{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CLs method\n", "The hep_spt package also provides tools to work with the CLs method. This method is oftenly used in High Energy Physics to reject models, preventing the exclusion when there is not enough statistical power. The rejection is determined comparing an alternative model, with repect to the null model. In this document you can see an example of how to work with the different classes and functions here present." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import poisson, chi2, norm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The CLs test statistics\n", "Here we are going to create four different models (related two by two). The first two will follow a poissonian distribution, while the other two will be gaussians. Note that we can only work with only one type o functions, i.e. either both models follow a discrete or a continuous function. We will then plot the distributions of the null and alternative hypotheses, together with their associated test-statistics." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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Fk956DKvD8fGxDg8PO6+DINDW1lbfuvb29lQqlfqC/+XlZVff6OPjY3me1zXfqH2VVm8pfd8EQSBJXce0XC53BZDe/TBq/mG++eYbSdKnnw7/vic3LctMriFOLV6mz+2M48C0cax3+d7BF7JIG3yBOEWcIk6133ZYAV3pgDkpl8udVp5pxJe7ewNXsVjstNL4vt/pNy5Jh4eHnRNZfDLJ5XJdy/u+33UJvV6vd7Ue5vP5qS9xxye33kv18fCcWbYti97AlNy2QqGgVqvVV4dBy8TvnVStVlUulxWGYWfa/v6+jo6OuuY7PDxUpVLpmm+aeo/aN0EQ9G3T3t7e0Pcad34Am484RZyapt6bGKfoSgfMQNwyk+yvHV9+DsNwqkvAV1dXkvpHjrl9+3bfetMu649q1apWq50T89XVlXK5nDzPm7r+5XJZJycnnWFhG42GHjx4IGm8bUszatuOjo766pBskUoT79OrqysVCgU1Go3OvhlUj0ajkXn40bR6j9o3Dx480N27d1Wv11UqlVQoFFLfd9z5AWwW4tRwxKnJ6r2JcYrECJgBz/MGDjl5dXWlp0+fDu2mkEXcP7j3BJn1hJmsY5pWq6VSqaSjo6NOfff399VqtaYKOAcHB7p7927nZB8EQafui9q2g4MD3bp1q1OHcYNo3A0krvOwZXO5XGe+LNLqkGXfPH/+XKenpzo5OVG5XFaxWBza+ut53ljzA9gsxKnhiFPDuRan6EoHTCkMw77L/7GHDx8OfYDeKM1ms9PtoNVqTVPFTPb29jonoV7DLrvHdUzjeZ52dnZUq9W6ulFIWti2eZ6nQqGg09PTiVoWgyDo1DvuDjJIq9Ua2rqWZV8ljdo3zWZTnufp8PBQz54904sXLxSG4dBnk4w7P4DNQZwiTsWIU+kyJ0bGmKoxptAzzTPGHEZ/58aYfE/5oTGmGP2buQxYJ41GY2jXgGKxqGazOVbrTCxu8dnZ2ZHU3/85fu9ZCMNQQRB0ug4kp0vtFsVBJ8u0VqmkuJtCb9eARWzbqDqMEp+o42V2dnbUarUG7o9mszl03Vn3VWzUvolHG4rFrcG9N+8mlxln/nVEnAIGI04Rp5LzEqeGG5kYGWMKxphDSYM6+VWttcfW2mNJFUm/McZ40XLnkhrW2lpUXk2sc2gZsG4uLy+Hlvm+L9/3M7fGJS+Fx60wnufp7Oysb1jVRqPROSllMegEmXyP5Ot4/fl8XmEYdrVeDarjKMViUVdXV33zL2LbknUIgmBknXtvpq1UKjo7O+uqc7Va7avz8fFx38g5o/bVqGMyat/0dotptVra3d0dum3jzr8uiFNAOuLUaMQp4pSU4R4ja21DUsMY0zUshDHGl3SdmC8wxgSSDiQdS8pba5MpZGCMKUTrSysD1kKj0eg8HG3Q2P9S+2QVBIGOj48ltVuD4umSOn2l45a88/NzVatV7e3tdV3qLhaL8jxPlUpFW1tbyuVyyufz8jxPzWZTjx8/7qx/b2+v61kM8XvFI9T4vt+pV3wCKhQKndF+Hj58KN/3lcvlVK1W9fjxYz18+LBTl0F1TL5PqVRStVrtu1R/cHAwsJUqbdvSjLNtyTr0tjb2ikc5CsNQl5eXqlQqffU+ODhQo9HoDH0ad73o7d4xal+NqnfavvE8T+VyufPMhzh4xYG193ikzb/uiFPAYMQp4hRxajyZn2NkjKmr3fLWiF7nJT2z1prEPM8kNSTF824nyuIUcGiZtTb7k8a668bzIWZgnMc58BwjrKPT09PUG4zTnufgsnV5jhFxCknzeI7RqDg1yrKfY4TVR5yazKzi1MSj0llrm8aY7Z7JebW7KgxKof8oaXdEGTZI7wn95oiT9ctv08tHLQ+k6b2hFpuPOIWRxk2MRsSpUaaNg9hsxKnlm2pUumQ3A2PMgdr9sRuSBg990pZWBgAzUyqVOqPZjHszKzYDcQrAKiNOrZaZPMcoupG1ZK2N+3en3TU21piHxpiLDLN9Ps46AbghfhJ4rVZLfahgsv/7sL7nWG/EKQCriDi1Wmb1gNeqpFLidaj+rgi3JQUjygBgZsZ5ajgPOt14xCkAK4c4tVqmToyiIVKr1towep231jaMMb1dETxJ52llg9Zvrb2foQ4Xku6NW3cAwOYjTgEAspjqHiNjTFFSU1IreoheXlI8qHuj54F4fmKY07QyAABmgjgFAMhq5BWjKDA8lFSIX1trj6PnQwxqPYv7b+9LOorm21V7FCBlKAMArIh1GBaWOAUA7pplnMrygNem2q1tlZ7pgVLGAY+6LMTL1LKWYT28edMeR9/aNzJmqguPAFZYHHCMWdrjiUYiTmGQ+Hkvb9680Y0bxClgU80yTnGmwERevXpX//f/Sv/+798vuyoA5uj779vf8XfffXfJNQHGE39m488wgM00yzhFYoSJ/OEPN/XqlfS///d3ev36pax9sxZdbgCMFreyv3z5Ut99950k6ebNm0uuFTCe+DP73Xff6eXLl3rzhjgFbIp5xalZDdcNx/zP/5nTrVvfS3ql16//Tf/xP0qjrmD+6U/p5f/n/0y3PID5+NGPfqRcjmeeYr3kcjl9//33evXqlf7t3/5tJuscFadGmTYOzuI9gE00qzhFYoSJvHlzQ//tv/1Y/+k/tfTBBy/1ox+91o0b6S1xd+6kr/N//a/08lHLA5gdY4zeffdd3bx5U7lcjns0sHZu3LihH//4x2q1Wnr58qVev3499RWjUXFqlGnj4CzeA9gU84hTJEaY2Js3N/S7332g3/3ug0zzP3qUXv7kyXTLAwCQdOPGDX3wwQf64INscWqUUXFqlGnj4CzeA8BwNAECAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnvZN1RmNMVVLdWtvomX4oKZDkS2pYa5vTlgEAMC7iFABgGiMTI2NMQVJeUlFSvafsXNLjOFgYY+qS9qYpAwBgHMQpAMAsjOxKZ61tWGuP1W4165XvaUELogA1TRkAAJkRpwAAs5C5K12vKECEPZNDSXvGGE1SJqkhAABmgDgFABjHNIMveAOm/VHtvtiTlgEAMCvEKQBAZhNfMZKUm0NZH2PMRYbZPh9nncDaevRounLALcQpAN2Io0gxzRWj1hzKAACYFeIUACCzaa4YhervbnBb7ZtfJy3rY629P6oiUWvdvVHzYb3RyANgTMQpOIdYCUxu4itG0XMiersbeHr7DImxyyatCwAAvYhTAIBxTNOVTpIaxph84rWfeLDepGUAAMwKcQoAkEmWB7zmJT2UVIhfR8+LkKR9SUfGGF/SrqRKYtFJywAAyIw4BQCYhZGJUfSAu6YGBAVrbZiYXptFGQAA4yBOAQBmYdqudAAAAACw9kiMAAAAADiPxAgAAACA86Z5jhGAWeMBEwAADMeDmjBHXDECAAAA4DwSIwAAAADOIzECAAAA4DwSIwAAAADOIzECAAAA4DwSIwAAAADOIzECAAAA4DyeY7RBGNp/ybLsYA4CACwNcXINcBCwRFwxAgAAAOA8rhgBm4TmUAAAJkccdRpXjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPPemXYFxhhP0oGkUJInqWmtbSTKDyUFknxJDWttM0sZAACzQJwCAGQxdWIk6cBaexy/MMZUjTFX1trQGHMu6XEcSIwxdUl70f+HlgEAMEPEKQDASLPoStcbJK7VblmTpHxP61pgjClkKAMAYFaIUwCAkWaRGOWMMdXE6z1rbTMKHmHPvKGkvbSyGdQHAIAk4hQAYKRZdKXbl/SbKIg8kVSJpnsD5v2jpN0RZV2MMRcZ6vB5ppoCSPfo0XTlwGoiTgGYDeLkRps6MYpa3U4lFSVVJTXVvlE1l7JYWhmwmjjZAWuJOAWsEGIpVtgsRqU7kVS11lai/9eNMduSWimLpZV1sdbez1CHC0n3sq4TAOAO4hQAIIupEiNjTF7StbU2kCRrbdkYcy2pLOlc/V0RbqvdShemlAEAMBPEKQBAVtMOvuCrP0icSlL0jIjergiepHpa2ZT1AQAgiTgFAMhk2sSoIelhz7SCpJO4PGqti/mJh+qllQEAMAvEKQBAJlN1pYsejvc4Ggb1OpocJJ77sC/pyBjjqz2STyWxeFoZAABTI04BALKayah0ao/wM6gs1NtAUstaBgDArBCnAABZzOIBrwAAAACw1kiMAAAAADiPxAgAAACA80iMAAAAADiPxAgAAACA80iMAAAAADiPxAgAAACA80iMAAAAADiPxAgAAACA80iMAAAAADjvnWVXAMAaefRounIAAFyWJU4SS5eGK0YAAAAAnMcVI2wMLmYAADAdYilcxhUjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgvHeWXQFgZTx6tOwaAACw2kbFSmIp1hhXjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4751ZrMQY40sqSgolyVp7mig7lBRI8iU1rLXNLGUAAMwKcQoAMMrUiVEUbKrW2lL0+pkx5spa2zTGnEt6HAcSY0xd0l70/6FlAADMCnEKAJDFLLrSVSWdJF5/mWhRy/e0rgXGmEKGMgAAZoU4BQAYaarEyBjjSSpaaxvxNGttGJUVFHVZSAgl7aWVTVMfAACSiFMAgKym7UrnSwqjAOJFr5tRAPIGzP9HSbsjyroYYy4y1OPzrBUGADiFOAUAyGQWiZEkteLWuKjvdklSLmW5tDIAAGaFOAUAyGTaxCiU5PX2wZZUlnSZslwr6xtYa++PmidqrbuXdZ0AAGcQpwAAmUw7+EKg/j7Y8bCmofq7ItxOLDOsDACAWSFOAQAymSoxstYG6g8cnqQg6rLQ2xXBk1RPK5umPgAAJBGnAABZzWK47uOe4Ut3JD2O/t8wxuQTZX5iZKC0MgAAZoU4BQAYaeoHvFprK8aYavQAvS1J+/FQqJL2JR1FZbuSKolF08oAAJgJ4hQAIIupEyOpHXSGTA/1NpDUspYBADBLxCkAwCiz6EoHAAAAAGuNxAgAAACA80iMAAAAADhvJvcYAYAk6dGj6coBAHAdsXRpuGIEAAAAwHlcMVojNBAAADAccRLANLhiBAAAAMB5JEYAAAAAnEdiBAAAAMB5JEYAAAAAnEdiBAAAAMB5JEYAAAAAnEdiBAAAAMB5JEYAAAAAnEdiBAAAAMB5JEYAAAAAnEdiBAAAAMB57yy7AsCs3L94NGKOUeUAALhtZCy9v4haAMvBFSMAAAAAzuOKERC5uEgvv39/EbUAAGB1jYyVi6gEMCdcMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM57Z5YrM8YUJHnW2lpi2qGkQJIvqWGtbWYpAwBg1ohTAIBhZpoYSapKOolfGGPOJT2OA4kxpi5pb1QZAEc9ejRdOTAacQrAZiOWTmxmXemiVrigZ3K+p3UtiOYbVQYAwEwRpwAAaX10trsAACAASURBVGZ5j5EnqRW/iIJH2DNPKGkvrWyG9QEAIIk4BQAYaiaJkTGmmOyvHfEGzPpHtftpp5UBADBTxCkAwChT32NkjPHU36omSbmUxdLKetd/kWG2z7OuDwDgFuIUACCLWVwxKlhrGwOmtwZMy1IGAMAsEacAACNNdcXIGOOr/0bWWKj+rgi3o/nTyrpYa+9nqMeFpHuj5gMAuIU4BQDIatqudHlJOWPMTvR6J3ota+2pMaa3K4In6dxa2xhWNmV9AABIIk4BADKZKjHqvZHVGLMnqW6tPY0mNYwxyeFO/UR3hrQyAACmRpwCAGQ1swe8Rk8HL0jyjDGtKBjtSzqKujLsSqokFkkrAwBgpohTAIA0M0uMrLXHko57poV6G0hqWcsAAJg14hQAIM0sH/AKAAAAAGuJxAgAAACA80iMAAAAADiPxAgAAACA80iMAAAAADhvZqPSAfN2/+LRsqsAAMBKGx0rR5UD7uKKEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRgBAAAAcN47y64A2h49WnYNAABYbcRKAPPEFSMAAAAAziMxAgAAAOA8EiMAAAAAzuMeIwDrY9QNBtyAAABAOmLpUFwxAgAAAOA8EiMAAAAAziMxAgAAAOA8EiMAAAAAziMxAgAAAOA8EiMAAAAAziMxAgAAAOA8nmMEZHRxkV5+//4iagEAwPoilmKVccUIAAAAgPNIjAAAAAA4j8QIAAAAgPNIjAAAAAA4j8EXsDLuXzxadhUAAFhZxElgvrhiBAAAAMB5JEYAAAAAnDd1VzpjjCfpIHq5K+mxtbaZKD+UFEjyJTWylgEAMAvEKQBAFrO4x6hqrS1LkjHGl/TMGHPXWhsaY86VCEDGmLqkvej/Q8sAAJgh4hQAYKSpEqMowFzHr621gTEmULtl7lhSvqd1LTDGFKy1jRFlADC+R4+mK8fGIU4BwJgcjqXT3mPkSaoOmH7bGFOQFPZMDyXtpZVNWR8AAJKIUwCATKa6YmStbRpjtnsm5yVV1A5Gvf6odv/utLIuxpiLDFX5PMM8AADHEKcAAFlNPSpdz02qB2rfnNqQlEtZLK0MAICZIU4BALKY2QNeo1F/StbauJtBK2X2tLIu1tr7Gd77QtK9rOsEALiHOAUASDPL5xhVJZUSr0P1d0W4rfawp2llAADMA3EKADDUTBKj6DkPVWttGL3OD+mm4Emqp5XNoj4AACQRpwAAo0ydGBljipKaklrGGM8Yk5e0ExU3otcxPzHMaVoZAAAzQZwCAGQxi+cYnQ8oivtv70s6iubbVXsUIGUoAwBgasQpAEBW0w7XHUgyKeWh3gaSWtYyAABmgTgFAMhqZqPSAcDay/I07w1+4jcAAFMbFSdXOI7OclQ6AAAAAFhLJEYAAAAAnEdiBAAAAMB5JEYAAAAAnEdiBAAAAMB5jEoHzMjFxeh57s+7EgAArLFRsfT+/UXUAq7iihEAAAAA53HFCDNz/+LRiDlGlQMA4K7RcRTAPHHFCAAAAIDzSIwAAAAAOI/ECAAAAIDzSIwAAAAAOI/ECAAAAIDzSIwAAAAAOI/humfk0aPpygGsCb7swMT4+gBY5RMBiRGwQnjiNwAAw42Mk4uoBDYWXekAAAAAOI/ECAAAAIDzSIwAAAAAOI/ECAAAAIDzSIwAAAAAOI/ECAAAAIDzSIwAAAAAOI/nGAHALK3wg+sAAMBwXDECAAAA4DwSIwAAAADOIzECAAAA4DzuMUJm9y8eLbsKAACsrNFxclQ5gGXiihEAAAAA53HFCFgjFxfp5ffvL6IWmCtGtQOAuSGOIg1XjAAAAAA4jytGGdFICwBAOmIlgHVGYoQOBlcAAGA44iSw2ZaaGBljDiUFknxJDWttc5n1AdbdyL7Ti6gEsEGIU4BbuAfJbUtLjIwx55Iex0HGGFOXtLes+gDAWmBwhoUhTgGAW5Y5+EK+p+UtMMYUllYbAAC6EacAwCFLuWIUBZawZ3KodktcY/E1AiDRhWAjcEVpJohTAAahy/pmW1ZXOm/AtD9K2l10RTYJT9wGgJkhTm0g4iSANMZau/g3NeZAUtlau52Ydihp11pb6pn3IsMq/8tf/uVf/n+ff/75xHX6H/9j4kUz+clPpn9/L8wwU9ryn6dXIvzX6dbP+69+Heb9/t6gn5JJU34Rwt72+wW//0ysQh3SjKrfCP/8z//8a2vt/z+byizPKsapVbDqsXLV4+SyY8Ai6rDsbdyE93c+lk4Zh0ZJi1PLSoyKko5mGHC2Jf1J0n+fsEpxpPrXCZdfVWzXetnE7drEbZLYrjT/uiGJEXFq87APp8c+nA77b3pzjVPL6koXqr+bwm21h0TtYq29P+/KxEFtEe+1SGzXetnE7drEbZLYLkcQpzYM+3B67MPpsP+mN+99uJRR6ay1DUm5nsmepPoSqgMAQBfiFAC4Z5nDdTeMMfnEaz8KRAAArALiFAA4ZGkPeJW0L+nIGOOrPcpPZYl1AQCgF3EKAByytMTIWhvqbZCpLaseAAAMQpwCALcssysdAAAAAKwEEiMAAAAAziMxAgAAAOA8EiMAAAAAzjPW2mXXAQAAAACWiitGAAAAAJxHYoSVZ4ypGmMKA6YfGmOK0b/5QcuuskHbZYw5iP48Y4xvjKkuq34AAADLtsjfgct8wOvKMMYcSgok+ZIa1trmkqs0FWPMQfTfp5JyksrW2rV7MGH0JchLKkqq95SdS3ocHytjTF3S3sIrOYG07ZLkSapKOlH7M7kW2yRJxhhPUvzZ21Xi+ETla/k9S9uudf6uJbYrlLQt6dxa20iUr+XxckHUYFJPHq9oOscMc8PnazrrHC+WZSm/A621Tv9JOpeUT7yuL7tOM9imQ0k2+ruW5C+7TlNuT11SoWfadc/rk955Vv1vyHYdRP96y67fBNtzkvi/L+lFvB3r/D0bsV1r+12TVO3ZLrsJx2uT/yQVos/c9YBzB8dssn16EP150feguuw6reIfn6+Z7MO1jRfL/lvk70C60rW/6MlWj2DQ5bo1E1prjaRb1tota22w7ArNUnR8wp7Jodbo6soo1tre7Vtpxhhf7RO9JCn6zAV6e6VlLb9nGbZrnb9rB/ExSNTbj/5dy+O16ay1DWvtsdqfwV4cs8l4av+geqH2j6+T5VZnZfH5mt46x4uVMs/fgU4nRpv+A3vdflyPwRsw7Y96+6NurUX3GBWjPrXrcu9U3AWw1+01/54N3a7kizX9rm3bqCtWlABKb3/srOvxchLHbCr8WB2Bz9dsrWm8WDVz+x3o+j1Gw3bs7qIrMmtRX9aW2tvyxG5WX+DcsiswR41EYK4ZY66NMdurfiK11jaNMds9k/OSKlrj79mI7ZK0vt+1nh+AZUkVa20Y3XvUay2Ol8M4ZlNa9XPskvH5mpF1jRcraG6/A11PjDb1B/Za/rgeQ2vZFZiXAa2VoaQHkk6XUJ2x2O6BFg7U/hw2EjecrqVh2xVNWuvvWnSlqKh2X/c42dvU8+Im45hNgR+rI/H5mo21jhcrZm6/A53uSqcN/YGd8uN6U4Tqb8G6rcH97tdGNDz3i57JgaStZdRnUtEVh5K1Nu5msRHfswHbtfbfNWttEN2zUomCtKcNOV6O4ZhNrmGtPbXW1qLGgfMhV01dxudrBtY9XqyYuf0OdP2K0cb9wI5agJ9Za28lJq/dj+s00VWI3hYsT+1Rc9Zd79CdnhI3/6+JqqRS4vWmfM+6tmvdv2vGGC9uqbTWBsaYUNKR2jegb8LxWnnRlYrerpq9qhnue9mU79jCrfNV+gXi8zWldY8Xq2aevwOdTow2+Af2Jvy4HqVhjEmOkuPbnmd6rJvox2kn+ET/9621axOgo+dcVOMf3NExWvvv2aDtUvvHwlp+16KbqeuSTE+RtwnHa13M6rvNMXtrnGSTH6vZ8PmambWMFytsLr8DnU6MIhv1A3sTflzHoh+fD9V+dkf8I/s4Kt6XdBQFtl31n3BW1ojtOo1+hMcP3VybUX+MMUVJTUmt+HMnaSeatrbfs2HbZa09XePvWqD+74yfmLa2x8thHDNNlGzyYzUbPl9T2KTfZou0jN+BJnookrOiD+eRpEttyI2XA55on6UrBjCx3uf9JOxFrY1r+T3LuF1r+V1LPFE8rnvdWluLytbyeG26xI+EQ0kNtY/ZcVTGMZuAMeawZx8+s9ZyxagHn6/prXO8cInziREAAHATP1YBJJEYAQAAAHCe68N1AwAAAACJEQAAAACQGAEAAABwHokRAAAAAOeRGAEAAABwHokRAAAAAOeRGAEAAABwHokRAAAAAOeRGAEAAABwHokRAABARsaYvDHmhTHmxBhzaIypG2Ns9P9q9PrZsus5LWPMuTHmYFnLz4IxpmCMuTbGVJdZD6wPEiMAAIDsfElfWmvL1tpjSSeSQmvtsbW2Yq3dk9SYdOXTJhOTLD9kmRNl3I5pl58Xa21DEkkRMntn2RUAAABYJ9ba5ohZLidZrzHGk7Q1ybKTLj9smSipmPvyC9DSFPsUbuGKEQAAQHbBjObpEiUYZ+NXZ/Llhy1jjPGiLoP+PJdfFdF2ACRGwKrjhA0AqyPD1SJZa5vGGD+656gY/ds5lxtjDqL7X4rGmJNockGSJykf3a9UGLb+cZePkpTe+dOWyandBa084XsOWt5L7I+CMSY/Yt3J7S1G93U9i/djdA/TdbRtw7avdz3xPUcnif3yTInkLu24YfPRlQ6Ys+jkn1M7eOxZa8tD5iso6pNtrS1Hy52p3fJYWlR9AQAzUZe0ba0NjTGB2ufzUnQ/ThB3NYuvqlhra9H/b0f3Lg004fLnkkrW2oYxJmeMqUb3Qw1cxlobGGPOFXVBG/c9e5eP/CaqQxDFt3NJW8PWnRS9T07tGBpGk08kXUX793rQ9g1YTyNKirai101jzGNJDxOzDTxug44FNg9XjID5O5fUstbWJD0bNjpOFBROEq+bkh4vpooAgFkxxhTV/rEfSp3zeXw1JZB0El0l8dKSoCEmWX47caXrSlI+beZIa8r37CwfX0my1gbRv01J2+Os21p7qrf7UJK8RJI0zvaFwwpGHDc4gMQImL+ZnLABAGtjV+p03SpEicFTqdMIVlH7KsSLtK5fg0yyfHT1oxhdnSmo3Ythru/ZI6/uREuJ5GOcdT+NEygl4uW025cw9LjBDSRGwJzN8IQNAFgPl2oP4d1I/JWl9o9ua20tGtb7liR/UPex6OpFn0mWj+6jCaKrLkNHi5vle/Zoakjsy7ruyIna9y0VkqPeZd2+DIYeN7iBxAiYsxmesAEAayDqOt314z4xMEE+HnggumqSHMwhUPt+1DRjLR+9r5fouZCLpnvReoa9Zy4xfZI6d5aPkhgvmfCYt88+Slt3l2gbPCX2bYbtS25HXN9kkrabWH/acYMDGHwBmKO0E7YSJ99EeSBpL7GK3cT/lQgeI0dFAgDMT/Qjv6j2jfte1AXsWdQIJrUHWqjq7TON4iG8Q3VfFblO3HtTM8Y8jAckGPLWYy0fDTjQTExrRf8eRPfzNHuXiWJNOdquwrjv2bt8lBhtS6oaY+rROuKGwqHrHqKaWDZ1+6L5StH6i9GVqYYxppS4unUtqRiXa/hxgwOMtXbZdQA2WjQyT11vT9hHki6ttcfRyddLXqqPgmscOHJq972ORw/qmx8AAADTIzECAAAA4DzuMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM4jMQIAAADgPBIjAAAAAM7biMTIGPMPxph/WHY9AAAYhDgFAKvvnWVXYEY+v3fv3j1JP1t2RQDAcWbZFVhRxCkAWA1D49RGXDECAAAAgGmQGAEAAABwHokRAAAAAOeRGAEAAABwHokRAAAAAOeRGAEAAABwHokRAAAAAOeRGAEAAABw3qY84BVL8ObNG7VaLb18+VKvX7+WtXbZVQIwI8YYvfvuu7p586ZyuZxu3KAdDeuHOAVsrnnEKRIjTOTNmzf63e9+p1evXi27KgDmwFqrH374QT/88IO+//57/fjHPyY5wlohTgGbbR5xisQIE2m1Wnr16pXeeecdffTRR3r//ff50QRskDdv3uj777/Xd999p1evXqnVaumDDz5YdrWAzIhTwGabR5ziDIGJvHz5UpL00Ucf6ebNmwQbYMPcuHFDN2/e1EcffSTp7XceWBfEKWCzzSNOcZbARF6/fi1Jev/995dcEwDzFH/H4+88sC6IU4AbZhmnSIwwkfgGVlrggM1mjJEkblrH2iFOAW6YZZzibAEAGCoOOAAArKJZxikGX8DCfPttevmdO4upBwAAq4g4CSxX5itGxpiqMaYwYPqhMaYY/ZufRRmAtjAM1Ww2R04bZ/l1sK71BgDXEKewSUYmRsaYgjHmUFJxQNm5pIa1tmatPZZUnbYMWCeVSkXb29syxgw8QVYqFd26dUtbW1s6PT0da91BEKhUKml7ezt12jjLr4NF1btWq2lra2uu7wEAy0acmj3i1OYyWW9UMsbUJVWttY3EtGtr7Vbi9Ymkc2ttY9KyiTbCmIt79+7du7i4mGRxTOCbb76RJH366adD53n0qPv1qFEUb96cslJj6q3fpE5PT/Xs2TNdXV3p2bNnfeW1Wk2+7yufn+zCqDGm74bCQdPGWX5VNJvNoftl3vVuNpt68uSJqlXaZUbJ8n1P4KakAYhTizdJnFq23jj58593v560Kx1xanLEqfUwqzg18eALUbe6sGdyKGlv0rJJ6wIsW7VaVRAEA1vbPM+T7/tLqNXqazQmaguZiXw+T7AB4Azi1GSIU26ZZlQ6b8C0P0rypygD1pLneapWq6pUKgrD3rwfwzx58mTZVQAAJxCnJkOccss0iVFuDmV9jDEXo/4kfT7OOoF5ODg4UC6XU6VSGTnvtDerrrswDFWpVJa6vc1mc6ktgQCwaMSp7IhTbppmuO7WHMqAtXZ+fq7t7W1VKpWh3RKCIFClUlGtVuv0TY5PwHE/8En7eQ8ThmHn5Hp5eand3V0Vi+3xVI6Pj/X48WOFYajz8/PO9GazqS+//FK5XE7n5+eSpP39fQVBoOfPnw9dX6zRaCgIAuVyObVaLeVyuc48T58+7cwXB+itrS0dHBxkrnesVqt1/n95eamHDx929l+tVpPneZ111ev1TreEx48fdx2DtPnjaQCw7ohTbxGn0GuaxChUf7e425KCKcr6WGvvj6pIdNXo3qj5gHnL5/MqFosqlUoDb3CVJN/3dX5+3vVAMs/zdHJy0nUinqVGo9E5UReLxa4bRg8PD5XP51Uul7tO5vl8XkdHRzo8POxMOz8/19bWVt/69vb21Gq1OgGjVqvp8vKyq2/08fGxTk9PdXBw0Jnv+Pg4tf90Wr0ldfrKx+srFova2tpSvV5XEATyPE+FwtunDNTrdUnt/d17DBqNxtD5AWBTEKeIUxhu4q500Qhyvd3iPEn1ScsmrQuwSs7OztRsNrtaiLLK5cbqaZpZb6ug7/td3QMKhYJarVZfl4FBy0nqaw2rVqsql8udfuv7+/s6Ojrqmufw8HDsvu1p9Y5bL3tb74rFomq1moIg6Nuevb3hY7yMOz8ArCviFHEKg01zxUiSGsaYvLU2Pkp+YsjtScuAtRbf4Lq/v993Yl6WLKMNHR0d6eTkRCcnJ5LaLVPJVqk0cZeAq6srSe3AOeiyvu/7Xa1r09Q7fq/e/te3b9+W53l68OCB7t69q3q9rlKppEKhkPq+484PAOuKOEWcwmBZHvCaN8ZUJRUkVaKHvcb2JT00xhSjeSozKMOa+vbb7r+XL7v/XHJ4eJj5BtdFyNL3+ODgoGsY1zAMx+qz7Pu+giDodA0YJJfLKQgG9podKO39437hhUKh6+/w8FAHBwfyPE/Pnz/X3t6eTk5OtLW1pVKplPpe48yP1WOMqUaPhOid7htjDo0xB8aYg56ywygWHRpj8lnLgHVHnCJOod/IxMha27TWVqy1xlq7Z609TpSFUVkt+rc5bRmwKU5OTnR8fDzWCXaZ4n7Lp6enYwcbqR0AfN+X7/tDuyG0Wq2hrWvNZnPs7gut1vCxXJrNpjzP0+HhoZ49e6YXL14oDMOhT3Yfd36sDmNMIWq062s6Ncb4aj+c/NhaeyqpHCc5xphzSY0oFh1LqiaWG1oGbAriVD/ilNumGa4bQIq4ZSitNa73BLvs4FQul3VycjJW9wTp7cm6UChoZ2dHrVZrYPBoNptD15vWgjfIzs5OZ529Go1GZ7ShWNx15Pr6euD6xp0fq8Na24iSl0FfoKqkk8TrLxONcfmehrkgccUprQzYCMQp4hS6kRgBU7q+vh7agnRycjK0LJ/Pd53gGo3GyNalSQ2qw6D3KRaLCoJgZB16b9itVCo6OzuT1P0QwaR4ZJ9kUIm7NQyrT1q9Pc/T2dlZ3/s0Go1OMOodSajVaml3d3fodo07P1abMcaTVEzew2qtDaOygtqjpCaFkvbSyuZYXWBuiFPEKWQz7eALgNMqlYqOj4/VaDRUrVb7Wpl83+8aRjTp7OxMT5486Zxwfd+X53kql8uqVCpdrXilUklHR0fyPK9v2rBnScTPoZDejr7j+74qlYqCIOicXHvrfHBwoAcPHqRudz6fV6PRUBiGury87NQ3uY5Go6Hj42N5nqcwDOX7ft9Noufn56pWq9rb2+t0XRin3sVisbNPtra2lMvllM/n5XleZ1/Gz3yIg1ccVJP7MQ6Ew+bH2vIlhVGi40Wvm1GiNKjZ94+SdkeUAWuFOEWcQnYmOdb6ujLGXNy7d+/excXFsqvijG+++UaS9Omnn3amfftt9zy/+tV467x5c9pajefRo8W+37qIn+EwTO8zGrD5Bn3fU5jRs8yHMaau9v1Ejeh1UdKZEt3njDHPJJXUHlCobK3dTix/qHbyUx9WZq3tu9M5epbeKJ/fu3fvL4lTi5Plc7tqcaB3oKKf/7z79Z07i6vLKiNOodes4hRXjDA3vSf0UTjhL1/cYgZsiFCS13uvkKSypMuU5WbfTwgradUSo94GRvQjTmGeuMcIcFypVOqMaDPuzazAigvUf69QoKiLnfq7zN1OLDOsrI+19v6oP0n/OuW2AM4iTmFRSIwAx5XLZeVyOdVqtaH9wKX2qDrx8xJKpdLSRyYCRrHWBupPcDxJQdTdLjegrJ5WNpeKAkhFnMKi0JUOcNw4Tw0/Pz+fc22AmTs2xhQSI9PtSPoy+n/DGJMclttPzJdWBmCBiFNYFBIjAMBaix7Y+lDtARUUJTTHkmStrRhjqtGDXrck7cdDdkval3QUle1KSo6pm1YGANhAJEYAgLUWXdVpakjyYq0dNj1MLFPLWgYA2EzcYwQAAADAeSRGAAAAAJxHVzqsjFHPb+A5RwAAAJgXrhgBAAAAcB6JEQAAAADnkRgBAAAAcB6JEQAAAADnkRhhbXz7bfrfOgnDUM1mc9nVWHvruh/Xtd4A3MF5ajbWdT+ua72nRWIEzNjx8XHqySQIApVKJW1vby+wVvNXq9W0tbW1sPdb1/24qHov+ngAWB/EqcVY1/3ocpxiuG7Mzc1fPVrwG445/6NH86iFLi8vdX19rZOTk4Hlvu+rXq/LGNNX1mw2lc/n51KvWRlWR9/3VSwWF1aPtP24Kgbtq0XVe9HHA1hLc4oDk7r5svv1y58/msv7EKcWgziVbhXjFFeMgBkKgkDValWnp6cTLd9oNGZco9kbVsd8Pq9qtbrg2qy2ZR5PjgeAQYhTnBeTiFPdSIyAGQrDUL7vK5/Pq1arjb38kydP5lCr2VqHOq4K9hWAVUOcQhL7qhuJETAHDx8+HOtkE4ahKpXKSt/oOKqOzWZzLVoSF2EVjifHA0Aa4pTbVuF4ruLx4B4jYEaS/XQPDg5UqVQyL/v06dPO/+Pltra2dHBw0JmebNm7vLzUw4cPlc/n1Ww2tb+/ryAI9Pz5cz19+lT1el3lclm5XE77+/tqNpuy1nbWcXl5qd3d3b6+vb3vcXR0JM/zRtYxDEM9fvxYtVpN1lpJ7Zt7Hz9+rDAMdX5+3nmvIAi0vb0t3/d1dnbW12qZ3LaswjDsnFyT2zasDs1mU19++aVyuZzOz88lqWsfDlpXr0ajoSAIlMvl1Gq1lMvlOvNlOZ5p9U5K2ze1Wq1zfMIwVL1e73RL6D0eafPH0wBsNuIUcYo4lc4kK7OujDEX9+7du3dxcbHsqjjjm2++kSR9+umnnWm9Q2YvevCFm0sefKH3Bsbt7W2Vy+W+k0zMGKPe79+gaZI6fcGT69ra2lK9Xpfv+52T+NnZWedEG9/UGIahbt26pXq9rkKhMPS9arWa8vm8fN/vbE+lUlG9Xs9Ux0FljUZD5XJZ19fXXfNVKpXOiXHUto1ijOkKJr31GFaH4+NjHR4edl4HQaCtra2+de3t7alUKvUF/8vLy66+0cfHx/I8r2u+Ufsqrd5S+r4JgkCSuo5puVzuCiC9+2HU/MMM+r6nWN27jJeIOLV4mT63Kzb4wssRgy/cuTPd+olTxCniVPtthxXQlQ6Yk3K53GnlmUZ8ubs3cBWLxU4rje/7nX7jknR4eNg5kcUnk1wu17W87/tdl9Dr9XpX62E+n5/6End8cuu9VB8Pz5ll27LoDUzJbSsUCmq1Wn11GLRM/N5J1WpV5XJZYRh2pu3v7+vo6KhrvsPDQ1Uqla75pqn3qH0TBEHfNu3t7Q19r3HnB7D5iFPEqWnqvYlxiq50wAzELTPJ/trx5ecwDKe6BHx1dSWpf+SYIA5DzgAAIABJREFU27dv96037bL+qFatarXaOTFfXV0pl8vJ87yp618ul3VyctIZFrbRaOjBgweSxtu2NKO27ejoqK8OyRapNPE+vbq6UqFQUKPR6OybQfVoNBqZhx9Nq/eoffPgwQPdvXtX9XpdpVJJhUIh9X3HnR/AZiFODUecmqzemxinSIyAGfA8b+CQk1dXV3r69OnQbgpZxP2De0+QWU+YyTqmabVaKpVKOjo66tR3f39frVZrqoBzcHCgu3fvdk72QRB06r6obTs4ONCtW7c6dRg3iMbdQOI6D1s2l8t15ssirQ5Z9s3z5891enqqk5MTlctlFYvFoa2/nueNNT+AzUKcGo44NZxrcYqudMCUwjDsu/wfe/jw4dAH6I3SbDY73Q5ardY0Vcxkb2+vcxLqNeyye1zHNJ7naWdnR7VarasbhaSFbZvneSoUCjo9PZ2oZTEIgk694+4gg7RaraGta1n2VdKofdNsNuV5ng4PD/Xs2TO9ePFCYRgOfTbJuPMD2BzEKeJUjDiVjsQImFKj0RjaNaBYLKrZbI7VOhOLW3x2dnYk9fd/jt97FsIwVBAEna4DyelSu0Vx0MkyrVUqKe6m0Ns1YBHbNqoOo8Qn6niZnZ0dtVqtgfuj2WwOXXfWfRUbtW/i0YZicWtw7827yWXGmR/A5iBOEaeS8xKnhiMxAqZ0eXk5tMz3ffm+n7k1LnkpPG6F8TxPZ2dnfcOqNhqNzkkpi0EnyOR7JF/H68/n8wrDsKv1alAdRykWi7q6uuqbfxHblqxDEAQj69x7M22lUtHZ2VlXnavVal+dj4+P+0bOGbWvRh2TUfumt1tMq9XS7u7u0G0bd34Am4E4NRpxijglSf/h0YoNVTmJX/ziFz/9yU9+8pOf/vSny66KM/7whz9Ikj788MPOtN5hRt/9l4sF1kh6990xF7h/f6r3azQaKpVKqtVqunPnjra3t/vmqVQq+qd/+if99re/1Z///GdtbW3pxYsXOjg40Ndff62vvvpKn3zyiT7++GNJ0hdffKFf//rXev36tT7++OPO5e7PPvtMd+7c0cnJiZ4/f67nz5/rs88+08cff6xms6m///u/19dff63f//73ev36tT777DNJ7daf+L2ur6/1ySef6L333tPPfvYzNRoN/f73v9edO3fk+77+6q/+Sr/85S9148YN/fDD/2vv/mHjyu57gX/PwoDjAAbGlKsAARK6TbGgVsV7CLACTHZBKsnbpZOU8lUStpMrharcSmmSLo5UvJ40IBep7CXcbPdEJEBgGDBWHmOxgeMAe14xZ1ajETkccv5x7v18AIJz7+/emXPn37m/OX/uH/Kd73wnf/3Xf52f/OQn+au/+qtv7vOsMk4+zueff56PPvoo3/ve9955Ln73u9/lRz/60XvrZx3bLJc5tsky/P3f/33+5E/+5Mz7/PGPf5x/+Id/yGeffZaTk5P88z//c/7u7/4uf/M3f/POdjdv3sx3vvOdvHz5Mp9//nl+9rOfZXd3N/fu3Xtnu4ueq4vKPeu5+fzzz/O3f/u3+bd/+7f8+te/zsnJSf7whz98U7FOvx6//vWvz93+Imd93mf48Twb9Y16av3met+uefr0L79M/vjH8/+m/fF/335n+bKXpVBPqafUU2c/jecFXMeIK3EdI7bR8+fPZw4wnnU9hz5zHaPFqafW7zpex2j6B8QLt1/ydYy4/tRTV7OsesqsdKzM9Bf6qn1XhcEM0wNqAdaeGP364m1mmf4B8iySp+2lnto8Y4yAzrp79+43s9lcdjArAKyaeup6kRgBnfXgwYPs7Ozk5cuXMy8qeHJykrt37yYZVVJXmZ0JAC5LPXW96EoHdNZlrhruQqcArJt66nqRGAHQCaWUwyRHtdYzLy5SStlPMqi1vpxY9zDJaZLdJMe11pN5YgB0j8QIgK3WEp69JHeSHM3Y9DDJNxdrKaW8SPJknPCUUo6SHFwUA6CbjDECYKvVWo9rrU8zat05U0uepuN7U61Ap227i2IAdJDECIBzdeh6GYMk31zWvSU505d0HyY5mBVbaQkBuLRl1lMSI66klNG1sb7++usNlwRYpXGFM/7Mb6NSyp3JcUXN4IxNv8hoPNGsGFtCPQX9sMx6yhgjruTb3/52/vCHP+Srr77Kd7