKOMJH0F3MIpcg5FmGSsKrsIYTBcYN5hqfaBJHEAGzToJSz6C86e6WbHovPTbP4uEOdwPOjj/N/rK/xW5lZCtOupm64kQ6mFP4S+JwQosRD7qONQL3znmaJcDTTUacthChRFByTepBQ82M8x6TkWeypBaSWSamQDaNPEknOMRmtp3iWwcbeAo5t0AxjRqeCTmZPQivO4gGrSjkSKbn+17/h7p99m2LfIM/8y/dQWX8ck43M4mgGMQXPRCpBLMGzBc0ooRUlTAURgmxXnfeyLCKJpBlErCrniFKFYwoSoLfgZO0hohgrZ1KxLUYbIUqCZ2dKLkxhqlVn1/9cxtoTH8lJf/JUwhRWezZCJfQXHGpBgmtCM5SYMqW/5HHCqjLtMCFNJf0Fj75VDu0oJU5TBgougqw7a08uq3TeH9OKQbN8aZHjwuTNne8U77e+wdfTp3dFloO1ubgVeFxnQtp6sjTUIaXUyLEQTnN0OFrpqNMZRiM1H9MUWEKQKjAMweqyhx+m5CyTwZJLJW8TJZKegku1EZIo8OxsIlg7SmkFMZWcQ7UZMdaMMA2DJEloBZJ7HryDoV9/B6Tk5PNew/pTziBVMFoLSaVECEiUymIHStEMIgJT0I5TDLKOpKYAy8yUhmUKetwcUgjKOQdBmAXFleq06HAAQc42KbgWqh6Scw1ytkOUpjhKMfmbb+FaBo+74LWU8y6tMKUVpfTnBKvLBTYKaAYpjmlSytmdyWeCNeUihmDmd51lRAWMNwLiVLG65Oqdv2YvNohxXmFew0vNX8Luc2DtI4/p/Q8pJbWjBEYAhBB/B/zdwomkOdocSTrqtCJohgmNIKY372CILLWyHsW0goR2lGJb2SLcU7DpL7rEqaTqR2zb06QVJRRzFqtKHrZp0JM3Z/r/75psIoCCY9GojbHzl9+jNvRH1j3uAo5/9JPJuxZBIlFSUfMjXEsgMKl4Nq5lZpk/UlJ0XVDQihMMlSkN06BTC2AgDIFjClphQhgran6QNSoSClMIpJQ0gwTbFAgUecdiVcXDFoIrL/8CQXU3T3rte+kv5wCDNa7NeDPCsSH8/9l783DLrrLc9zfGmO3qd7+rT1IEQgJIY7ABOYCAh0YRjnLsEbxy9Cpiy1EfPYqIoufR56JcG1QElAtih3QKXI4crgJKJChdCISkKtXubvVrdqO5f4y1d3YqVamqJJVKyHrzpPbac8215tirdn3fHN/3ve+rDYuNhGbs+yEWmK9FNNPoLs3jOFQcWqifdXLoUpALZ3hg45zlofWvhz/7VnjT8+DF74K9j73f1nRPRhi+5T5fxQyXFIW2BGfElkD543eHyliOdyesj3JOdCcMM83GqADhnbvyyhAoSaceMcwN46yikQRUxnKsO2GUa3p5RaQ8Y/dUP+dEP/Py1+MSIQRZCYfnIo5+/D18+s9eQ3tpL9d+1/+g9YjrkUqRV5ZJoZFSTp0PJbnWXhspK6icoRYFKCmwWCSCMFIkoT8mhaPQhn5eeOOZWCEVOASRhKwo2RjlZGWFxSceKYSXt04j/vmdb2H91pt41H95BSr20h31yPciHI65NKBdi8hKjXWO/fMpX7W/w55OysG52gXvArZ3c9ZBGkms87u5oppZZj4ksfRweOn7IWnBn78Q1u8/Zeh7Ql6bMZkfZLinY40bw5x+7idqkL5cNMo1zSRgXGiUlCBgsR77wDyVZAgCQT0KmFTeZlIKQeD8xM2oqBhMKpZbMXP1iONfuJGPvvNNtFcO8vQfejWiNsf6MCOU0Egka/2MWhxirQUrqJyXwMgrTWEsRW7QMRjr2cG4Cm2l38nkFVKAQBBIn8j6eUVZOdLQS2pklcM4h3MC4SxJGBEpqErN2//4d9k89iWe8uL/TlSrEwjJINPkuU+m1+5pceWC5NQ4ZKWVgvBKr/XEW25eDDFwJnQ3w13QOQDf93fw5/8Fekd8orgfcD6ewncCH3DObe46/IRLu6QZ7mvc07HG7qQiCSMCJYmV9JLWgWQ8de/aHBeU2hFKwWoroT4liJXGsjWYsDYq0NZSVo4wFFjj0NpRSxVtlfGbv/16Pve5m/jqb34xcuURCOXHPpMooBOHNJOYrZH3S66sY6WT+Ckja6msoBkp6qGlsJZcW7LSMiq8rEYc+l6CNY40kczXUhZbMRvDAiUFC82YygJ5RTMKcDgM/ueTVnPDO/+IfNjj23/sl8mIaacBvXGJtYJ63fcNakmItgYhBMZZhplmVPgR12YSUl2EyPxM6O6hid2EtrOWkhYOw49+AlR4v63pfDuFQ8BfCiFC4EPA3wNnjqfO8ADHPR1rdM7tuGfUk4C1Qc6o0J5oJiVpFHJ4JUEJyTD3UtWT0nC6nzPKKwZZgQOywpINNZUGJR3rH/9nXvfut/Gs534L/+MHf4JPHhtxfCuj1JrSCdppyKGFGsbC3k6KsVATgsVGxCAvOdUvaISSSlu6mUYbi5SSyVSfyFiDwOstxaEiDULmpyziRhIyKSuMhTgQNJKAQAiUUMhAMOj3ueGvfpdGo8XTvv9n2CokShoyAUvNmI1xBQiKylKUBh1bGpFibVAQKEkzDrEOTvZzVprx3X6+u3sI/ayYCd3NcHao0Etwf+JPfJK4xGJ655s+ei3w2ulI6jOAlwJ/IIT4PN6m8/3OudOXdIUz3Ce4mLHG7WCljWNtOPGaPji6o5JCa7QBYkGZl8yXEe1UkZWOU+tjFpvelP5Yd8zRrZxAMtUDsjDp8en3/SkmH/OdP/HLzO87xJc2fALRziGloh1IQgQnejnX7muzf6HOraeH9POS3jhnkHvy23Ir4Vh3gnN+vQ7juQYhWAdSgUQipd8xhIHiZC9nsRHhwoBx7rkVwll6hSUNDHQ3+fe/+h2Wrn4sj37Wd7CZQagM9UhyapgzLg2tekBuNAbF6WFOO1Go0PdfAObr4TSRurv16j1zIsza6KKE7mZN6YcYrIaP/x6kc3D46ZfUB/pCp4+GwN9O/0cIcS3wbLz8xTed7TVCiAPT51fxAxlvcM697oxzBPA64DnABPj+6RjsDJcJu4PVXCPk5FgzHumpCbzDCcFyK2a+HjEsNCf7GVJAXlk6tRDnINMOgaCeSHrjiq1hxon/+CdOfPxdPPzr/jPPfP63MyktN58c0M+8LEUjVhjjQEC9HpGXmtPdjAMLdT9SmkYYC5G2FFN5jFIbzHQzY6w33olCCfj+Rxh45dKyMqwNcrS1FNpgAeMccSiwLqQuDJu3fJovvf/NXPvUF/KwJz6dSCk2JiXSwjCvGBQVvUnBYhkz10h43IE2aaQYZAMGWcGellc2tc5LdOxpp14244zPdvfOoBlH90jo7lIq3s5w+XA+Ke7vUu2cKR0AACAASURBVE/n18I/4QU//zpudFdfMmLbRTWahRBzzrmuc+5zwOeA37qb0zXwU865T053Gv8mhPjg9LXbeDZw9fT/rwF+f/p1hsuEU4Oc7qTEAcNRyZ5mjcI41vsZjThkLpBUxusBteKAUEhqUYA1FaVxnB7mSCHItUEKiSrHfPHdf0g+HHD9d/0M6eIBjm5lnB4UjIqKWCmiUBGpEO3AGdgc5AyyktNBwPq4YF8nIQlDCmuo25BKlxzZGGIc5EXlewHS6yTlpfHubA6khEo7ggDy0iAFHNkc0UpjOomimcYMZMktH30/t37sA3zdf305h695NNoauuOSoqqYOD8uG0qBEAGF9mWkzVFJPVIoAfvmUkIl2Ne5wzylMo5w183cmYF8feDomoIwkDslogsVups1pR+aeI/5Gl4dvJGnqRu5UV99ya5zsdNHHwIefyEnOudOAienj4fTktM+fDLZxvOBtzjnHPBxIURHCLFn+toZ7iUutsRQVIYT3QmNOMDi2BwVGIcnfAnh+QYiwDrH+qjAGDt1TTOc6GbEsaQovY/A+iDnyOc/yWfe+2ZWH/MkDj3nOVRSYIsC5yLyyjdo00jRLzSTSjOXRgyLkklpSQNJXRk2BgZjHKvthCSQ5JUhDhVCCNpxQF5qtHZU0hFIH/hzbcEJENBOY7KqpNBgsXRqMVEg6eWWIu/x2Xf/MdlkzHf+9GtZWlkmVoovnBpSaC/TUVMBUQC1eoKSinGhvaNaPSbXhlYsMdowLhzLTXfORv7uQF5oS1Z5At+o0Fy11NyZELuQHsKsKf3QxIAGN7sDXCuOXNLrXGxSuEeFLCHEFcDjgH8546l9wO27vj82PTZLCvcQ24lgWGgGk5KFerxTo94uMQB3SRYAXzjdZ1BUjEuDcZYoEBRacKybUY+8TlE/r8hKy0oroZyWjb68OWS1GVOWls1JCabisx98G0c+/a9c9/yX0dp/NVpb9JQgVhnnyz4OLII0lGyNCrRxVJUmiUOUlGTaG+B0JwVRINk7V0cKwbjSNJOQvNTU4hCB70kY64k3kYAwVDSSkFqkEIQUxhCKwHspJxFs3MyH3/Z6Hv/1T+FbvvOlZJVjfVQiIjgw5+0/14YFq+2EflYwKjSdmqKVBmjrkAKyytKaC0AGRMH02Dka+duBvNCW9UFOPQ6ojGFcaNYGGXO1eIf5fD7MlFMfurjBPpxl0QPOX266p+WlC/FT+L7th8Dcru9xzr3lAl7fAP4a+HHn3ODMp8/ykrsM8gkhXga8DODAgb3nu+RDFrtLFEWpkULQnZQEQTINGGo6msqd6tG3bY0RzlFox0oz4ebTI3COhVRxeuDr6c3E18h7WYlEsjXJ2dOqcSKfIIBhrqm0Zbi1xkfe+rvUGi2e/fJfRQcpVeVQYUBhHMY6tIEoEIRKYaz1DV/wBDALsXMESpJVhjgQDDKNthMaaUgYSlwOOMeoNAhAKknoxFTJ1LOZQ+EQgBP+ms4J0igAa/jU+/+So5/8ME94wQ9w/dc+iYmG3BjSWDIpNEkQsNpOyCtNb5KThCE1KTm8WKc7KSmNRVvHfD1GCoMBmml4twF9O5APspIwkATKB/BR7n/mYVHyiJX2BfUEHsrKqbtjgWotXebV3P/4Rf3SS36NC9kpXLnrcQxcgQ/m553Cno6y/jXwVufc35zllGN4gb1t7Meb+NwJUy/oNwA8/vGPuojp74cWdpcoKutII4W2jkFWstRMCBSc6vu68+56dFZoEBAIQX/iRzyNM2yMSnKjiALhZa+No6ospdasDSzdUcmJfkYkJZvG0j96E5/46z/kkU95NgevfxZz9YTCWKrAkBtHOxIkYcrGIKceh0RKsTXJKQpNFCqUkGhrGeaavDQEYQB4FdFxoZkUhlocIATEYcBC3dGbaLQDnKUoHFEYkAReRsM5S1Z4VVIpHMONk3zuvX9MENd42g/9MnPzi5zoZZTTMlgjVmSFb2SvdBLaScAX18YEUhArQX06brrUinEO6rFCCkO7FpFEdx/MtwP5pDDUY4XWPhFetdwgCoTfYVxgk/ihrJy6OxbEe66exYJLgPMmBefcq7YfCyGe75z7lQt54+lk0Z8An3fO/fY5TnsX8KNCiLfjG8z9WT/hnmN3rdlbOzoCJcimUgnawCiv+GJeklVeHmL/XA3noNQGh6AwmkYcYJxkvVcRCMlio0YcSo73co53M5JI0UpCtsYlm8OcRhRy9Ib/ly9//O+5+tkvpXXlI8krqCWKpTCh1IZBVpFNHdQQfqKnkXqWc7seoqQijgJ645xRYci1oxVaxrlFBZKFesRCPSQJAzYG3rs4CUKE1ERSMMktgZKkkReyC6RnMY9LQ6wURz/xAb780Xfz6Ke/gKuufwYar9V0xUINJQXHuxlRoGikAeu9nN7Y8yWuWKwzzErmajFprFjtJBjrmKtF1GJFVfmJqbtTOYU7Ank/LxmVhlqoWGr5HVxl3EWXfmbKqQ8d7JSBbv0IvPen4IV/dEm1kC5lT+FJwPcCnxZCfGp67OeBgwDOuT8A3ocfR/0SfiT1JRe5nhl2YXetuV2LWB/kVNNSTWUcm+OcrXFBPQ5pJRGFttx0ckAnDRnm2jdw8S5kW5OSQVbSShNGVYVxiu4o93e1hSUJLePSIKzl3979RsqNo1z3Ha9ERy36E83iSkKlLYXQXLXSIi8MR7fGbIxKFuoJlXEUWlNqRxR6rSJrLFEgCSR4WSbPL0hCQTuJyCpHHMJCI0YIy9aoIg0CAjX9RRaQhiFJJFBK+JJY9zSf+cBbkDhe/LOvpUgWSJUgigIiAYGSVMbuBOhRXrHaSSitZX1Qcni5wRMOzREo76cMd4gE5pUlELCySwH17hr7cah4xEp7p8QXKD+l9FAp/cxwL/Gx34PxBiw94pJe5mKTwvde6InOuX/iPElkOnX0Ixe5hhnOgd215igQ3u94XBAFAVJAVVmWGimnRzmDXJMEvlzzpbUhw7wiChRSCqrKMSkL0um0TxAoRsbQy0rqYYCSgBCYPOPz7/xdjAi57kWvREYR4IhUCM4rqS62aqSB5GQ3IysN++dTiiriZC+nst7oflQYtLVo4zDG72ik9PaU9cj/isaxolVTrLRSapGkO9HMNyQLzZjNYYGSijT0WkwI2NOM+ZcPvJPP/9P7eMzTX8D1T38unXpMWVmi0AveYWFUVJRTV7R2GtCblDhjaacxyw3J4eUGQogpT8MjDhXL02CvtbtDEvsCuAMP5dLPDPcCt/wj3Pz38LRfgPDS3kBccFIQQswDxy/hWma4G1zIeOmZAUdKwVIjBiEoKsOXN8YYawkCP0k0LjS9SYVzlmYSsj4uEQJCKQmCgLx0NOKANPRTM8bCsNCstlJ0PuATb/0N6qtXcvBpL0IIBc7f2a+0YpJQkUYBzViBg8VGhJJenG6QlTjnGOcGbR1ZUZGVgqz0JWLnAOGbss5ammmMRHrjHD3VF3KWREnCSGBcxP44oKgslXGs3fYF/vINbyRqdHjBK17DlVfup5PEHN0aU5SWhVbMMDPkRqNQaOsnrdaGBUEgWKwnJKFCCM/baCcB+87YJZTGEilJM/ZjoBfDHZiVfh7auOipoMkWvOvHYP4q+PqXX5pF7cL5BPEOAr8JfCPQ84dEC/hfwM8652675Cuc4aIYrNsBZ/drjLWcHBRsjUuaiSJRXmAuDhWdmn+vhWbCAhBIySAz5LqkPykYFBmTIqRdC5mrxZzojllbO8GH3/QbXPFV38Der3kO1vmZ/ryy1CJvfGNx9CcVecvSn5RTOe2MvLL0xgWDLKfQkGlN5UCXDoufXlACrAVrHIPMEAaGduxLW7mxtGsx4Fjr5xjrOLzQoJGEnFrf4F3v+BOOfeHfeeQzvoNHf+03cGihwVIrYWuUo6SkUw9opxH9rCAbm+mYaUSlHVluWO0krLQS+pOSWhwSKUEUqp3dwPowxzqYlNrzIeyEa4Jyxh2Y4dLhk2+B0Sl4yT9AmFzyy51vp/AXwP8FfLdzzgAIIRTw7cDbga+9tMubAS7uLnR7R3F8qguklOB03wdjgJPdHOYE2lpO93JaaegnehAs1GNvaVkUrA0KWrFgoRETSEl3UtKpBxSDCf/wh7/Go5/yXB79n56DkoL1QYHWhk4twjlHXllCJWjVQ27vjljrlzhniULFxihnc1jQm1SECgzsNJ/llIU8rezghJj6QDhu7+Wkkd8t7Juv8bDFOhLB2igjwPK//+Hv+PC73s411z+FF77m91FRTFZ6z4fexIvoZZWhnUQY6+ikMY04op95i85OLWRt4G3HIyU5vNwkCiQOt/PZ9bMK66by4ErSiALyUvDF00MWG/GMOzDDpcGTXuFF8FYffb9c7nxJYdE59xe7D0yTw9uFEK++dMuaYTcKbZECuuM7yhat9M7SzNs7gxO9jDRSZKVmXPryTHdc0IhD4kBg45CTvZw0FESRYqUdMyksRaUJVEgrDomjgFpsSMKQNAyox4rcaPrdDT74x7/GE5/5rTz7W16Ic3Bka8yeTsz6sKQ3rujnFVEAZRUiEUzKio1RyaTUGCswGMa5obJeryhUeHkL5xOBBMJAoJRE4EdBASrrCKylFcfcvjWh0IYD83XK4zfx+re9kVZnjh/9xddy7TWPoDsu2RwXVEWBsgGnp+qukRQoKeiOvbxEVTnAcWAupZGEXmPMweIudVNtfJIAKI1lUmoCdQfPIA4kmQWEoNKGhyJ3YIaLw/lIZwABmp8L3sabzbM46lamR4/e6ZzLpX30b0KI3wPezB3M4wPAi4EbL8mKZjgrTvYzaqE3vNHGcbKfeWMX7kgI3aykkfi7/lODglYakFeGQaYx1rOIc11xaLFBIKEeB4wLQy2WbI5yhgONEoIsr2glystHGId2jmw44T2/9xqe+k3fzNOe921UxtKbFCAc1jqSQDFU3nnNGO+jvDn2RK9xqZHAqCgpqmmJCL9L2DZ/UxIqC9KCno5oOnzCoLJEgSUvBbGqEMCtt3yZD/3JOxh2N3jud7yUb3z6U9kaV6Sh4pS21CKFFAlb45xKO5qJotKONFbkpaEoLc5Z9nZqDHJP9EsDhRN+Ums7sGtjWGr6LXukJLm2NKI7/tlk2jKuNNVU4bTShsqIWQN5hnuMGjm/E/4uz1A3cptb4c/Ms+7X658vKXwf8APAq/DyEwKfHN6N5yDMcH9gu/O6PQEjpn84v1XYLi85B2EgQQjSWNEdl/QnmiCUXhnUTlm+zjLILaudlGTKHN5yUBnDyUGJdY7lZsxqo8b6qGKc5XzgTf+TK659LNc/6/kAVNYihPcjGGbepxkgrzRKSPqFphX7BBEGPhAbO00IysvDO7zMtVIQSu9aVhkoNSil6aQRhbHEoUTi2JyUrK2fZOtf38f6rZ/lCc94Aa/8rv+KEb7fAKCtIwokw9yQhopmGiGyCotARhYFdNIAB9NJJoV2jmFZcXixCbAzbhopyVIz2Qns7TTkZD8jrwxJqMgqw/qgYKEdUI8loZJ+d9BKZslghnuEfazzx9Fv8XBxO79QvYQ/N8+839dwPj+FEq9c+vv3z3JmOCuEYE87YZhXU+kHyUI9ZHNcghizOSpYanq5ZW09Ya2ThAwmFVEIOMFcLd7R7AHBo/a2AdjIC27bHJKXjlYSsNSMsQ5K50XbGlHEB/7iT4mTlCd+8/cQSUktlPQmhmFeEYeKQEi2sopI+sRjMHRHJVoHgCAOFb2y2ikPKbyErph+jQRIJQgjQQNFPZZersJaOklIqR2bmxucuuEf2LjpBvY9/ht5yg/9OgeX5zk+KDm0UGeYV1MbTIuUkAQSIQSjTDNfj5lvRFjn6I5LXxJLAw7M1+7UN9gO5MvnCOhxqLhqqcGt6yPPsC4NczUvf92uxdOez0ytdIZ7hmvFbbw1+jUUlu+v/jt/9ms/x69ehnXcE49mAIQQz3POvee+XMwMZ0cceCP37TJGoS0nehmREqSRRArv9LVYj+hnFQBJ6KeOFhsJoRJEQYBzjr3tmOPdjKwy3HSyT29SYi20aiG3bmTEAXRqEen0/Fs/8wluv+lGfviXXkeY1ujn2ltWCkEjDdkY5AyzilogKI0jkIokEIxDTX9SkcQBtThASrDl1PvAQRr4HoLWfpcwX4tpJCGtJKSZeCmL41sT8mGXIx/7e05+9mPse8w38KT/9qtEtZYnuQXQTiPC6W5nMZlaFjpHz8GgqNjTiSm1D/p7OgkSSWUMh+brnqvAnfsG50MzCXnEaot+VnH71phaJJlvJTsN5dnE0Qz3FLe4vXzYfhWv0y/kNrfnsq3jHicF4HpglhTuB5wpgLYxygFHK41YHxSU2rI1LhDAajuZeidbDs7XmVSaykBvlKGdQ1tf798a+mQghMDhxfBCJXBTElllK/bGmg+/44/41pf9DHGtRj3yo6ylcSAFnTAkDRQ3Htmin3npjGYcklXaeyw4HxxPDTPPj1DeMMo6CJXA4hPefD0klJJQCuabEYuNmNuPHeNLH/objn76Xzj42CfzhJe8irjRJglDWqliuZUwX4sJA0kUSA7M1TyprJVMORkjuuMSg0NKibOOsrK0awGjQuz83Gf2Dc7kIbTT8Kxjv9u7CXPGhNFs4miGi8FhcZyfDt7BT1c/xJiUn6guP5f3HicF59wv3ZcLmeEOnI2ottpOOdXPOLqZ8+X1Ic0kZHNQsNJJaaUhSgpO9XM69YjVaa38VD+jl2mMMfQmBcZaxrnBCTje7dJKQsalZn1UeBG5OGSQWwLt1Uff/76/4NB113PFw68liRRFZVFKkVcG50AEgkwbAiURUhJK/zivLNZp5uspxhhM7hDKcxcEfvRUSEEsFY1Y0Yoj+oVmLhAc/9IX+eA/vZcTX/oMhx7/NJ740leztDRPEoQMi4ralBC31IiZb8QcXmrcZXR0fZiTV166Ii80p4c5R4YlpwcF16w2WGklO25xu/sG2zyEQCmS0PNB1of5nfoKu9FOQ0737Z0a07OJoxm2cbfTQdbAx14P/+s1ENV59vdcBfsuyKrmkuNCpLNbwJJz7pYzjj/GOfcfl2xlD1Gci6g2V48otEFKwd5OysaoJLMOOcrZM51y2Tef0owD5moRXzjdp6z83f/RzRxvNu8Yl4a9nYRJofn8iQF75lNiJclKTVkZr0lUGVQ15gs3fITnv+K3acYBW5OSWzfGtJKASaFppyGtWsjxboZFUA8ULlC0axGVdUih2D9X4+jmhMW68sY2WUFlHHnhbTQPdFLm05BJWTH5wo185IYPkQ82ue7Jz+Zhz/pe6vUGc7WQQa7pTQqaSYh1lu5Es9RJmKtHDHN/Vy8EpIFibZBz08khaayQQnDr5gjjoJ5IxmXFLZsjokixr3PXyaB+VhGou/JB+ll11j5DHCqWmgmZPbePwgwz3AWnP+sZysdvgGueB8/9bWiunP919xPOx2h+EZ68tjaVwf5+59wnpk+/iQt0YZvhwnEuotptmyOsg1rk72LXhiVR6Kd6uuOKVhLQSgNuPjlgmGu6WcHeTkKnlkwbxgECKK1FSklhLLl1nO4VRAraccjmpMIBhxfrfPJDH2L/Ix5DvTPPp0/0MQYaoZ9o0taRa8vtvYxRZmilkjCAQW7obw7JtWW5mTIpDEoK37g2FhC0Yt8MjoWkGHT59Mf/mS9+4h/pLC7zNc94Lo+6/skc7xVYbUljxUo7YdlZjm1mdMclSSRZbiboynLL2ogrFuuE0gvZ9azmgJIkocQ5ONodEypFJATaWOLAsdqsMcj0WQP9toT2bgSKnR3I2RAqSbs52xnMcFeci4/w5vC1PEreyquqH+Fdn/p6+NQNdznnUnEQLgTn2yn8PPAE59xJIcQTgT8TQvz81BvhHrmwzXD3OJdcwrgwJIEiCAQIyWIzYpR5qQVt/Ws+d2LIsa0Ry62UJArYGGq0LYgDycakIJKCdhIyLDSnejnzaUCsJBNt6ee+QZ2GijBQHP/SZ3j8Ex/F1qhgmBv2d3zN3QGdNJqOZmoaUcgg914LnXpAKCWOAilhkFfkZcWoMmjjaCSKOIDRbZ9m83MfZXLyFg4/7kk88yU/w8GrrsI5wf75OpFSOLzfswPW+97P2eB7Jvvn6pTa0h9rNuKS5WZMbixaO070MupxwCDXFKXFOEsnjSitYK4WUY8kg0JPk9Sd4eXG78pKvtAm9AwznAtPlp/mFruXkyzws9UPkhPSpXW5l3VWnC8pqG1/A+fcvwohnga8Rwixnwsw2Xko42L9kbdxLqvFeqywjp2R08VGjDGWWqKYr0XctjFhlJfMNWLiQJFrjcUxyg2tJOBUP8OqgMVWyNYkI5CSWuwnfQ4mIUc2xqyPc8Ig4Hg3o9cb0NMhMvf8AwNsjgqkEH7aKBJUxpv4VNpLWFSV1y+KgoCicuSVRiqJrDSjYzezdtuNbH3xk6Tze7jqcd/Ald/zcjrNJvON2PsqJCGbw4KNccGk0JTakgYa4xzGOAIBsfK8AikFc/U7fn2dw5vkaEsU+N1UEgk2RwadOOpxQCsJKSxEgTproG+nIevDnN2s5N1N6BlmuFgs0+UXwj/nW9THeLN+Jr+kX8JJFi73su4W50sKQyHE4e1+wnTH8FTgncB1l3pxD1ZcjIDdmTiX1eIVC42dxnEaOoSDNApQ+N2FELDQiJj66ZCGvkxjp97Fjz0wx9qg4GQvZ2tUcGghZWvkXda2xjlRJEkKRSgUSsLcngOsHbmZZP8TEFKwPixJQ0UgYG1UEitBK1FsTUoQXul0DNQjhURQFDnlyS9w7KYbWf/ip4hrLZYfeT0Pe/EvcHD/frLKUFaWyjoWGzHrw4LcGLS2hFIwyiuiKOD2rTFZYRkVJXvnalgHgRRetkKIaWNYUFaeGZeGyhPSrODKhSbGDAmF521o68hKzf75Gu00vMtnv90jOBd5bYYZLhQKw4vVB/iJ4K9oBhae/LO8+Mk/wYvvB0G7e4vzJYUf5owykXNuKIT4z8CLLtmqHuS4GAG7M7Gtcnqqn3Gq7yWmF5sJcaA4tNAg7mdsjv3xA/N1VlsJpwY5zUSxPioJAtgaFeSVZlJa5hsR8/WE6/a1OTnIOTQp+dgtGxzbmmCsI9MV/VxTU5J2M8ZZ71e874nP5ua/+klqcwdYvu7r6I01rhYTSrxvAZBrz0swxlCUYyanj7K5dhtbR26if+I25vddwcHrHs9jn/rNiMYiWIcKJKutBOscx3oZgRBUxnLlYp0T/QnldOS1lUaMpz4LjVTRSFOkFExK7fkL2hIpQasWkgYS5xwnehOWWgmF8eWqAwt1nrlc52Q3Y21YEErB4eXmWZvMuz//c5HXZpjhQvFjwd/yiuBv+LD5Kp76f/4pLBy+3Eu6YJyP0fzv5zheAW+9JCv6CsDFyiifWWqqTf1+V9vpzm5he6dxaLHBocUz3sA5stKyOSpZH+S+Xu4cQggSKWmmId1xSTMOCaWXpmimEcOpr4GYitFNJiXGOYJAUess8thvezmfft87+OJH3sX8oUfSWFwhiGosNCLGozHZqEdv4zT9tROU4yGNlf109h3myid+E80DjyBNUw6vNAkEnB4UDPOSTj1CKj8JtK9TZ74R4JzvmXiFVUM1FURabEdsDhzzjYhmEnFsc0J3UrHQDAkDwZ5ODVNZbxgUKW+iYxyBdASBRDhHMw5ZPPDAvzub4cGPJbq0xIRb3D7epJ/F5+wh3m+/mtseRAkBLs5k5x3OuRdtf72Ui7r7dUi0Hl2uy18QQpFRllMdoikqbQmFd+rajVIbjm6NyCrrZ/8F5LlhuZOQhCHOTv0FhGVzmLHcSu/y+qwaUxQ5iaoIZc648MJwB+drXLNXkQQVpwdD9s2lHNsc0IxK6kHOZjXBWkcj9l4IW4UXrgujgLIyrC4v8LQf+Ek2Tp5gfPLLkPWI7JCkjIiSiGZrgdXDh0nmVlDNJdLQ1/STQJBVjjQoqEpACSKlSUJNLABjmU8FiXJkRY5SksoITmyNqCcBcSwY5JpRJogCh6k0Yd3SSrzHQSsB7RxXzguMVfSzHOEkndhPV82lEfMNhRQl3XG50xMotaWflZTGESlBO412WM33FMZMHvC/jzNcWgRoXqw+wI8Hf81N7gDfXv4yN772Oy/3su4xLoa89rDp16svxUIuFEJE1OsPv5xLOC/2RIbj3QliWkKqjAMMe+ZqJGeUJk6vDRnqnHoSEEiBto7b+0PSKmWh09w5L3KOSWmo1xvklWFzVFBoS3dS0EojCldSqZK6yZlvC9r1iNVmSgUs1BPEZIQM64ztJjI0HB2ukdYC4lCSFZoj/SHOCay1BFoymFTklaZdm6Oz7wr2X/UUklCyp52w3ErZGBZU2iIk5KXhto0JOY56QxFLhc0rmmnAZm4otOOaPQ0W6hHrw4JxadmXJkRSUbicUWFJQoGWOVGcTGW0CwrjUApEFGNQiNCw1E7ZN19jXGjCOCKVAqs0w7xCW0ccK1YWGlOVVb+DStM6RWXojTPCSJFMd1+9wrCa3DtegdajB/zv4wyXDk8Un+dXwjdxjbydfzRfxav0913uJd1r3BuZixnOgSRU7JursTkqmJRewG7fWRICwNqwoBYpwuk0TKgErTTk1KDgiqU7kkI1lZPOK59wosA3VE/1LJs6Z1L6pvIwqxg4R6EtS40Ya2GUa4QQ3LI29F4DAx+ItS5pJjWOjUuSwDOFtROEUiAcSCkIlWA+DWkmIce6GZW2VNpyqp9TGMfeTkpWGhqxol9orIHV+ZiyCsm1Y6WTcvVyk049ZlJof10quuOSxUbCYitlzjjGheYRqzEORz+rUEqQCFhpxdTigHocslCHuUbsjXY6Kf2sogJqoSRSEeV0PfEuTaPtx/emzzPDDGfDM+UN/FH02xxzi/xg+ZN80D6Br4RJ/VlSuETYTgznQl4ZTvQyPnO8R6gkK62UpZY3dymmTyfaqQAAIABJREFUzx3dHLPUjFFSUmqzk2iiQO2UPVQgOL6V8cXTQ+JA0qlFDPKSrUnJbetDFpop47xiqZVQVZrTg4JPHukSStgsLePS0B9XdBohpXW0p05sSSgRJiEIFOPSEoeWlXaEdnBkK0NPrTe744Jj3Yz5esRcEhCHAautlHrkmcCdekw7DdHaIoADCzWKquJ4r6BVC5mrhXTHFVujgoet1JhUltVWSrGgWesXWBwrzZRGEhCHXmJjrhZRSzxjeXNcEEchTSUpKu+LsK1ptFtyYmaXOcPF4qwEMmuhfxTmrgD9DPiXOfZf/3/wR9G5/60/2DBLCpcBeWW4ZX1Ed1yw2kxYGxWc6mdsjXMmpUYbWGklVNpy28aYgwv1nZ3GIKsotGFUaHpZRW9csjkqsNYhBPTzkkYcoKTi1LBkVFr2dFKObIwZ5xoB7O2krA1ypIXCWhYbIVYKlBAsNyO0hb6DTqRYaEQYJFvjgvl6jDGG1XZCoQ1bI43JNQfmU0rjSOOQ1WaMdY5xZbj+qgVv/jMu0c6RhAHGWmpxxKP2eWXRUWHItSGJAnqTknbq5TzywnLFYp3r9rVppdHOZ7fdlM9KSxIpHtXp7JR/dj93puTEufgfM/G6GS4Ypz4D7/lxGJyAH/0ERHV40o9d7lXd57iYpHBR+yIhxBuB5wFrzrlHneX5pwJ/B9w6PfQ3zrlfuZhrPFixOfLkrHoUks4HGAHdUcFNJ0fMNyOuWGiw2k4QCPZPZZmT6V1yd1JirGOYa/rjEucgChW9SclcEDHIK7Su2NMJqEWSsjKs93MQgs+d6BIFAXs7KcZY4khRVJq8dISBICsNN58aUk/DaaO6TmYCTOUdypZbMbduTtDaYi3M1UNO9CpGWQVCoJKQwjrmlaQRh7STiCRQfOZYj2YcTuUnHMd7E67d26YeBYwKw3w94urlBluTirVezkIz5srFxk5Qv1Ai4PY479lwLv7HrHQ0w3lR5fC/fwM++juQtOGbfh3Cr5ydwZm4mKTwP8/4ej68CXg98Ja7Oef/c8497yLW8BWBQvv6f6AEQkj2z9UoK0MtDlhqxByYrxEHilFRcevGaKdUVGjLUjPh5lMDlJRIKVE4jPW19MI4rlys72gTrfdLVufSqf2l4Fg3pxYpmmlIYRzFpKIWKpSyPP7QPP922xa5tmSFpjM1rEmjgCsX4ulYa+XN6itNpT0HIpKS3FhaaUCoJM5ZOrWIQIppEIa9nRqTyktyNJOA6/a2KbRhUhjPNUgicm0IpGDfQspcGnFoseF/5ntBBNyN7YRxrp3EDDOciSt+9r0s0ePt0as5LE/yl/opvGby3fTe1oC3ve+y6hNdSlxQUhBCvBl4BYBz7v8RQswBv+Wce+m5XuOc+4gQ4or7YpFfaYinJjXa+Dv0OFAkUcDB+ZSFKVGt0D4Ybo5KVlsJJ3oZW5OSKxZqU3/kin5W0kxCVtsJw0yzMcqQCIy1nBrkNCJFqQ3jwktF1ALF+iDfMeBJwoDCWuZqIf2sYqER066FrLRSSm2JVMAkr+isNmnEIVsjz2reGuWMK8vGMKfUDqUEi/WQOBTk2rE+yHn0gTmk8Ilh/3xKPQkotGWQlUwKgwOaaUgSSDaGBWEgSUNFZbyB0HbAvi8bxHe3k5hhhjvDW+Cu0+Zf7TX8kv5+/sk++nIv6n7BhRZUH+Oc621/45zrAo+7D67/dUKIfxdC/L0Q4iEjm7HQ8BM147KirAylNmjrmKvH1AJJpS1rg5z1QU4gJSvthEBKNocZH/zcKb68Pua2jZFn93YnU8kL/1d5epDTn5RsDHK6k5JJaagFimGmiSJJrBRpqNi+P7ZOIBEc62ac7k/oZSWTUrPYirluT5PFZkISeie0OJAM8wIHSGcpKkMSSfbNpQwyS17BfC1C4M8NFDjnm76FtqwP8h2ZCilgMCk51c8JA0mgvLe0QJBGPuiDf52xlvVhzrHuhPVhjrGWQs8axDNcGjxG3MI7o19kLxuA4Of0Dz5kEgJcePlICiHmpskAIcT8Rbz2XPgkcMg5NxJCPAevp3RWDoQQ4mXAywAOHjx4Ly97+ZGEisNLDU6EitP9DCEE1yw3sEIQKS8DffvmmCiUXL3a8Hf02tCbaI5sjH0T2lo2e34UtTcuSSLFYiPi2r0tjnVznBD0RiXDrEKkIQfmEipjp17OAZESaAvjomR9VODwpaxWHDHMNa6bsZQaVto1skJDHLBnLmVSaUb5hKVmjeWmpZ6ECCEYF5rFZsxyI95RINUGFpsJlTZ0s5JACZiK+i21ErS2fPZEn4PzNZDOO74Zy2IzviPoO8fJgR/bTUMvwHeyn7PSjC/j3+AMlwu7Y4FqLd2n7y2x/Ih6J68I/obTzPHRlz8K9j3hPr3GgwEXGth/C/ioEOKv8PuqFwGvuTcXds4Ndj1+nxDi94QQi865jbOc+wbgDQBf/dVf/aBUZ91NOIsDST0OiAPJStvP1S80fJDbHBUoKdjbqbHQ9PIOAP1JRW4saRhgDPQmmlHhfRLSqQeylJJhoRF4kblJUTHIK6x1DHPY00549P45sspw2/qQI5sTjBMIoJEEnBpktGshCs+U3hoWPP7KJca5xoCfWEJy5VKDSAnWRgVpKGnEEfXYN4SHRcWedkpl3J0auRujAicgCgRL0+Z5FAjm6xHGOXRlvABdK0EKQbg91iAE4O7Q5HXTP8SDfx58hovH7lgQ77n6PosFK2zxuuj/5mvl5/k78/X8YvUS/uMhmBDgApOCc+4tQogbgKfjp5Be6Jz73L25sBBiFTjtnHNTrwYJbN6b97wvcWYQX2jEdyGfXcg52+ftJpyNcs3Npwbsn6/TTAIq4zjenbBvrnYHt8E5TvRzKmMJpJ8MKkqDtZbKWkpjcNYxKjR751IC5csuvYmf1S+NIVSSItPIGHrjinY9YlRUFJU32tk3l3DrxgRrLbVIeSJaZYnTkCRU7OmkJIFC1iRFqVlppZywGeujnFAKamGAkILCeHvOhXpIK41oJAFSsJMQupMSIQRCQLsW3YlctrfjzwmDc08F7WmnDLKKbJo49rRT7IPy1mCGBypeHvwtjxFf5qfKH+Kv7VMu93IuKy64BDRNAhecCIQQbwOeCiwKIY4BvwSE0/f6A+DbgB8WQmggA77DOfeA+Kd+ZhDfHbS3R0O3yWX1xE8MWcedztmNMwln41JTj0O644Lx1PBF4J2/WknoSydCUI8k2lpK7RAS2qlXJL29mwGONJJMKsfJQcYjV1sY42ilAa045FPHupQVhJFAO4jDgLkk4ujGmD2dGs45lhopnXrMbesjpJTM1UJ6uWaxEbFcT5irj3cmdtYHOXllqMWKZhWyNS5RytJIYj8yGwV+jLSV3Ik3sD05tNSMOdnPOdGbsKedoqS8U/C/O36BdbDcukPUbpRrhkXJkU0uyqtihhnuDEebMX0avEZ/N280z+bLbu9X7FTRheKSkdecc3erCOWcez1+ZPUBhzODeBSIneMLjZjj3Qlb45JWEiKk4PSgYLWdEAWKzVFxFyZzoe2O8un290I4jnUzrlhokIaKYV5x45EuT7xygcZ09xCFAe3AN2B94nEMsy5KeDXRiXHUkwAMWAfz9ZBIKdZHBaGQDG1BI4oIA+GltYcFUSDZ00l2zO6HuUYiOLI5ZqWZECnBaiulk4YcnK8Th4q5WsQorxBC+M9EgLW+gTwONI89uHynZLCN3ZNDoVJTb+mctUHOYiMGITg1yO82sJ/JLxjnhpO9CXs7tXs1ojrDQxsxJb8ZvoFrxFG+tfwVMhK+7PZe7mU9IDCjc54FhbY7I5DbCJWg0HYnYTi8CmqopDeln5Q755yJOJBTUbw7vj89LKhFAWEgEUIwzDXtNGJc6p3g20rCnfMRgsVaRBoHHJyvESlFPQ6YT0MWGiFrg5z983Uetb/NwYUa842ApVbK3o4P8O00RkpBpS3/frTL2iDnE7dscaKXgYCVZkxhLHHoex2NNKQ/8Rad8VSyo9KW492MSEquXmnwsOUae+dqZ00I259jsOtwHEj2dlJaU4ObUEnSyO8ETvUzim2HoN2f3XSMVAovSTEsSvZ2atSTAIHXZgqDO6aVZpjhfJhjwNuiX+X56qP8nXkSGbOhhd2YyVycBdtBfHuHAHcI0m3f9Xs/X88zCKQgq8zOOWdie3cBPrnUo4DBpOLKpbof2bReAXX/XHKnpGKs5ejWhMPLTWqRYqGZkIYBaRhwcL5JLy/YGlckoWShHrPcjLlquUkcKgIlOd6dMMwqkiBAO4fDIZXAIdgYFaQRjAvNpNC0axGLoeSqpSaHFutU2nKyl7FnzhCHioVGzGRKsHN43+I0UkjJOTkD55KWyCpNPU4vmHuwm19wZJOZhtEM9xj7xTpvCX+dfWITXvQWXnnt83nl5V7UAwyzncJZsNCIKbWh1BbnHKW2lNqw0Ih3EsZcPaI03hCmMt4Oc/ucM7EtjicFdMcl/dxr/HfHnoAmBeztJDgn7pRU1kcF9Tggmu4mWmnI46+YY2NUUBrDcjPh0fvbHJir87DlBrd3JxzvTnYmm7Y1inpZydZUsdUBC/UYIWDvfIOlZsxqO6WRKObrsTenEQIhBUl8xx34XC1Ca8tCI2JPO6FdCxHT9zoXZ2CuFlFpnywdbmciKY3CO+0gwAf2C+EebCea3ZhpGM1woXh18EYWxIDvLn8Orn3+5V7OAxKzncJZcHfS19t3/VGgWGkl3h+g0Byc96UU8A3nMyeStl+bV4ZGkrJQjzk2bRi305BaFHBsa8x83e8eKuMY55orFuvklaE31f6JlOAx+zoIJSi1n0xaaEQIBEVlOLIx9gG/k3LzaW/ec7qX0a77iaIDczW2hiWr7YSVVkogvaHNyV7G2rjwBDLhvY5Xa9FOoI5D3xPoZiW68p/J9vioNdaXf87QJjqXtER3Ut5jcbqZhtEM9wavrP4bC2LATe7Bz3e6VJglhXPgXNLXuxNG5Xzw3Q78u6eWpIATfS9pfXChzt5OekYDW3JgvsbaMOdkL+PgQp3HHZr35ZxpIjq4UEcbx+bYN4jTUJGVhnoSsNyMaaYRm6OcUW5YG+bsnUupR4EXtjs9pCj9biIKJFGgyAqDsV6WIg19M1sbRygF1jmc9dNLYvqfsY7arlLNduDdPT46LCqEc4QqOmvj92zSEvcmsM80jGa4WOxlgx8M3stLXvVWUOHlXs4DHrOkcA9wroRxojtha1J6l6+JZrEZ0UpCNkfFThlqrh7d5c6/UYtYaMR34TwA3Pj/t3enMZKU5wHH/09VX9M9vXMvuzu7s8ByBMKVhXAEi2CDMJBYYBnJOJYhDhKyiRUjfwmOEkOcw+FDguLIAVkBG0gEjhw7RgiS4AREYo6YWJjDHF4MeJcFdnZmdmb6vp58qOqmp7d7Zna3p2u75vlJre2uo/utqe16ut7jed+exXUcb1Y2vxpmciSJ66eKmM974w62jAwwGPf+ww/EXH62N8dE2pulbJskWSxUmM0W2Tuf54zJIWazZdLxCAdyRfJ+tdBJqUFGUwkirjcuYjZbYnL0g7TV7S7ICdc55NxER3phtxxGZrU2kOHe2O0cI3Mw9zaMn7DyTuucBYUuKZSr/HI2x4aBqN/rRpjLlplIx7yG2YjLgXyJaMFhJlta8sv/QDaPqpIeiB00LmI4FadQqjQGbm3yR0DnSl77xXsLeaYXs7iOEHUd4hGXStXLnCriNQjX1BvhPJqKsX+xQCoepVxRMqUy8VgE1QonbUqTiEWYy5bIl6tEXSGRjB50oW69IL89k23bPtDc8Nsp9bVd2M1acqlyZ/RvmZL3ub58Cw9aQFgVCwpdMuM3CgvenMyJiEOlpsxmymzcECfqCslYlOnFwkG//FWEt2ZzjA9WG7On1cc8bPDnbq4PcpvLlkjFI7iO8M5czp+zoECuVKVYyTOSiuMIjKXjqMJQMsq+hSLgTaMZcx2yxUqjwXkiHWd6sch0psS20Qib/RHGpUqNSnHl/x4rTV7TrdTXxhyqWyIPcKH7Mlx9Jw+e9TtBF6dvWJeNLvHmOohTqlYR8ZK+oZAtlRlJxShXlQ2JCMMpL0Dky952I8mYNzNZtcZA1PX77H+QCTQV9xqgS5UaiYhDqVJjz2yWYqlCLOLNjXDSpjSOA6VyjcVCidFUnO1jg0QcqFaV8cEoxbKXaTQRj6AKirJvvsDL78z7I7CVfYuFJb2thpOxFY+7Uw+jEX/f5gFsNq7A9Mo483zSfQLOvREsIBwSCwpdEo84uI5XvTMyEGWxUKZQqbJleMDLRdTUpbXSlLhnLu9VJcWjLiLSGAw3nSkSj3i/6reNplBRds/lvdHKUZfpTKlRjz+UjHHa5DDHTqSI+6k5Ttm8gfN2jOO6kCtVGRmMsn0sRdxxeHMmQ6XmjYZ2HacxF3SlUiNXquIITI4kibXWC7U77pbBZfWcR41UFy0D2GD13U+NOVz7GeLK0tfgsj8Puih9x4JCl9THNjgiTI2lOG1ymNGU19Bcv8gCFEoV70LpCLWa8sv9WRJRtzGPgvq9gLKFCmOD8Ub7BCpsGR5gajRJMupNlpMpVBqf73V5TXDCxnSj++xwMsbZ28c4c9sIKExnCuzLeKm6ZzMlyjX1psgEFvIVpsZSHD8x2DZ/03LqgWH7WOqgaiEbV2B67QLnZUDZoxMc+8c/DLo4fce+mV3SPEAtV6qSjLns3D7KKVuGGhfZmUyR9ECMbaNe76GKKqlElIGow9T4ICKQL1epqjI1liIRdYn7dw2KMpct8c6BPNOLRUbTMaYXC20H2DUrlKu8sneeiOMwkoyTLykOUK7VmM0WqVS10WbRbuDdkVqpesmYbvoN5yUeiP0Fn3D+O+ii9C0LCl1UH6BWT4cxkylSaMrnU8+plGj6ZX3q5g2Uq4ojwqahhHcRrXqzmtVHJ78/X+DVvfPsPZBnPlciU6zgAgOxSCMI1e9G2mVoVfW6qQ6nYkRccEUYiDqUSjUWi2XSiShTo4d2d7BaK1UvGdMtDjX+JHI/b9c28nDt/KCL07es91EXdUq5PTYYJ1us8P58nkjEYWM60bgAu47D1KifAiNX5kC2yMZ0opEpde9cjky+BCK4joBAxBXEcahqre14ieZ5Ht6fz+O6QqWmxCMux00M8sa+DAv5MsdNDHLceNpLs9HmfbrFup+aXviY8xSnOLvhmm/x2mkfD7o4fcuCQhe1S7ldLFf52d55to2m2Dw8wJ65HLtnc2wd8eYUKFWqH/zCn8sx6Oc6qu+fLVdxXZdjkl5G1YgjFCo15vMlxgfTB5WhNTBFIg6L+TLFSo10Iko6HuW4sUFms0W2jQ56ifY6TA5kTL8Qanwh8gM45jQ49eqgi9PXLCh0Ueu8CQCZYtkfvFZPbZFi30KB9+YLbBtNLqnyabd/raYMRB1GUjFypSoFf6xBwnUaKaibtQamjekExbLX00dQFvMVXAcuOnnjqrqcGtMPJmWGOCW48GZwrFb8SFhQ6KJ2KbdzxeqSC30i6rJtNEmuVD2o6qfd/o4jjAzGG2Ma6ikoqrVaI8Fec3qMhUKFkWR0yedtHRngvfkCGwZiTKQ7TxtqTL/aoxNM3fY6H0zmbQ6XBYUuap43oVqrMb3o5RraPJSgUK42LsSrnXehXFVSUZdkLELMdcgUyiwUKghw6pYhgIPaMA5ki0QcWXIX4TpO467EmLBJUKSKa3cIXWJ/xS6qd0stV2u8tT8LAqdPDqEIu2ez5EuVjl1Hm/dv7lF0/MY0Oya8uv+hZIxjx1Ls3D7KcDK2pKqoPlvbRDrB9GKBhXyZvXM5du1bZPdsllTc4r8Jp2vdx3k2fhNkZ4IuSijYlaLL6mMLdmxMU1PlgJ/OYaFQ4e39WU44Jr3s4LBOGVjbLWvXBjGYiJApuuxfLKAKqbjLYNzL1Fqf18GYMPmo8xyjx0xBaizoooSCBYU1UKx4/fHfX/DmQfAm0XFZyJe7Wp/fadrQqipbR1ONxmbwEtzNZIpWhWRCZZAc5zivwUlfDLoooWHVR2ugPgo5FnGIuv70lgipeISZTLFrn9Np2tBkLNrIi1QXdcXyDZnQOc95hahUYcdHgi5KaKxZUBCRe0Rkn4i81GG9iMjXRWSXiLwgIju7XYZ6n/1fTGd4Zy63ZHTxWhobjJMtVNCaelNrVmqUqlUm0p3nMz4c7dogJkeSbPAHvjXr1LhtTD+7++IyuDHY+utBFyU01vIq8W3g8mXWXwGc6D9uBO7s5ofXA0JNIRnzUlL3KjAkoi5TYymqqo0U2ZuGvMFq3b4w1wNDcyK7TncQa5HbyJhA/cpvwxW3QzQRdElCY83aFFT1SRE5dplNrgLuU1UFnhGRYRHZrKrvduPz240uri/vRb36luEBVJWYP5dAuaqN0ctrrXke6fp8z4ea+dSYvjB1nvcwXRNkfcIksLvp9R5/WVfUk88162W9eqeqnV5dmNvdQRgTJi41ePNJKGaCLkqoBBkUpM2ytsMRReRGEXlORJ6bnp5e1ZvXe+Y063W9evOFeWwwzkym2PP2DWPCpPlakCjOwr0fg/deDLpYoRJkUNgDbGt6vRXY225DVf2mqp6jqudMTEys6s2Ppnr1INs3jAmT5mtBIu6P2h87IdhChUyQQeEh4Dq/F9L5wHy32hMg+OqbZu1GHscible7pxqz3sSoQDQJqfGgixIqa9bQLCIPABcD4yKyB7gViAKo6l3AI8CVwC4gB3y222XoNDq419qNPI66Qq5kdwrGHK6oVGBoB0i7mmhzuNay99GnVlivwO+v1ecfTTqNPLZxA8YcvqEYkN4UdDFCx65KPXA0tW8YExpDW+GS24IuRehYUOiBo6l9w5jQiCZh69lBlyJ0LCFejxwt7RvGhEZ+DmbegLEdQZckVOxOwRjTn+begl0/DLoUoWNBwRjTv+Ibgi5B6Kzr6qPW+Y1t7mJj+kwsFXQJQmfd3inYKGNjQiBm7XTdtm6Dgo0yNiYEohYUum3dBoWgs6gaY47Q+Mmw6fSgSxE66zYoHA1ZVI0xRyCWhHg66FKEzrq9AtooY2OMOdi6DQo2ytgYYw62rruk2ihjY4xZat3eKRhjjDmYBQVjjDENFhSMMcY0WFAwxhjTIN4EaP1DRKaBt9usGgf297g4QVpvxwt2zOtF6zFvV9WJ1o1EZBF4rWel6r1un/u2f8dWfRcUOhGR51T1nKDL0Svr7XjBjnm9WO0xh/1vE9TxWfWRMcaYBgsKxhhjGsIUFL4ZdAF6bL0dL9gxrxerPeaw/20COb7QtCkYY4w5cmG6UzDGGHOE+iooiMg9IrJPRF7qsF5E5OsisktEXhCRnb0uY7et4pgvFpF5EXnef3yl12XsJhHZJiKPi8grIvKyiHyxzTahOs+rPOawneeEiPyviPzUP+Y/bbNNXES+45/nZ0Xk2KZ1l4vIa/66W3pZ9rW20nd+zalq3zyAi4CdwEsd1l8JPAoIcD7wbNBl7sExXww8HHQ5u3i8m4Gd/vM08DpwapjP8yqPOWznWYBB/3kUeBY4v2Wbm4C7/OfXAt/xn7vAG8DxQAz4aevfq58fK33n1/rRV3cKqvokMLvMJlcB96nnGWBYRDb3pnRrYxXHHCqq+q6q/sR/vgi8Aky2bBaq87zKYw4V/9xl/JdR/9HawHkVcK///LvAJSIiwLnALlX9haqWgAf9bUMh6O98XwWFVZgEdje93kPIv1y+C/zb8EdF5FeDLky3+NUFv4b3K7JZaM/zMscMITvPIuKKyPPAPuAxVe14nlW1AswDY4T4/B8NwhYUpM2ysHev+gne8PUzgb8D/jXg8nSFiAwC/wLcrKoLravb7NL353mFYw7deVbVqqqeBWwFzhWR01o26XSeQ3n+jxZhCwp7gG1Nr7cCewMqS0+o6kL9NlxVHwGiIjIecLGOiIhE8S6O/6Sq32uzSejO80rHHMbzXKeqB4AngMtbVjXOs4hEgCG8apXQnf+jSdiCwkPAdX7vlPOBeVV9N+hCrSUR2eTXsyIi5+Kd05lgS3X4/GO5G3hFVf+mw2ahOs+rOeYQnucJERn2nw8AlwKvtmz2EHC9//wa4L/Ua4n9MXCiiBwnIjG8RuiHelPy8Our6ThF5AG8XhjjIrIHuBWvgQpVvQt4BK9nyi4gB3w2mJJ2zyqO+Rrg8yJSAfLAtf4Xp19dCHwGeNGvbwb4I2AKQnueV3PMYTvPm4F7RcTFC3D/rKoPi8hXgedU9SG8QHm/iOzCu0O4Frz2BRH5AvDveD2R7lHVlwM5ijXQ7juvqnf37PP7+/+VMcaYbgpb9ZExxpgjYEHBGGNMgwUFY4wxDRYUjDHGNFhQMMYY02BBwbQlIsceTpZGEfm0n7n0BRF5SkTO7LDdcX7my5/7mTBj/vKOmTFX+flfFpFPt1l+toi86L/v1+t9/lu2ucov9/Mi8pyIfKhp3fV+WX8uIte37mtMWFhQMN32JvCbqnoG8Gd0nj3qduAOVT0RmANu8JffAMyp6gnAHf52S4jIbSLyux3e9zLgP9osvxO4ETjRf7SOngX4T+BMP/XC7wH/4H/eKN74kPPwkrHdKiIjHT7fmL5mQcEsJyIi9/q/nr8rIsmVdlDVp1R1zn/5DF4KgiX8X+kfwct8CV4mzKv9550yY65IRDYAMVWdblm+Gdigqk/7A77ua/q85rJnmgaEpfggn85H8RK2zfrH9hjtg4oxfa+vRjSbnjsZuEFVfyQi9wA3icgk8OE22z6oqn/VsuwGvHkPWo0BB/zMl7A0y+WSzJgiUs+MuX8V5b0U79d+q0n/M+o6ZtUUkY8DXwM2Ar/VWqaV9jem31lQMMvZrao/8p//I/AHqnrQL+x2ROTDeEHhQ+1Wt1mmy60TkdOB+/3Xm4CSiNzsv75EVWfwfr1/6xA/b+lC1e8D3xeRi/Cqvy49lP2N6XcWFMxyWi+dhfNkAAABfUlEQVR8KiJ3sMKdgoicgVcff4V/sW61H29inIh/t9Cc5bKeAXNPc2ZM/33O8t//NuAtVf12y/uei5cfyAX+z1/2EF57QnM11opZNVX1SRHZ4Wci3YOXi6Z5/yeW29+YfmVBwSxnSkQuUNWngU8B/6Oqf73cDiIyBXwP+Iyqvt5uG1VVEXkcL8nbg3iZMH/gr65nxnyapZkxl+VPOvOqqlb9RWe1rF/0M6o+C1yHNydB63ucALzhl28n3lSPM3iJ1/6yqXH5MuDLK5XJmH5kDc1mOa8A14vIC8Ao3i/ulXwFrw3g7+tdO+srROQREdniv/xD4Et+BswxvIyY+P+O+cu/BKx2UvYrgH9bZv3n8e5eduHN7/uoX6bPicjn/G0+AbzkZyr9BvBJf9rIWbyqpB/7j6/6y4wJHcuSakJBRB4DruvneRWMORpYUDDGGNNg1UfGGGMaLCgYY4xpsKBgjDGmwYKCMcaYBgsKxhhjGiwoGGOMabCgYIwxpuH/AUt1NwmtIV/1AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%pylab inline --no-import-all\n", "import uncertainties\n", "from scipy.stats import norm\n", "\n", "a = uncertainties.ufloat(1.0, 0.1)\n", "b = uncertainties.ufloat(2.0, 0.3)\n", "c = a*b\n", "\n", "mean = [b.n, c.n]\n", "cov = uncertainties.covariance_matrix([b, c])\n", "\n", "# Always use a fixed seed for reproducible data generation.\n", "np.random.seed(1)\n", "Nsamp = 1000\n", "xs, ys = np.random.multivariate_normal(mean=mean, cov=cov, size=Nsamp).T\n", "_x = np.linspace(xs.min(), xs.max(), 100)\n", "_y = np.linspace(ys.min(), ys.max(), 100)\n", "\n", "def plot_cov_ellipse(cov, mean, ax, points=100, fill=False, **kw):\n", " d, U = np.linalg.eigh(cov)\n", " thetas = 2*np.pi * np.arange(points)/points\n", " xs, ys = U.dot(np.exp(1j*thetas).view(dtype=float).reshape(points, 2).T\n", " * np.sqrt(d)[:, None])\n", " path = matplotlib.path.Path(list(zip(xs+mean[0], ys+mean[1])), closed=True)\n", " ax.add_patch(matplotlib.patches.PathPatch(path, fill=fill, **kw))\n", " \n", "# definitions for the axes\n", "axis_sep = 0.04\n", "hist_size = 0.3\n", "gs = plt.GridSpec(2, 2, \n", " width_ratios=(1,hist_size), \n", " height_ratios=(hist_size,1),\n", " wspace=axis_sep, hspace=axis_sep)\n", "\n", "axScatter = plt.subplot(gs[1,0])\n", "axHistx = plt.subplot(gs[0,0], sharex=axScatter)\n", "axHisty = plt.subplot(gs[1,1], sharey=axScatter)\n", "\n", "# no labels\n", "axHistx.tick_params(labelbottom=False)\n", "axHisty.tick_params(labelleft=False)\n", "\n", "# the scatter plot:\n", "axScatter.scatter(xs, ys, alpha=0.1)\n", "axScatter.set_xlabel('b={}'.format(b))\n", "axScatter.set_ylabel('c={}'.format(c))\n", "plot_cov_ellipse(cov, ax=axScatter, mean=mean)\n", "\n", "# demonstrate what ufloat errors are\n", "axScatter.axvspan(b.n-b.s, b.n+b.s, color='y', alpha=0.1)\n", "axScatter.axhspan(c.n-c.s, c.n+c.s, color='y', alpha=0.1)\n", "\n", "# histograms\n", "axHistx.hist(xs, bins=50, density=True)\n", "axHistx.plot(_x, norm.pdf(_x, b.n, b.s), '--')\n", "axHisty.hist(ys, bins=50, density=True, orientation='horizontal')\n", "axHisty.plot(norm.pdf(_y, c.n, c.s), _y, '--');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we determine the period, phase, and amplitude of a sine wave using a least squares fit. To simulate the errors, we provide Guassian samples of the errors." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:46.379859Z", "start_time": "2017-09-12T23:18:46.025937Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%pylab inline --no-import-all\n", "import numpy as np\n", "import uncertainties\n", "from uncertainties import ufloat\n", "from uncertainties import unumpy as unp\n", "\n", "np.random.seed(2) # Always use a seed so you can reproduce your results\n", "\n", "def f(t, A, w, phi, np=np):\n", " return A*np.sin(w*t + phi)\n", "\n", "A = 1.0\n", "w = 2*np.pi\n", "phi = 0.1\n", "\n", "N = 50 # Sample size\n", "ts = np.linspace(0, 5.0, N)\n", "fs = f(ts, A, w, phi)\n", "f_std_dev = 0.1 # Error in data\n", "dfs = np.random.normal(0, f_std_dev, size=N)\n", "plt.errorbar(ts, fs+dfs, f_std_dev, fmt='+')\n", "plt.plot(ts, fs, '-');" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:46.859628Z", "start_time": "2017-09-12T23:18:46.381694Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.009+/-0.020 6.269+/-0.013 0.13+/-0.04\n" ] } ], "source": [ "from scipy.optimize import curve_fit\n", "\n", "params_guess = (1.0, 2*np.pi, 1.0)\n", "params, pcov = curve_fit(f, ts, fs + dfs, sigma=f_std_dev*np.ones(len(ts)), \n", " p0=params_guess, absolute_sigma=True)\n", " \n", "A_, w_, phi_ = uncertainties.correlated_values(\n", " params, covariance_mat=pcov, tags=['A', 'w', 'phi'])\n", "\n", "print(A_, w_, phi_)\n", "A__ = ufloat(A_.n, A_.s)\n", "w__ = ufloat(w_.n, w_.s)\n", "phi__ = ufloat(phi_.n, phi_.s)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:47.065974Z", "start_time": "2017-09-12T23:18:46.861509Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fs = f(ts, A, w, phi)\n", "fs_ = f(ts, A_, w_, phi_, np=unp)\n", "fs__ = f(ts, A__, w__, phi__, np=unp)\n", "errs = unp.nominal_values(fs_ - fs)\n", "plt.axhspan(-f_std_dev, f_std_dev, color='y', alpha=0.1)\n", "plt.fill_between(ts, errs - unp.std_devs(fs__), errs + unp.std_devs(fs__), \n", " label='uncorrelated', alpha=1.0)\n", "plt.fill_between(ts, errs - unp.std_devs(fs_), errs + unp.std_devs(fs_), \n", " label='correlated', alpha=1.0)\n", "plt.ylabel('error')\n", "plt.xlabel('t')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Above we demonstrate the difference between correlated and uncorrelated errors in the model parameters." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we use the Cholesky decomposition of the covariance matrix $\\mat{C}$=`pcov` to [generate correlated random values](http://scipy-cookbook.readthedocs.io/items/CorrelatedRandomSamples.html) for the parameters. We check with a histogram that these are indeed correctly generated:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:47.770458Z", "start_time": "2017-09-12T23:18:47.067882Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import norm\n", "\n", "M = 4\n", "plt.figure(figsize=(6, 2))\n", "C = np.linalg.cholesky(pcov)\n", "labels = [r'$A$', r'$\\omega$', r'$\\phi$']\n", "dA, dw, dphi = C.dot(np.random.normal(size=(3, N*M)))\n", "for _n, (X, dX, label) in enumerate(\n", " zip([A_, w_, phi_],\n", " [dA, dw, dphi],\n", " labels)):\n", " _x = np.linspace(X.n-4*X.s, X.n + 4*X.s, 50)\n", " plt.subplot(131+_n)\n", " plt.plot(_x, norm.pdf(_x, X.n, X.s))\n", " plt.hist(X.n + dX, density=True)\n", " plt.xlabel(label)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2017-09-12T23:18:49.238540Z", "start_time": "2017-09-12T23:18:47.772214Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "labels = [r'$A$', r'$\\omega$', r'$\\phi$']\n", "data = np.transpose([A_.n + dA, w_.n + dw, phi_.n + dphi])\n", "data_frame = pd.DataFrame(data, columns=labels)\n", "scatter_axes = pd.plotting.scatter_matrix(data_frame, diagonal=\"kde\")\n", "\n", "plt.tight_layout()\n", "\n", "for _n, (X, dX) in enumerate(\n", " zip([A_, w_, phi_],\n", " [dA, dw, dphi])):\n", " _x = np.linspace(X.n-4*X.s, X.n + 4*X.s, 50)\n", " scatter_axes[_n, _n].plot(_x, norm.pdf(_x, X.n, X.s), '--')\n", "plt.savefig('Correlations.svg')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# To Do" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an exercise, use such randomly generated data to check that the parameter estimates are correct." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda env:work3]", "language": "python", "name": "conda-env-work3-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" }, "nikola": { "date": "2017-09-05 21:24:57 UTC-07:00", "description": "", "link": "", "slug": "uncertanties", "tags": "", "title": "Uncertanties", "type": "text" }, "toc": { "base_numbering": 1, "nav_menu": { "height": "48px", "width": "252px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": "block", "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 2 }