/73U0XB1iRr776KsnoM7+NSimDvN/6kyQ7M3abFTvrMV7NsdmHl7lPFqeegn5YZj2lxYgrGVcyv/nNb/Lll1/m66+/7lKXG+i1Wmu+/vrrfPnll/nNb36TJNt8Yrl/zix1b85YN0+MLaGegu5aVT2lxYgr2dnZyVdffZX/+q//yn/+538mSf7nfzZbpt//frOPD131p3/6p9nZuVQjyrVQStnN+RMyDPN+l7kbbftZsffUWm/PUZZXST6+aDuW56x6atPWUU+qC+mjZdVTEiOu5IMPPsif//mf582bN/nyyy/z3//93/ntbzf7S9yf/dlGHx46pZSSb3/72/nud7+bnZ2dfPDBVnYw2EuyU0r5qC1/1JZTa31eSpmuRQdJXtRaj8+Lrbi8LNFZ9dSmW4x++9vVP4a6kL5YRT0lMeLKPvjgg3z/+9/P97///STJv/zLZsvz+PFmHx+4XqYnXCilHGR0AdjnbdVxKWVyWu7diW53s2Jsiel6atN++tPVP4a6EK5OYgTAViul7CX5JMn+eLld12hym4ctPiilvGlJ070kn7Yud7eSPJrYZVYMgA6SGAGw1VqrzklmJC8tUXo6tW44sc/LeWMAdNNWdhoHAABYJokRAADQe7rS0RkXDTg1IBUAgPNoMQIAAHpv4RajUsogyf28vSDeyeSUpm0moNMku0mOJ6Y+nRkDAABYl2V0pbs/OS1qKeWwlPLLWuuwlPIiyZNxwlNKOUpy0G6fGwMAAFinZSRGB3l3CtTXGbUAnSTZm2oFOi2l7LcWpVkxriFjdAAA6KpljDHaKaUcTiwf1FpPSin7GXWvmzRMcjArtoTyAAAAXMoyWozuJflZS3Z+mrcXxBucse0XGV1BfFbsHaWUV3OU4cO5SgoAAHCGhVuMWne45xklO4cZdaNLkp0Zu82KAQAArNUyZqV7luSw1vqo3T4qpdxM8mbGbrNi76i13p6jDK+SfDzvfQIAAExaKDEqpewleV1rPU2SWuuDUsrrJA+SvMj7XeZuZDQ993BGDAAAYK0W7Uq3m/eTmedJ0maXm+4yN0hyNCu2YHkAAAAubdHE6DjJJ1Pr9pM8G8dbq9LY7sR03LNiAAAAa7NQV7p2Edcnbbru12316cT1ie4l+bSUspvRjHOPJnafFQMAAFibhSdfaEnQyTmxYd4mPC/njQEAAKzTMi7wCgAAsNUkRgAAQO9JjAAAgN6TGAEAAL0nMQIAAHpPYgQAAPSexAgAAOg9iREAANB7EiMAAKD3vrXpAgAAsByPHy8Whz6TGME6qbEAAK4liRF0icSLHiulHCY5qrUeT6wbJLnfFm8leVJrPZmIP0xymmQ3yfG8MQC6R2IEwFYrpewn2UtyJ8nRVPiw1vqgbbeb5LNSyl/WWoellBeZSJRKKUdJDtrtc2MAdJPECLaJFh94T2shOi6lvJO4tETo9cR2p6WU04xakJ4m2ZtqBTotpey3+5sVA6CDzEoHQFcNkhyesf5Ga2UaTq0fJjmYFVt+EQG4LiRGAHRSa/G5ObV6L6PudoMzdvkio/FEs2IAdJSudAB01tRkCvczmkThuN0+z85lHqOU8mqOzT68zH0CsH4SI7hOjCGClWiz092ttY67w72ZsfmsGAAdJTECoA8Ok9ydWB7m/S5zNzKanntW7D211tsXPXhrVfp4vqICsAnGGAHQae16RIe11mFb3muzy013mRvk7XWQzoytvLAAbIzECIDOKqXcSXKS5E0pZVBK2UvyUQsft+Wx3YnpuGfFAOggXekA2Gotgfkkyf54udb6tF3H6MUZu4zHGd1L8mnb7laSRxPbzIoB0EESIwC2Wpt57iRTyUut9TRJmbHfcGKfl/PGAOgmiRH0yUWz3pkVDwDoKWOMAACA3pMYAQAAvScxAgAAek9iBAAA9J7ECAAA6D2JEQAA0Hum66Y3zFQNAMB5tBgBAAC9JzECAAB6T1c6vqErGQAAfSUxgmWRWQIAbC1d6QAAgN6TGAEAAL0nMQIAAHpPYgQAAPSexAgAAOg9iREAANB7EiMAAKD3JEYAAEDvSYwAAIDekxgBAAC9JzECAAB6T2IEAAD0nsQIAADoPYkRAADQexIjAACg97616QIAwDKUUg6THNVaj6fWP0xymmQ3yXGt9WTRGADdIzEC3nr8eLE4bEApZT/JXpI7SY6mYi+SPBknNaWUoyQHi8QA6CaJEQBbrbUQHZdSzkpc9qZaek5LKfttn6vG4Ex+O4LttpTEqJSym9EvdcMkqbU+n4jppgDA2rWWpOHU6mGSg1JKrhJLIjEC6KiFE6OWFB3WWu+25c9KKb+stZ7opgDABg3OWPdFklsLxADoqGW0GB0meTax/MNa6/iXNt0UANiUnRXE3lNKeTXHZh9e5j4BWL+FpusupQyS3JlMZsZJ0QVdGM6NLVIeAJjwZgUxADpq0Raj3STDlugM2vJJS5SW0k3BL3EAXNEw79c3NzIa23rV2HtqrbcvKkiryz6+aDsANmcZiVGSvBm3GrUxRnezxG4KAHBZtdbjUsp0fTNI8uKqsVWVFYDNWzQxGiYZTI8VSvIgyS9m7Dd3NwW/xAGwgONSyuSY1t2J7t9XjQHQQYsmRuMuB9PrdjO6yN5SuikAwHlKKXtJPkmyP16utT5t4XtJPm0zqN5K8mhi16vGAOighRKjWutpm4Bh0iDJqW4KAKxDa9U5yRnJS5sQaLz+5TJiAHTTMqbrfjo1zfZHSX7YbuumQHe4pDkAQGctnBjVWh+VUg5bd4MfJLk3cR0j3RQAAK6Ji37j8xsgfbaMFqPUWs9ManRTAAAAtsFCF3gFAADoAokRAADQexIjAACg95YyxojtYEAlAACcTYsRAADQexIjAACg9yRGAABA70mMAACA3pMYAQAAvScxAgAAes903dBcNJ35BWEAALaYFiMAAKD3JEYAAEDvSYwAAIDeM8YImN+FA7EuiAMAXFNajAAAgN6TGAEAAL0nMQIAAHrPGCNobr96fMEG6ygFAACboMUIAADoPYkRAADQexIjAACg9yRGAABA70mMAACA3pMYAQAAvWe6bgA6rZQySHI/yTDJIMlJrfV4Iv4wyWmS3STHtdaTeWIAdIvECICuu19rfTpeKKUcllJ+WWsdllJeJHkyTnhKKUdJDtrtc2MAdI+udAB03XQy8zqjFqAk2ZtqBTotpezPEQOgYyRGAHTdTinlcGL5oNZ60pKc4dS2wyQHs2IrLCcAG6QrHQBddy/Jz1qy89Mkj9r6wRnbfpHk1gWxd5RSXs1Rhg/nKikAG6PFCIBOa93hnmeU7BzmbTe6nRm7zYoB0EFajADotFLKsySHtdZH7fZRKeVmkjczdpsVe0et9fYcZXiV5ON57xOA9ZMYAdBZpZS9JK9rradJUmt9UEp5neRBkhd5v8vcjYym5x7OiAHQQbrSAdBlu3k/mXmeJO1aRtNd5gZJjmbFVlFIADZPYgRAlx0n+WRq3X6SZ+N4a1Ua2524+OusGAAdoysdAJ3VLuL6pE3X/bqtPp24PtG9JJ+WUnYzmnHu0cTus2IAdIzECFiex48Xi8MKtCTo5JzYMG8TnpfzxgDoHl3pAACA3pMYAQAAvScxAgAAek9iBAAA9J7ECAAA6D2JEQAA0HsSIwAAoPckRgAAQO9JjAAAgN6TGAEAAL0nMQIAAHpPYgQAAPTetzZdAAAAeuLx48XisEJajAAAgN5baotRKWU/yaDW+nJi3cMkp0l2kxzXWk/miQEAAKzLsrvSHSZ5Nl4opbxI8mSc8JRSjpIcXBQDAABYp6V1pWutRadTq/emWoFO23YXxQAAANZmmS1GgyRvxgstyRlObTNMclBKyXmxJMdLLBMAANvC5Axs0FJajEopdybHFTWDMzb9IqPxRLNiAAAAa7VwYlRKGeT91p8k2Zmx26wYAADAWi2jK93+Ga1FyUS3ukvG3lFKeTXHZh/Oe38AAJxNTzb6bKEWo1LKbt6fcGFsmPe7zN1o28+KAQAArNWiLUZ7SXZKKR+15Y/acmqtz0sp013mBkle1FqPz4tNP0Ct9fZFhWitSh9ftvAAAADJgonRdBe6UspBkqNa6/O26riUMjkt926t9XiOGAAA20ZfO7bY0qbrLqU8TLKfZFBKedOSpntJPm1d7m4leTSxy6wYAADA2iwtMaq1Pk3ydGrdMG8TnpfzxgAAANZpmRd4BQCA1TFtHiskMQKg81q37Ttp192bGAs77gp+mtFFxo8nxr7OjAHQLRIjADqtJUWHtda7bfmzUsova60npZQXSZ6ME55SylGSg3b73BgA3bPQdYwAYAscJnk2sfzDiZafvalWoNNSyv4cMQA6RmIEQGeVUgZJ7kxeDqJN/pOW5AyndhkmOZgVW2FxAdggXemA9TFolvXbTTJsic6gLZ+0RGlwxvZfZHQJiVkx6C/f03SYxAiALttt/9+MW43aGKO7SXZm7Dcr9o5Syqs5Nvtw3vsDVsgPdMwgMQKgy4ZJBtNjhZI8SPKLGfu9WWmpgNWQ2LAAiVGH+C4AeM9p3h8rNJ5++yjvd5m7MbHPebF31FpvX1SI1qr08TwFBmAzJEb0xu1XjzddBGDNaq2nbQKGSYMkp7XW41LKdJe5QZIXs2KrKisAm2VWOgC67unUNNsfJXnSbh+XUvYmYrsTM9jNigHQMVqMYE6vXs2O3769jlIAl1VrfVRKOWwXev1BknvjKbuT3EvyaYvdSvJoYtdZMaCLTM7QaxIjADqv1npmUtMSpHHs5bwxALpHVzoAAKD3JEYAAEDvSYwAAIDekxgBAAC9JzECAAB6T2IEAAD0nsQIAADoPYkRAADQexIjAACg9yRGAABA70mMAACA3pMYAQAAvfetTRcAluX2q8ebLgIAAFtKYgQAQJI5fmS8vY5SwGboSgcAAPSexAgAAOg9XemA6+Px48XiAABXpMUIAADoPS1GAAAwDz0bOk2LEQAA0HsSIwAAoPckRgAAQO9JjAAAgN6TGAEAAL1nVjpYklevLt7m9u1VlwIAgKvQYgQAAPSeFiMAeqOUsp9kUGt9ObHuYZLTJLtJjmutJ/PEAN7jOkdbTWIEQJ8cJnk2XiilvEjyZJzwlFKOkhxcFIO+uqjbuC7jbDNd6QDohdZadDq1em+qFei0bXdRDICOkRgB0BeDJG/GCy3JGU5tM0xyMCu20hICsDESIwA6r5RyZ3JcUTM4Y9MvMhpPNCsGQAcZY7RFjNej9wxq5QpKKYO83/qTJDszdpsVg611+9XjTRcBri2JEQBdt39Ga1Ey0a3ukrF3lFJezbHZh/PeHwCboSsdAJ1VStnN+xMujA3zfpe5G237WTEAOkiLEQBdtpdkp5TyUVv+qC2n1vq8lDLdZW6Q5EWt9fi82PQD1FpvX1SI1qr08WULD8D6SIwA6KzpLnSllIMkR7XW523VcSllclru3Vrr8RwxADpGYgRAL5RSHibZTzIopbxpSdO9JJ+2Lne3kjya2GVWDICOkRgB0Au11qdJnk6tG+ZtwvNy3hgA3WPyBQAAoPckRgAAQO/pSgcAAOswz4XIXax8YxZOjNoVxe+3xVtJnkzM4DMe7HqaZDfJ8bwxmOZq3QAArMoyWowOa60Pkm8upPdZKeUva63DUsqLTCRKpZSjJAft9rkxAACAdVpojFFLhF6Pl2utpxm1AI1bkPamWoFOSyn7c8QAAADWZtHJFwZJDs9Yf6MlOcOp9cMkB7NiC5YHAADg0hbqSldrPSml3JxavZfRdR8GZ+zyRUbjkGbF3lFKeTVHUT6cYxsAAIAzLTxd99RkCvczmkThOMnOjN1mxQAAANZqadN1t9np7tZax93h3szYfFbsHbXW23M89qskH897nwAAAJOWeYHXwyR3J5aHeb/L3I2MJmeYFQMAAFirpbQYtesRHdZah215r9Z6XEqZ7jI3SPJiVmwZ5QEAgK100QVeXQB2ZZZxgdc7SU6SvGnd6XaTfNTWHbckaTwOabeNP8oFMQAALsnF0OHqFkqM2nWMzmrlGY8zupfk07bdrYxmq8scMQAAtsyrV7Pjt2+voxRwNYtO132apMyID/M24Xk5bwwA4LrRgwm6bZmTLwAAAGylpU3XDYvSLxoA4AImZ1gZiRHQHSoLAOCKJEawRgalAgBcT8YYAQAAvScxAgAAek9iBAAA9J4xRgAAW8DsrbBaEqNrwmRZAACwORIj1sYvXQAAXFfGGAEAAL0nMQIAAHpPYgQAAPSeMUYAdFopZZDkflu8leRJrfVkIv4wyWmS3STH88YA6BaJEdAfF03/aHrIrjqstT5IklLKbpLPSil/WWsdllJeZCJRKqUcJTlot8+NAVxb6ror05UOgM5qidDr8XKt9TSjFqBxC9LeVCvQaSllf44YAB0jMQKgywZJDs9Yf6MlOcOp9cMkB7Niyy8iANeBxAiAzmotPjenVu8lOcooaZr2RUbjiWbFAOggY4zWRHdOgM2YmkzhfkaTKBy32+fZmff+Symv5tjsw3nvD4DN0GIEQC+02enu1lrH3eHezNh8VgyADtJiBEBfHCa5O7E8zPtd5m5kNDnDrNg7aq23L3rg1qr08fxFBWDdJEYAdF67HtFhrXXYlvdad7rpLnODJC9mxdZQXIDVMZ33uSRGcI28ejU7fvv2OkoB3VJKuZPkJMmb1p1uN8lHbd1xS5LG45B2a63H7fasGHAF6jmuM4kRAJ3VrmN0VivPeJzRvSSftu1uJXk0sc2sGEA39bhFSWIEQGe1C7qWGfFh3iY8L+eNwSrcfvV400WAXjMrHQAA0HtajFgav3QBALCttBgBAAC9JzECAAB6T2IEAAD0njFGAADAfDo8nbfECGBsni/zLf7CBwDOpysdAADQexIjAACg93Slgy3y6tXs+O3b6ygFAKyGeo5NkhgBAADLscWTM0iMmNvtV483XQQAAFgJiRHAZWzxL2EAwPlMvgAAAPSeFiMAgDXQJR2uNy1GAABA72kxAgAA1uMaj9WVGAEAsBVc54hVkhgtiYmoAABgQRtsUTLGCAAA6D0tRnzDbDkAAPSVxAhgma7xoFIA4Hy60gEAAL2nxQg6xGw9AJujS/rmqQdZhMQIYJ10tQOAa0liNKdtOFe56JeqV7dnxwEAoK8kRs02JD4AAMBqbDQxKqU8THKaZDfJca31ZJPlAYBJ6imA/thYYlRKeZHkybiSKaUcJTnYVHm2waKDOg0KhS1gDNK1oZ4C6JdNthjtTf3ydlpK2a+1Hm+sRADwlnoKOsasdcyykcSolLKfZDi1epjRL3EqHNgQFcYW0KK0FuopgP7ZVIvR4Ix1XyS5te6CrItubFwHFyU+i+4vcboGJE7L0rt6ioupy1EPdtumEqOdeTcspbyaY7P/9atf/Sq3F3g3/vu/z44PhhdscIH/u9DesCV+NTs8OOtUk/X6p3+aHf+Lv1jo7n/+85//pNb6fxa6k+vh2tVTbN7wV/++6SKwahfUYyvffwk6X9cu+CvvrHpqU4nRmyXf3x9///vf//bnP//5/7vi/h+2/+e+nf/jine8YRce15ZyXNvj3WP6/eYKsmRdfK2S5MP8x38k3Tuuq9i6eooLeQ4X5zlczHqev+7UtWdZaT21qcRomPe7KdzIaErUd9Rab6+6MONf+9bxWOvkuLZLF4+ri8eUOK6eUE91jOdwcZ7DxXj+Frfq5/CDVdzpRdqMPtPdFAZJjjZQHAB4h3oKoH82khg1x6WUvYnlXVOgAnCNqKcAemST1zG6l+TTUspuRrP8PNpgWQBgmnoKoEc2lhjVWod5W8m83FQ5AOAs6imAftlkVzoAAIBrQWIEAAD0nsQIAADoPYkRAADQe6XWuukyAAAAbJQWIwAAoPckRlx7pZTDUsr+GesfllLutP97Z+17nZ11XKWU++1vUErZLaUcbqp8AACbts7zwE1e4PXaKKU8THKaZDfJca31ZMNFWkgp5X67+a9JdpI8qLVu3YUJ24dgL8mdJEdTsRdJnoxfq1LKUZKDtRfyCmYdV5JBksMkzzJ6T27FMSVJKWWQZPzeu5WJ16fFt/JzNuu4tvmzNnFcwyQ3k7yotR5PxLfy9eqD9oPJ0eTr1dZ7zVgZ76/FbHN9sSkbOQ+stfb6L8mLJHsTy0ebLtMSjulhktr+XifZ3XSZFjyeoyT7U+teTy0/m97muv+dc1z32//Bpst3heN5NnF7N8nvxsexzZ+zC45raz9rSQ6njqt24fXq8l+S/faee33Gd4fX7GrP6f32N2ifg8NNl+k6/nl/LeU53Nr6YtN/6zwP1JVu9EGf/NXj9Kzmui0zrLWWJN+rtf6g1nq66QItU3t9hlOrh9mi1pWL1Fqnj+9aK6XsZvRFnyRp77nTvG1p2crP2RzHtc2ftfvj12Ci3Lvt/1a+Xl1Xaz2utT7N6D04zWt2NYOMTqh+l9HJ17PNFufa8v5a3DbXF9fKKs8De50Ydf0Ee9tOri9hcMa6L/L2pG6rtTFGd1qf2m0ZOzXuAjjtxpZ/zs49rsmFLf2s3aytK1ZLAJO3Jzvb+nr1ktdsIU5WL+D9tVxbWl9cNys7D+z7GKPznthb6y7IsrW+rG8yOpaf1m71Bd7ZdAFW6HiiYn5ZSnldSrl53b9Ia60npZSbU6v3kjzKFn/OLjiuJNv7WZs6AXyQ5FGtddjGHk3biterx7xmC7ru37Eb5v21JNtaX1xDKzsP7Hti1NUT7K08ub6EN5suwKqc8WvlMMmPkjzfQHEupb470cL9jN6HxxMDTrfSecfVVm31Z61v5LamAAAGxUlEQVS1FN3JqK/7ONnr6vdil3nNFuBk9ULeX8ux1fXFNbOy88Bed6VLR0+wZ5xcd8Uw7/+CdSNn97vfGm167t9NrT5N8oNNlOeqWovD3VrruJtFJz5nZxzX1n/Waq2nbczKo1ZJD9KR16tnvGZXd1xrfV5rfdl+HHhxTqtpn3l/LcG21xfXzMrOA/veYtS5E+z2C/BntdbvTazeupPrWVorxPQvWIOMZs3ZdtNTdw4yMfh/SxwmuTux3JXP2TvHte2ftVLKYPxLZa31tJQyTPJpRgPQu/B6XXutpWK6q+a0wznGvXTlM7Z229xKv0beXwva9vriulnleWCvE6MOn2B34eT6IsellMlZcnbr1DU9tk07Of2m8mm3d2utW1NBt+tcHI5PuNtrtPWfs7OOK6OTha38rLXB1EdJylRo0IXXa1ss67PtNXvrMsmmk9X5eH8tzVbWF9fYSs4De50YNZ06we7CyfVYO/n8JKNrd4xPsp+28L0kn7aK7Vbe/8K5ti44ruftJHx80c2tmfWnlHInyUmSN+P3XZKP2rqt/Zydd1y11udb/Fk7zfufmd2JdVv7evWY1yxXSjadrM7H+2sBXTo3W6dNnAeWdlGk3mpvzk+T/CIdGXh5xhXt5+mKAVc2fb2fCQft18at/JzNeVxb+VmbuKL4uOxHtdaXLbaVr1fXTZwkPExynNFr9rTFvGZXUEp5OPUcflZr1WI0xftrcdtcX/RJ7xMjAKCfnKwCkyRGAABA7/V9um4AAACJEQAAgMQIAADoPYkRAADQexIjAACg9yRGAABA70mMAACA3pMYAQAAvScxAgAAek9iBAAwp1LKXinld6WUZ6WUh6WUo1JKbbcP2/Jnmy7nokopL0op9ze1/zKUUvZLKa9LKYebLAfbQ2IEADC/3SQ/rLU+qLU+TfIsybDW+rTW+qjWepDk+Kp3vmgycZX9z9nnWeY8jkX3X5Va63ESSRFz+9amCwAAsE1qrScXbPKLq9xvKWWQ5AdX2feq+5+3T0sqVr7/GrzJAs8p/aLFCABgfqdL2uYdLcH4x8sX5+r7n7dPKWXQugzurnL/66IdB0iM4LrzhQ1wfczRWpRa60kpZbeNObrT/n/zXV5Kud/Gv9wppTxrq/eTDJLstfFK++fd/2X3b0nK9Paz9tnJqAvagys+5ln7Dyaej/1Syt4F9z15vHfauK7Pxs9jG8P0uh3becc3fT/jMUfPJp6XzzKR3M163eg+XelgxdqX/05GlcdBrfXBOdvtp/XJrrU+aPv9Y0a/PN5dV3kBWIqjJDdrrcNSymlG3+d323ic03FXs3GrSq31Zbt9o41dOtMV93+R5G6t9biUslNKOWzjoc7cp9Z6Wkp5kdYF7bKPOb1/87NWhtNWv71I8oPz7ntSe5ydjOrQYVv9LMkv2/P7+qzjO+N+jltS9IO2fFJKeZLkk4nNznzdznot6B4tRrB6L5K8qbW+TPLZebPjtErh2cTySZIn6ykiAMtSSrmT0cn+MPnm+3zcmnKa5FlrJRnMSoLOcZX9b060dP0yyd6sjZs3Cz7mN/uPW5Jqraft/0mSm5e571rr87x9DpNkMJEkXeb4hucFLnjd6AGJEazeUr6wAdgat5Jvum7tt8TgX5NvfgR7lFErxO9mdf06y1X2b60fd1rrzH5GvRhW+phT9vJuopWJ5OMy9/2v4wQqE/Xlosc34dzXjX6QGMGKLfELG4Dt8IuMpvA+nvh7kIxOumutL9u03t9LsntW97HWevGeq+zfxtGctlaXc2eLW+ZjTjnJOXXfvPfdPMto3NL+5Kx38x7fHM593egHiRGs2BK/sAHYAq3r9Dsn9xMTE+yNJx5orSaTkzmcZjQedZZL7d8edzDRc2GnrR+0+znvMXcm1l+lzN/s35KYwWTCU95e+2jWfb+jHcMgE8/tHMc3eRzj8k4mabcm7n/W60YPmHwBVmjWF3Ymvnwn4qdJDibu4tbE7UxUHhfOigTA6rST/DsZDdwftC5gn7UfwZLRRAuHeXtNo/EU3sO82yryemLszctSyifjCQnOeehL7d8mHDiZWPem/b/fxvOcTO/T6poH7bj2L/uY0/u3xOhmksNSylG7j/EPhefe9zkOJ/adeXxtu7vt/u+0lqnjUsrdidat10nujOM5/3WjB0qtddNlgE5rM/Mc5e0X9qdJflFrfdq+fAeTTfWtch1XHDsZ9b0ezx703vYAACxOYgQAAPSeMUYAAEDvSYwAAIDekxgBAAC9JzECAAB6T2IEAAD0nsQIAADoPYkRAADQexIjAACg9yRGAABA7/1/rqULFoqUUsEAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import hep_spt\n", "hep_spt.set_style('multiplot')\n", "\n", "fig, (axs0, axs1) = plt.subplots(2, 2)\n", "\n", "for i, (ax0, ax1) in enumerate((axs0, axs1)):\n", "\n", " if i == 0:\n", " alt = hep_spt.cls_hypo(poisson, 16)\n", " null = hep_spt.cls_hypo(poisson, 8)\n", " else:\n", " alt = hep_spt.cls_hypo(norm, 16, 4)\n", " null = hep_spt.cls_hypo(norm, 9, 3)\n", "\n", " a_smp = hep_spt.rv_random_sample(alt.func)\n", " n_smp = hep_spt.rv_random_sample(null.func)\n", "\n", " cls_mgr = hep_spt.cls_ts(alt, null)\n", "\n", " # Plot the line referring to the percentiles\n", " ax0.hist(n_smp, 40, range=(0, 30), color='blue', histtype='stepfilled', alpha=0.5, label='Null hypothesis')\n", " ax0.hist(a_smp, 40, range=(0, 30), color='red', histtype='stepfilled', alpha=0.5, label='Alternative hypothesis')\n", " ax0.set_xlabel('a.u.')\n", " ax0.legend()\n", "\n", " # Plot the test-statistics for the two hypotheses\n", " ax1.hist(cls_mgr.test_stat(n_smp), 40, range=(-10, 10), color='blue', alpha=0.5, label='Null hypothesis')\n", " ax1.hist(cls_mgr.test_stat(a_smp), 40, range=(-10, 10), color='red', alpha=0.5, label='Alternative hypothesis')\n", " ax1.set_xlabel('Test statistics value')\n", " ax1.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Running a CLs scan\n", "Oftenly, we have a model that depends on a certain parameter, which we use to determine the rejection. In this case we will assume that we are looking for a signal on a sample, which can only be explained by an alternative model (so our expectation is full-background). Our parameter for the scan will be the effect of our new model (the number of entries over the background). The value of this effect might vary in the alternative model, thus we can use the CLs method to reduce the allowed value-space for it. We will consider that we have three bins, which might be related, for example, to different independent samples with tighter cuts in each of them." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Limits:\n", "- 90% CL: 2.3174\n", "- 95% CL: 2.8024\n" ] }, { "data": { "image/png": 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OZ6ismTNnhq4HpwZ0VYff74/o0U22aHWlsv5EkwC072KZ75nI55Ji6tKb2Tj+2YiFSLvJpnG/I5g37lqu2eDlwm/+TsWjUPEovFgM990E1vNAZUEBOhi9CL3EX1a2Zbo96H0R4tm7oXMQ25vgVYJYMcAloGeR0aP1nM/urm/eHH89cbBYLDEFoI2NjRiNxpiCpWCvnsViYf369dTU1OB0OkND5i6XKzRftGPvaLA9saqoqGDChAmhADRYZ1BPdQQD01SmlIpWVzwpn9JNAtBwfnQMlUvXgWLwO6Djb+++Ppd2Iw8byZgNq1hVtpATX3mYHLWVZkMe7545hS+Xvs4/D/kFzz/zA47dM40b3lzNlU/AOR59fHAs3H8jLJkF9SNhATAG3St6EbqXdEQ6X5xIokQFsb0NWg9Cv83GoqcaCDFAzZ6tFxx1ngMKkJ0N116b+jZ14nA4yM/P7zGpeU1NTczzDYO9isEybTYbNpuNQCBAaWkpNTU1mEwmmpri+1VqNBopLCzE7XZjsVgiguOe6ujPPY+d+Xw+TCZT6vOzKqUGxAF4gOY4y7ABCrB0c4+z7R5TvM/1sm0ri4qKVOr8TSmFekehxitC/xmbUHOnlqiPOUIp/Xe+ajKiHDejjvgY1fG/YQp1nkI9qFAb0v8tIseAOw5USh2vlJqhlLpcKXWLUmqRUupZpdQqpdR/lVJfKyESraGhQTU0NCS3ku3blZo8WansbBX8WatAfz55sr6eAWw2m7JYLF1edzgcymw2R5zX4Ue4xsZGZTQaQ881NjaGXa+vr1c2m001Nzcro9Go6uvrI8rweDzd1tGRy+VSFotFuVyuiGux1NHVdSCi7V2J1sZYz5lMpoj6S0pKlNPp7FV50V5/d3r5/d/lD3EZLQ0XnOzR3Z8BJiCglOo47tDX5zLYBcBNnIjeXzS4+ilghLuLTsU0dB2lLOM1w3RyAmBbCH4TLJ0Jp70OKGgFXgCuB8YDJwG3Aq+jZzsKEZ+vgHXACuAp4C5gDnAZMB04Er0oawx6osh3gWuA3wCPob8730VPy07AkKkQiTRypE61ZLOF5wG12TIiBVOQw+EIrSrvzO124/F4WLFiRcQ1o9EYluIIdFqgjkntO/eaNjU1MXXqVIxGI7W1tRG5Rb1eL4WFhTG3vaSkhLq6uqg9nbHUUVtbS1VVVcR10IuYEi1amX3tCe64gCne3uQ+6y467U8HCegBbSunGXB2c10BjkQ914t2pbgHVCmlWpRSJyulUF8r1DWqQ/9m4wRF2TMKlJrKavX7/S9TX2dlhf5KXz0V9YM/oPZrDe8VDf53sELNUqhlChVI/7ePHIP+GKaUmqCUOkMpVaaU+plS6m6l1NNKqZeUUh8ppXYpIZRKUQ9oP+PxeJTNZlMOh0M5nU5ls9kieuI6CvZwejwe5fF4lMPhCOu9dDqdqr6+XrlcLuXxeJTL5YroqQvW6XQ6lcvlCvU61tfXq5KSEgWoioqKbnv4bDZbt72VXdXR8Xqw7S6XS9XX1yuj0ahMJlO39TY2NobaWFJSourr6yPONTY2Rr2vublZVVRUKEBZLJbQ181ms4XqdjqdUcsLqq+vD31tOn7dY5GoHlCDUgPjL3+DweBBD4H3uKrBYDA40RPJylWnVesGg6EEqAUmpOJarAwGw8qioqKilStX9uXxOHyAnt6qV2Y/DNyAngEIwJtTYe7d8MpZjGUTs68qwPrnLzi4ba3/prGw+DqoqYCtB0evYShwFnre6MXA0Ul7LULEKwc9/3Rch4/jOp07FMnpOrCtXbsWgIkTJ6a5JUKkXi+//7uMyQZSANqIHubO6S7IMxgMFnRvKYBVKRWxQW0wQFVKlXY4ZwTq256Juk9WX5/roqz5QGXHc0cddRQbNmyItYgE+h1wdeizfwGldMgnpYC/Xgxvngq/vY3hu+BHf4CbHMOY3NgKwO5seOpyvWipYXL3tR1H+6r604H9EvtihEiyIcBhRAaqnQPWg5AsAP2TBKBiMBv0AajBYDChF/bkogPPjvMvfejluU6llDvKs/Vt/5zRVbDa1mtZTPuqdiN6CL3bOZx9fa4n6esBBR1h/gBYGjqzHj2j7r2uHlnxHbB4sZw+n5uG3s2FL7XntgymcXqhLY1Td4zAeehg9DwybBspIeJyANF7UccBx6L/FBs4Wz4MJBKAisFs0Aegg016A1DQ8fQpwIbQme3ALOBP0W5/7Cq44QHYNQKG7OHYmbdzQ/ZCrlzawoi2WDSYxunJK/RtPckCvoUepr8ImIj0H4mBLAs9IWUSMLnDcSwSmKaXBKBiMJMAdJBJfwAK8AZwJh3XsO8D5qPXFUf4dAzMnw+PXQ37hsCorzDeMJ+fDl/EHOcejvxE39Zs1HNEF18HnxwZe2sm0D5UX4Re7yzEwBcMTDsGpZPQPabyLkgFCUDFYJaoAFTSMIleOA2dbr5dFnA7enB+eOfbx34GNVZ45yS48HnYfiCBO+7l7m9+ickPpcvgtW9BTgDs1TqN0x/LYPobxJQVZz2wCDgXOBidfOdx4Iv4XqQQGW4f8CHwHPBb9PSYKehtH45HvxNuA/6ITjPVmp5mCiFEN6QHtJ/IjB5Q0L2fFiCyHW8B3wM+6erRf30bqubBsplg3KbPfXEIUzds5sYHYOYy2K9tef3qU/U8UXcJ7OnDKqRTaR+qn4IM1YvBbAhwDNGH8vdPY7v6L+kBFYOZDMEPMpkTgAJsQqeVj0xe+wVwKTrZfI92Z8NxH8CxH8LCmxl7yNvMfgiueQTy2oreNBYevF4P0Tf1cQXSONqH6r+DXvohhAgGpp2H8iUw7YkEoGIwkyF4kUbj0KmZIh0K/BO4KpZi3j0Rto+CFRYoqOfTeU/yK+sRHPEJlNfA+5Ng3KdQdStsPBwescLEht63dhM6XcLF6KH6y4FXkL1vxGC3F72T1LPoiTRlwInoofxJ6GRr84FlwPvA12lppRBiYJIAVPTR94Drol4ZBjwK3E8P32CnroGPjoaf3QtD98BTs+DYD9l9exWPzjyQE96D4hfhbxfA8Baw1ugcoi+cC+f9Awz7et/q3cDv0YnvJwP3Ea0fV4jBbA+wFnCj53yXASegA9PJwEx0YOoCGoBv0tJKIUT/JkPw/URmDcEH7UbPtuwyGyge9K+v5p6KWj8ebr0T/vgD/fm0VbDqtNDlYz/QWZ2ufIJQGqd1x+k0TktmxZbGqSvD0H09VnTie5kvKkRvDEUP20/udBzNQN1GQobgxWAmc0AHuMzaCak77wOFQEuXd/wH3V+6Npbi3pwKNy+E6x+E0rY9BFqGwbBWMICxGX76KMxZRNxpnKKZBFSg85vmxFeUEIPcfoQHpsFFUP0/MJUAVAxmEoAOMpnZAxrkBK7p9o5twI+Av8VSXPBbMvhte+N9epvPu+fC6Xp505A9cMlzcNN9oVPsGQLPXqZXz6+aTlxdmdm094p+K76ihBBh9kPPNT0TPRnmTGB0WlvUWxKAisFMFiGJDFKBXvvetYOAPwP2WIoz0P4tuzsbll+qh+PPeA0ufRY+OJa9Q8Fdqk+duhr+8ENQBihbBm98Sweg338GhrZNTxuxAyorYfNo2JulP1ZW6vPRtABPAWegZ7/dTwzTCIQQMfgGvVvy/eicpYeg9zWzomdo/zd9TRNCpIz0gPYTmd0DCnopzxRgY493/gG4ml6kx94+Uvd+3j03tLUnVidULoBDvgzdNnYTEWmcNo6D2p/C95fC+A16MVPQ7mxozIfpq2DnyJ6bkY1eflGB9IoKkVxH0t47ehZ6l6fMecdJD6gYzGQIfpDJ/AAU4GXgbPROLd1bA/wP8Glviv90jA46f3dVaGtPPjgOxnwedtvwXfCjP+jh+cltaZsU0d8Fu7PBYYMFC6Jc7MZkdCB6OTJXVIjkG40ORoMB6RR0HtP06OkXsCGDguXuKElGJ/pAhuBFBjoL+FVMd05FB6Gn9qb4sZ9BbQX8ewpc8DeweMODz7afpbsPgEfL4YT34Jz/g9b9un4HDG+B2Q/3phHa+8CNwFjgCnTifflRLkSyfAksB34GFAC5wPlAFfAqst1o+rndbrxeb7qb0Wdut5v8/Px0N2NQkQBUJNht6GRGPRsLvITuReyVE96Hv10ET/+w/dwb0+Hkt3WS0A6LmDzntG/v2ZW8rb1tQLsWYAn6FZ+E3pte5ooKkWxfAS8At6J7RQ8CitA/f14EtqevaYOQ1+ulvLw83c2Ii8lkoqSkJN3NGFQkABUJNhQ9y9MY093ZwJPAQvowwyu7Q6/HfTfBO1Pg/BfgnBfh7SmhS1t72MKzJRtGJuD31XvADejA+kqkV1SI1GlFTwH6LXAuemLMVOAXwJ+ALelr2gDm9/uxWq34/X5yc3PT3Zy4mM1mHA5HupsxqEgAKpLgKKA25rsNwFzgeeDAvlb55BWwcK5OFOotBrMPZj0J/z2CxbP1XM+ujNilN2Savbh91Xw8WtBBdcde0UD8xQohYrYXqAPuBS5BzyGdDFwLPEMsiyVFz0wmE06nk4qKinQ3RfRDEoCKJCkBejckcwGwGjimL9Vlt8Lce/Sy9p/fA/t9E9ra8+4Jl9Co8tlNeBS6m2z8+41jVYGBQzfD4uuhYRKUuEhY12XHXtGfAG8krmghRK80AI8APwSOAEzoGdyPAR8i78zBzefz9es5rP2RBKAiie5D5/eL3fHoIPScvlaZ2wz3zIV1x+tEoMNa2fneaUznDRzY2Mxo9pLFZkbjwMZJWW9x2gW3cclyvbXnMR+BayasngZFK/vaiEi7gSfQ6ZumAA8ivaJCpNd69Azun6LTPI1Bbz+xCPg3uhdVJIrf76e4uBiDwRBx5OR0n0vE5/NRUFBATk4OgUCAmpoaSktLwwJGt9sdOux2Oz6fL6yM6upqampqQkfw3tLSUgKBAFVVVRQXF0fU7fV6Q/cHP3Zul8FgCGuD3W4Pu090QSklRwYewHz0n+Sh46ijjlL9z9tKqf1Vb78E3yjUzxXx/7f5YMXBmxWoro/RXygUasg3qIpHUJ8e1n7x+QtQJ7yTgHZE+W+4Ql2pUG8o1L70f8vJIYccYcdBSqkLlVJ3KaVeV0q1qqCGhgbV0NCgupKcnxiJ/y+RTCaT8ng8Ua95PB5lMpmUy+VSjY2Nyul0KkDV19er5ubmmMpvbGxURqNRuVwupZRSDocj9G+n06mcTmdEexobG0P32my20DWHw6EcDkeo3CAdErVzuVxhzwWf7VhXc3OzAiJee+eyBpKevv876fJNlu53uBwxHsDKoqKiiP+z/cMDqq8v/XcKtb+K88esYW/3AWjWnrD7D9iB+uVvUNtG6Rv2GlC/uxJ1xMfJ+0VwokI9qFDN6fsWk0MOObo9hiulzlZK/Vo1NKxSDQ3vq64kP3RMzH+J1FUAGgzQ6uvrw85bLJZQEBiraOU0Nzcro9EYca/NZguVHwx+g4IBcbTyOzIajVED5M7no7XLZDJFnBsoEhWAyhC8SIHrgYv69ORPgH8Bh8ZTfU95ljpd3zUC7vgV5DfCA3Ngz1D4yRPw4bE6ab0xCXmW3kV/lcYCVwGrkBlpQmSW3eifRrej54zuBtaiFzQFgB7yvQ1S5eXlVFRUYDabI65t3dr7HHidy6mrqwP0UHnHIy8vD6NRZ2MxmUw0NTWFngkEAqFrXfF6veTm5ka9z2QyRcwXNZlMvX4tg50EoCIFDMDj6DlWvfctdNL6yB9fMZq9GLJ3d3199Gb48uCI01tGw40PwMS18Mz39Ton20Lwm2DuQhjWEqWsOO1Gf6VOA04GFgPbEl+NECJuCtgJfA58BLyN3qJC9rLvyO12Y7VaI877/X6mTp0ad/nBFFAWiyXssNlsodX5drsdl8sVembp0qXMmzevx3K7ClJzc3Px+/1h53oKaEUkCUBFihwMPEVf93M+AngFKOvLwzffrbszOwehQ78Gw15oOAH+/L0uH/fnww+fgcI1sOI7kBOAhTbdIzrrSchK0lqFd9C9omPQvaKrkV5RITLbbmBzuhuRMYJBWudeS7/fj9/vx2KxxF1H597NaHJzc3E4HKEFSPPmzesx6bzJZCIQiL5UtKmpSXo8E0ACUJFCM4Bb+vz0AegMfnfQyzB25PUkj4MAACAASURBVE5YNR1sDt3bmbVXf7z1TnjnJLilCq5+rP3+r/eLWkx9od7989wXdJ77Iz+BJ6+Et06B8/9O0qLDYK/odHSv6ENIr6gQov9yOBzYbLaE9BoWFhYCRKx6B0LD5F6vF7PZTEVFRZfTAaKV29TUFDUI9fl8CQmeBzsJQEWKLQCm9flpA3rzvT8BI3vz4MidsGABbD4U9g7VHxcsgBMaoOrW9ojWPwFMfnj8yugBpQFePFfnub98CXx8JJz0Lvz9Qvjnd3QvaTK9A1yHnit6NfAm0isqhEi/aMGayWTCbDaHDVe73W78fn/Cdh0yGo3U1tZit9vDznu93lBwGvy8t+U6HI6Icqurq3E4HBHBc7RAtaee2UGvuxVKcmTOQb9eBd9Zo1JqlIr3y/KeQplUgteF/np+++r4c15QbDiy2/uH7Ub97B7U1pzgQ6ilpaj8/6RuJesUhXpIoQJxfj3lkEOO2I6GhiWqoWGNUir6kbp3f3z/xau5uVnZbDZVUlKiAGUymVRFRUXYivPm5mZVUVGhnE5nRAqjWNXX14fq6Fx+kMfjUTabTTmdzlC6p45tMBqNocNkMqmSkpLQqv3GxsZQ+SUlJWHPejyeULs7pn6K9lwwrVRFRYUClMVi6TI1VX+WqFXwBqWk/6Q/MBgMK4uKiopWrlyZ7qYkyDPoHUnisxWdOvpfcZfURgF/+BHceD805elN4qttYHVCVtfvlYMCcMtd+rHhLfDNUHBa4fZfw5eHJKpx3TsA+D4wBz1UL4RIjrVrlwATmdjFPhsG4l9ckwqKgf/7P9jb2rHXMjgH1W63xzQfVIRbu3YtABO7egOE63LGnASg/cTAC0BBJ1l6Iu5SvgF+jt5dKGG+OASuWwzPtv1gKloJv7sKTOu7fWzcRlhQCVc+AUP2wfaRcPdcuOcXsLNXcwbi8z30TgYSiAqReD0FoImRBRwI5AAHAUOTWdmAZbfbKS4ujjpn0+fzUVVVFbZCXvQsUQGozAEVabSIPu78Hma/tpKcJPBH9KGbwV0KrhI45At4/Vuwe3iPj206HH76GEz5N/zlYhi1AxbMh4+OhmsehqHfJKqB3fszcApwGXreqBCiv9mHzi+6Hr016AfoFfZfp7NR/U5xcXGXAebSpUspK+tTbhWRANID2k8MzB5QgHp01svERGYvo4OuLQkprc3WXHj1DPjeX/TnCvjkCL0MvgdnvqxH8Kev1p9/eIxefP/sZfQ1I1WflACVwAmpq1KIASs1PaDdGQEY246e/zAe7Hw+H16vNyx1kt/vx2w2y2r2PpAh+EFm4AagAPcCv0hYaRvQQ9BJ6/n7Yxlc8STMnw83L4ShPSQCVXDpcrjzVjjuQ31q1TSwVcMrZyWrkZEM6PmylcCk1FUrxICT/gC0o2x0IJqDngmewr9sxaAkQ/ADnMFgmG8wGFTwAIo2bNiQ7mYlyU3AuQkrbTzwGnBpwkrsxGeGr4fBrVUwbTX8+6Tu7zfA8svghPf0MPznh+oe0ZeL4K8XweT3ktXQcApYhu4F/SGwLjXVCiGSqgW9G9Na9J/dHwNfoYfwhchcEoBmKKXUfKWUIXgAL40fPz7dzUqSLOBJIHHLxUcCLvRCnISrtsOLxXDUBvAVQGEdVM7vMoF90J79wHkNHP0R3Ha7XqB00d/g31Pgsav0AqZUUOgcBJOBy9G7WgshBoJvgC/R7+p/A36gGUjSdm1CxEECUJEhDgWWJLTELPRwsxs9MJVQxV5490S47kEdWd5eCQX1sH58j4/uHAm/vU3vDrroetiXBVc9Dv85Bu6yg7E50Y2Nbh/we2AicAV6N2shxECxF2gCGtH71H+Enh2fopWQQvRAAlCRQc4lkXNBgy4DXgeOTHTBo3bAg3PgpbPg6P9A6zA47POYH//yELhhEUxcC0tn6vyh9mpozIef3wPDWhLd4Oj2oUP/49GJsfzd3y6E6HcUekX9BtpX1H8BtKaxTWKwkwBUZJg7gYKElzoFWAP0vANwH5z1ih5H/9uFOooE2HYgvPatmB5vPBq+vxSmvgn/PBtym+GeufDBcXq7z6wUjZ7tRWdlPRb4KfpXlRBiINoOfAK8CzQAnwK7kY19RSpJACoyzP7oGYojEl7yIcA/gTMTXjJwwG44psMg9ty74cxX4Ib7YUdsr6VuKsxYAef/Hd45EY76Lyy5Qq95Ou8fpOx3w17gMXSG1gr0kgYhxEC1Cx2Avg+8hw5MdyDBqEg2CUBFBjoGWJyUkg8CXgDOS0rpbRQw5jPI2geLboAT34UV34ntWQO8cD6c8hbMehI+PhKmvAP/uABWzICCumQ2PNweoBb9f+Na9K8lIcRA1ooeml9H+4r6bciKepEMEoCKDDWLROwVH80B6J2CSpNSOjrr2e2VsGYqnPwWbJgAlhVQ4dRD8zHYNwSemgXHfQC/uBuacuA7/9K9pH8sA1Njshof6RvgEeBo4DogRYv1hRBpFVxR/x/aV9Q3ISvqRaJIACoylAF4GJiQlNKDA/1XJ6X0Nqe8DW+eCnfcCvu3Qm2FTgbalBNzEa3ZcO8v9Ip5hw1ahkHZMlh3PDwwB0Zv1veN2AGVlbB5NOzN0h8rK/X5RPkaeAjIB+agB+2EEINBcEW9H72i/j/AVqRnVMRDdkLqJwb2TkjdWQ2cgR4QTjyFXnf/v0kpvYOGiXDV7/SS98ev6nMxh38CCyrhyicgS+lcovffAJc+BxPWt6+BAtidrVfUT1+lUz8l2jDgGsAOjEl88UJkrJ53QpqawtbEY02czw8F8oCDkS1BBw/ZCUkMEtOA3yStdANwD7AgaTW0mbQWXjsdHry+/dybU2H5Jb0qZuMRcPXv4KR34PkLdSaoX90Jx68NDz5Bf57fCHMXJqD9UbQC9wMm4OfomWNCiMFkD27301RX27Fayygu/jZu97J0N6pP3G43+fn56W7GoCIBqOgHbMCMpJVuAH4N3Je0GtoM2Qcjdul/t+6vuzEvWw4zl+ox8154/wS4+HkoWgnfDO36jTy8BWY/HE+je9aC7kGeANwMbE5udUKIDOF2r8BkGofNNgun82Zcrkrs9l9QU3MXOq1T/2EymSgpKUl3MwYVCUBFP5CFTpWel9RabkSnH0rJm2K/b+C6xXqSpmsmTGqAp3/Q68wnLxfBkB7WBORt7Xsze2M3cDc6ELWj91wRQgxcfv8mzObjQ58bjaOw2y/Hap2HTuu0Fv2TIPMXLpnNZhwOR7qbMahIACr6ibHoNOnJdRWwFOh+V/cEyFJw3UPw3glg8cDWg+FHT8P3/gybxvaqqK09xOU9XU+0XUA1MB6Yh16qIIQYWAKB7Sxd6iEQ2B523mI5FQC/fyOwE72lRTCl067UNlJkNAlART9yEXBD0mspAf5CiqbUj/8YXjwHHr0aDtwGf/2uTmC/Z0jMRSyerRccdWXbgXDEfxPQ1l7aCdyFDkR/hV5DK4QYGIzGUfj9m/D7N8Vw9150SqcGdK/ol2Rar6jP58Pr9aa7GYPK0HQ3QERnMBjmA5Udz23YsCEtbcksDuAldF665DkP+D90yPtVUmtCT0K9+ndw3gtwzSMwcxkMjf2H8903Q8mzesFRx4VIX++nh+ePaYT3J4OtGpxWUCn+s3MHcAewCD3N4WdA7ImohBCZqrn5nxHnfL4PMBpHYTIdHnbe79+I1VqF1/tmxDNGo5Hm5uYu6/H5fJSXl+P3+1m/fj3Lli3D4/FgtVqxWCyAXkQUtGbNGsrKyjCb2zdfrq6uxmg0hj7Pzc0FYOnSpdTW1lJVVYXb7aZzZiCv14vf7yc3N5empiZyc3NDc0WD7fL5fCilQm1Ys2YNU6dOlTmlPZA0TP3E4E3DFM1a9H7xyZ/k7gPOJYXzGYNvx2Diivtv0PNFr3lED9t3YcQOvdp99sN6zufWPHjoWlgyCxba9FongJfPhJ8+Cv85NqmvolsHoYPQm9r+LUR/I2mYulZQcDllZcXYbLNC57ze1VitVTgcczCbj8PrfROrtYr6+qcwmcZhNB4KjAZygeijP36/n4KCAmpraykpKaG6ujq0cKimpgaAioqK0P35+fl4PB5MJhPV1dVs3bo1NMezuroaAJvNht/vx2QyAWAwGMICULfbzZo1a8LmhgYD2WBdgUCAnJwcPB5PKBiOVtZAkqg0TBKA9hMSgHb2KFCekprWAsVALANNCbVprO7WbM2Gs16Cx66Go/u2BdKlz8Li6+CwL/RwfeUCuPfnsDeNYyBGdPqmG4HY9ocSIjNIABpdTc1yXK4VeDztWykHAtvJyfkO9fVPhS1YKi6+juLiaWGBqp4VmIsORg+gc+xiMBior68P69kMBAJMmDAhogfVbreTl5eHzWYjPz8fh8MR6pH0er1YrVYaGxsjyu8YE+Xk5LB+/fqwntNo56O1Kz8/H5fLFXZuoJA8oGKQuxo9WzP5JgKvoncASqlxn8IffgSHfq6Xu5/0Dtz7M73VUS8tv0wvtH/iCj1MX22H1dPgpOTOZOhWAJ3+agJwJ7C9+9uFEBnM79+I0/lcWPAJUF5+BxUVl4QFn0Fbt27rdGYferxpbduxmc6bkHQO6Orq6gAdVHY88vLyQgGiyWSiqal9FnogEIgIKjvzer3k5uZGvc9kMkXMFw32oorYSQAq+ikDUAMcmZLaxgOvACekpLYOLluuJ3BevgR2HwC/uBdOf03vrNRLzbnwkyfg3Bfg4yOhwAd1hXD7bXqn0HRpAn6JDkTvQs8ZFUL0L3b7g6xY8VDEebd7BVbrpRHn/f5NTJ06qZsSdwH/Ra+g30BXPxmC8zMtFkvYYbPZQsPkdrsdl8sVembp0qXMmzev29fj9/u7DFJzc3Px+/1h53oKaEUkCUBFP5YDPE2qvo3HoJc/nZqS2jrIa4IlV+itj8ZthNXT4cb7+1zci+fqLekXXa8XKd32W3jrFJj+RgLb3Adb0WmbJqDTOO1Mb3OEEDGyWu+ktvaXGI2jws7rVExE9H76/Rvx+zeFUjZ1L9gruq7t8y/o2CvauXczmtzcXBwOBzU1NdTU1DBv3rweFwiZTCYCgUDUa01NTdLjmQASgIp+7nQ6JQtIqlzAC3w7ZTV2cOHfdW/oNQ/DQ7Pbz+8zwI4RUFkJozdD1l79sbJSn49ixyi4YRGc9TKsO659p9D/vUkvaEqnLehE9ib0NqmSOVCIzFVTsxy7fVZY8On1rg4Fn9E4HEuw2WZFBKyx+QSdBWU9sIPCwgJAr0jvLDhM7vV6MZvNVFRUUFFREdO8zMLCQpqamqIGoT6fL2zBkegbCUDFAPBL4KyU1TYK+Dtwccpq7OCgr+Dh2XDMR/pzBZz/dzD59cTOLaN1nqUto/Xn01d1GYQCvHYGnPw23DkP9mXBTffDuyfq3PjpthmYiw5E76O/bewnxMDndq8I/dvv34jPtw6vdzUu1wpMpsMxmQ7HbD4+LBh1u1fg92/C4ZgTR80KPWayDqNxE7W1C7HbbWF3eL1eCgsLwz7vDaPRiMPhwG63h52vrq7G4XBEDLlHC1R76pkd7CQPqBgAhgC/B6YAXeeSS6ThwLPAFcAzKamxC6unwYvnRb/WMhwa82HhXFiwoMsiWrPhl3eCu0QvtD/lbfCcA49dBXPvhkCak3Z+gU7bVA3cAlQA3eTdF0KkQCCwndLSW6JeM5nGhf69YsVD2O2LKCg4nkBgB0bjyIiFSj3x+dZRVfUEoIf7i4unUVIyo+1qCyUlJ2M0fo3dbiU/fzK5uWMwmwtCQWJFRQUTJkwIlZebm4vZbA7lEfX7/aFAs7S0FIfDgclkoqKiAq/XG0q9FAgEwvaM7/hceXk58+bNw2QyYbfb8fv9ofRN0lsanaRh6ickDVMsngMiJ7sn017gOsCZ0lo7MTbDtm4mwI/eDJsPjamood/ooLNyAWS3wmeHweyH4E+XJKitCTAOHYz+gG7yewiRRJKGKdNlAwcDefj9n+BwOMJ6Lf1+fyh4jGU+qAgneUAHGQlAY3Ut8EhKa1TonrnqlNbaQdbe7rc3ytrb64Sfx63TvaGnv64/X1YKcxbFHMemRBHwIGnITCAGvZ4DUJEZDNjtNRQXX4DF8l06x0I+n4+qqqqwFfKiZ5IHVIio7gUmp7RGA3qD0DtTWmsHeVvjux7FB8frLemvX6SnkM50QcMk+PFTtO/WlGYvASejh+c7ZxMUQghQFBefhMv1JPAe8DnwTejq0qVLKSsrS1fjBj2ZAyoGmOHoWZlTgdQmt5yH3tHn+pTWCsxerBcctQyPvJa9G66NzM0XC5UFi6+H5y/Se8if+yI8NQt+8IzeGfST1KRg7dZe9AKlZ4CFwI+RYXkhRDuLZRq5uQdRXV3bYW7qCPz+JoqLLVgsxWlt32AmQ/D9hAzB99ZD6NmZqfcU8BN0cJQSO0bo1e6N+eFBaPZuvZXn8xfqZJ93z4VDN/etDgWzlsD//gxym2H7SLA74JFruh/9T7XTgcXo5WhCJIsMwQ8Uw9BzRQ8G9ktzW/oPGYIXolvXAt9LS82XA25g/1RVOHInrJoONkd4HlCbQ5//9W/g95frfEsv9TFdlUHnwp/UAO7LYNQOeOg6WPltOObDhL6auLwGmIEb0Ft9CiFE11qBTejdlj5CT+aRTrlUkQBUDFAG4DH0munU+x/gb8ABqapw5E6damnzoXrB0eZD9ecjd8Jdt8BZL8HnY+A7/4SqW3Ty+j744jAodcNlbvj8UDjrFXjnJB3rDtnT8/OpsA9YBBwLPN72uRBCdE2h/2T9D/Au8CnwdVpbNBhIACoGsDx0ftD0zAq0oHdNSvsOwWM/gxUzYN6dsG8I3FoFF/8Vtub2ucjll+ne0Mev1OmaHLfolKQn/TtxzY7Xl8BVwBlA5B4pQggRzdfoAPRd9B70qV1LMJhIACoGuG+jd0pKj9OAlcAhaWtBm6F74c5fwt8ugNyt8PcLweyDr/qyFZ7WnAtXPQ7nvgAfHwkFPqgrhN/8Coa1JLDtcXoDKARmA7IviRAiNgq9MfC76G0/ZS+2RJMANEMZDIb5BoNBBQ+gaMOGDeluVj9ViQ4F02MK8ApwRNpa0MEF/4C3ToFpq6BsKRy4Pe4iXzwXTngPFl0PQ/bCr+7QVZz2egLamyAKeBg9LP8oMiwvhOiNrcD7QCOwK81tGTgkAM1QSqn5SilD8ABeGj9+fLqb1U8NBZ4GDkpbC44FXm37mHZHfgIvnwV3dOgZfm8ybDuwz0XuGAU3LIKzXoZ1x8HEdfDqGXDfjTBiRwLanCBbgXL0nyN1aW6LEKK/aQYa0HNFM+gHWz8lAagYJMaj+8DS50jgZTIkRdD+38B+bauGtuTB+f/QQ/JvnRxXsa+doRfb3zkP9mXBjQ/AuyeCxZOANifQm8CpgBUdlAohROy2AeuAD4H4R5EGKwlAxSDyfeCitLbgUOBfpHNCQBQ7R8DoL8GfD6e9Ac6KuDKRtGbDL++EqWt0PDthA3jOgceu0tvWZwoF1KB7pR8hhXlbhRADxFfAB+hgVFI49ZYEoGIQMaDTlI9IaytygBfRq+QzwlH/hde/BdZHdPR4jRN+/Hud4D4Ob58Cp76pF9+3DNMLlhomwf88l6B2J0gTOmvsNGBVmtsixGDl863D7V6B17u62/tqapanqEW9sQM9LL8Wnc5JAtFYSAAqBpkjgd+muxGMBJ4HLkl3Q4KyW+GRa+H3P9KTNp/+ke7CfG9yXMXu2Q/umqeH5V89HcZ8Ds9dCktnwiFfJKjtCVKP7pm+Gp3CSQiRGj7fOrzeNykpmYHJNA6r9U4CgfChbb9/IwUFl6ephbHahU5o34D+01YC0e7IXvBiEJoD/IF0L0MZBixD56p8Kq0t6eBHT+u5oKUueP8EWD8BTng/7mI/OF4vUJr9kM6LP9MFFi/cdB88dTkZtYH774Dl6D9TrgGGpLc5QmQ0n28dTudy8vMPZ+vWbZSVFWM2Hx9xT11dAybTOPz+TZhM47BYpoWu2+2LcLnuAsBkOpz8/MNpatpGXV0DgUD7Yp/c3AOpqLi0z+2sqnqirQ69QcnUqZMoKZmBz7eOpqZtWCzTsNsX4XavwO/fREnJDKZOnYTNNquXte0G/EA2cBiQi/T3RZIAVAxCQ9Cz/6aS7pl/Q4En0OvzH0xrSzqYuE5nlf/7BXDx8+3n9xkgq+9/0assWHw9/PVicFrhvP/T23v+4BmwOuGTIxPQ9gQJANejUzY9iN5jXggRzutdjcOxBI9ncehcQcHluFxVmEyHA7rn0m5fFHZPaektmEzjQvfU1a3FaGzPSRy8FrwOUFx8HU7nvD61s7p6CR7PapzOeWFl+v0bqalZjsu1ArtdB5kOxxzy88dhtz8YCor7rgWdzP5TYAx6cxQJRIPkKyEGqVOAn6e7EYB+Ez5AOtPlRzFil95zM+i1b+kh+Q+Pibvo/x6lF91f8QQ05cD5L8D7k2H2YjBkWILOt9E7KV0BZNiMASHSzmqtCgVuQfPmXYnT2T7R2+l8Dqv10k7PXYLd3v4nd25ueAo4o3Fk2Oc1Ncsxm48PCx5jpYPf1Xg8iyOeN5kOx2I5Fa/3zV6X2ztfAx+jk9p/Qbo7PjKFBKBiEKsEJqS7EYAegf4tUJ3uhnTl17eDrwAK6mFZafzlGXTv56QGcF8Go3bo3tGXiuDYD+IvPtGWoFfL3w9kyJb3QqRVILA9NJzekdl8HNXVS0Kfu90rMJuPC7unsHASbveK0OdNTV91KntHh39vx+l8DodjTq/b6POto7p6Sbc9pybT4VRUpGo2/jfAJ+hA9DMGeyAqAagYxEaQ7tygnd0MOMmoKZHac5dA6TKdcb5sGcx5AFr3j7vYLw7THa2XueHzQ+HMV+HfU8B+FwzJsEjvK+AmwIzO5yrEYOb3bwIgNzd8g4/g54HA9lCQ2vme4HC7378RgMLCiRGLjoLs9kU4HNf3qY1VVU/E1HNaWjqjT+X33R5gE/AOeng+w37YpYgEoGKQOxf4YbobEaYCvUQqoyZoH7gdlpbp/Tb3+xoenANnvArrxyek+OWX6d7Qx6/UC/LvmqenoU55OyHFJ9S7QBHwY3QfhhCDUbDns6lpW9j54OdNTdtC/+44v7OjYBDrcMyhpua5tnMbQ2XrxUFfhS1Y6g2v900sllN7vM9imUZh4aQ+1RGfvegA9B1gI7qHdPDIqN9xQqTH/wL/QG+zlhl+AIwCSoDWNLclxABcvximrdar5OumQrEH1h0PQ+MfSmrO1blCn/kB1FRAgQ/qCsFhh3t/BnMWwXUPQd5W2JoHi2fD3TfDzpE9l50MfwD+AsxH51XYLz3NEBlqgeFvXV67yHkiBRV61V19zX953vpul/dWqgtD/64peIXPfF9Fvc9cfgQX15wEwKf126gtfLXLMsvrzmBsQXxbExuNo7BYTsXn+6DTwp5NoY+dez67Elw173avwGQaF/q8vPwOVqx4CNA9qsG5miUlsfVYBgLbycuLrQ1dBcmpsQ/4HNgMHIxeOR//CFOmkx5QITgEuCfdjYhwEfACOmdoRplaB2+dAt/7E9x/Y0KCz44858AJ78EDcyBrn95VadM4uOUuGL1FL8QfvQXs1bBqenr3mt8O/AI4GViZvmYIkRZO5zyczvbE8B2H0WMNPoPM5uMpKZkRCj5rapZjtV4SCgzLy++gpGQGJSUzwuaPDiz70EHou+hFSxnT/ZAU0gMqBABXopearExvMzr5NrACOB+d1jhj5AT0vNCOk1X/WKaH5Q/fFHfxO0fqfeSXlsGfvwsHR3nxw1sgvxHmLoQFC+KuMi4NwNnozV7vBsZ1f7sYBDr2XHanoOLIUG9oTyrqz4zpvrEFB8VcfzxMpsNxue4KBYRG48jQ8Hkw5yfowLQ3PYzBhUf19TpDck3NcsrKikPXjcaRMZVpNI5i69Zt3d7TF719Pb2n0NthfIlO3TQGnVN0YJEeUCEAHUk50enhM8upwEvoQZmM0jH4fP00vX3nKW/B/52TsCpePx1UNyuyhrfA7AxaR/ZH4Dh0NoOv09wWIVLBaBwV6pm0WKaFVrAbjaO6nCca7CntvII+qLz8Dmpr2xPTeTxvht1bWDiJurqGHtsWa4olv38jPt+6Hu8LWrbME/O98dsKvAc0ondaGjgkABUi5FjgV+luRFQnAK8C49Pcji4d8x+YsQK2jNZJPm+7HfYm5sdLXg9dv3lbE1JNwuwE7MAUwJvmtgiRanV1DaE5msEgtGNaJdABqb4WuTrd611Nbu6BYbsp+f2bwnKDGo2jIsqMZt68K/H51oVW23fF5/sgYvem7sRSd+I1o8daPkL/lOn/JAAVIowNSMdqyJ7lo4PQieluSDSjt8A/zoff/AoMCn57m16g9PmhcRe9Na/76805cVeRFOuAYqAUnflPiIGmuPg6amqWh51zOJaEpU2yWE6N6K30+T7ocnW63f4gTuetYec6B7F6CLzn2fFm8/HYbLOwWqu6va9zD213egpmky8ArAU+RM9C778kABUizP5Abbob0aVx6OF4c7obEk2Wgl/dAZ5iOPRz+Nd39JD86p7ToHRn8WzY3c30p+zdUPxiXFUklRs4HqhioC8pEINNcCV8UHX1EqzWS8N6Nh2OObhc4YuGnM7lUXN7VlcvYd68KyPOFxefGppPCrqXNda0SQ7HHIqLp1FcfF1E8BgIbKe6ekmv9pcvLZ0XU/CbfF8BH6D/1P0KPW+0fzEo1f8aPRgZDIaVRUVFRStXrkx3UwaJa4FH0t2ILm0DLgZeSXdDuvLZYXqT93dP1Cvmj+x7H+CIHXq1e36jnvMZtHsY7B0KI9tGo+6yw22/gT0ZnA/pGGAROvus6L/Wrl0CTGRiRg5HpI7fvxG3+5+hhT75+eOiBnM+3zq83jdDC5PM5uMicnv6/RuxWqvC9ozvqLT0ltDe7DU1y3sVNAbbUFX1BKB7VPPyDsJoHBlRjtV6cmkoNgAAIABJREFUJ17vm/j9m6iouKRD0vxNeL1vEghsx+N5sM+5SZNnBHqx0kEkeyuTtWvXAjAxtjdAl42RALSfkAA01QLoofjMTTW+C7gMnaopI+0ZAv85Bia2Te7fZ4BtB+kV9L00Yode7T774fY8oA9dC/f+HG5YBAsqYcg+eGO6jns/Hp/QV5Jw/4POPjs+ze0QfSMBaOL5fOswmcZ1ubq8L3lAB6fh6EA0h2QFohKADjISgKbDs+hU8Jnra/SOPK50NyQW1TfDojk6t9K33kho0We8Ak//EI7YCM1G+OmjenelTJYN3IrefnXgJVgZ2CQAFZkvGx2I5pLoQDRRAajMARWiS5cC3013I7q1P/AMcFW6G9KTvVnw/EWw8QgoeklvbZTAv31fPRNOflvnDM0JwLMleu5o9u7E1ZFoLcCv0RkOut4zRwgh+qIFWI9O4fQlOsl9ZpEAVIguGYAHycC9iMIMAR4FfpbuhnRnyD7wWuDn9+hJmr+4Fy5dDoH4tgPsqCkP/udPMOcBaN1fD9evmg7Hr01YFUnRiN716ruAP81tEUIMNK3oXZXeA74gkwJRCUAzlMFgmG8wGFTwAIo2bNiQ7mYNQkcAd6S7ET0yoDcTvbWnG9Np/2/gnrmw/BI4KAB/ugTMPqhP4Jp+Azw4B057Az48Bqa8o/eTv/JxMn6R6F/Rs47nAxnccSuE6Je+RieEewe973xit1DuCwlAM5RSar5SyhA8gJfGjx+f7mYNUtcBU9PdiB4ZgN+ik6BntEv+BD4zmOthvQnm3p3w4PAtMxTUw1M/hhG74PGr4Pc/hpEZnjavFVgAFAC+NLdFCDEQ7QE2ovebT+/OShKACtGjIejcoEPS3ZAeGdD5JuemuyE9Ma2H107XS9uXzErKYs0do2DWU3DFE7DzAPjR0+1xb6ZbC0wD7kT/uhBCiMTaQ7oT2UsAKkRMptAPwjpAx3LVZPicUIDsVlho00vXQadpuuF+ePeEhFaz5Ao90v/2FDjmI3jjNLjxPjJ+SH4P8EugCD1PVAghBhIJQIWI2a+BCeluREyCc0JvTHdDeqO2HBbdANNWwxNXJLToD4+D6avgwev0VNT7fgZ/+S7kbUloNUnxOvrPn0fJ+JhZCCFiJgGoEDE7gEzeHakzAzrZeeSGdxnq8qf0aqHdB8BPnoCrHoNdwxNWfGs2zHkQLlmuc4Ve/Dy8fTKc+XLCqkianUA58D30OlYhhOjvJAAVolfOQad+7x8MwAPojUUz3gG79Wqh3/1EJ/B8/CrdbfnBsQmt5k+X6Jyhr58Gh2+Cf50Nt90OWelfFNqjvwInAn9Jd0OEECJOEoAK0Wv3oneX6B+C2Uwr0t2QWP3kCVg9DY79AN49CQrr4NVvQWUljN6sI8XRm/XnO0b0qYr/HqXz4d85DwwKbq/UaUrHfJrYl5IMX6J7Qn9KupcQCCFE30kAKkSvjUbPsOw/soCH0UFLv3DSuzqB5/efgUnvg9UJ1XbYMhpUlv5Ybdc9pH0MQvfsB7+8E879P/j8UDh7Jfx7Cpz/98S+lGR57P/Zu/O4qqr1j+OfjSMqSqiZQ2Wgpc2BU6XhAA4pljlXNiqYzbeStEHsVyrqbdQKtEkr5xHTVDQ06zpBs9ogebtOmQPOOLF/fyxQUIYD5+y9zj7neb9evIAzrS8q+LD2Ws9CrQ39RncQIYQoAylAhSiT+4F2ukOUSgCQBDygOYfLgo6oA97br4TMMMg+bz1odiBsDYNx7nUnSI2GG36ApR2h9l5Y3FW9ZIWTbr2sLf4EbkMdQOCAuEIUKSNjC7NnryA1dV2xj0tOnmtTImE1KUCFKBMDVc5V0h2kVAJQu6kH6A7iKgOYPOjC4jNPdiC8N8TtYfbUgS5LIH4MnC4Hz/5btSkNdUD/oxxU79eWwC+aswhRFhkZW0hNXU+vXh0IDa1PXNwosrIKLjDJzNxORIRjfnIJF5TXHUAI52qMas30gu4gpVIO+AhVuHymOYtL9tV0734XmQHqqv7q22Baf2i+Eb67CQZNgpl9PTKEpb5HnaA0BngCmV0Q9sjI2EJS0lzCwhqwb99B+vaNJjy8ydn7s7IOk5w8j1692hMa2oDMzO3Mnr2S8PCriIpqCUB8/DvMmjUGgNDQBoSFNWD//oNs3LiJrKwjZ18rJKQ6sbF3lTnn6NEf545RH4Dmza+mV68OZGRsYf/+g0RFtSQ+/h1mz15BZuYOevXqQPPmVzN06H1lGlMUTwpQIdzyLDAN+Fl3kFIpB3yMOg14ut4oJau5T635LO5+D1p7s9olP3kg9JoDM/pBVCo8+ZbqEOXNTqAOIEhB/f1eqjWN8HWpqetITJzC8uUTz94WETGAWbNGExraAID9+w8SH/8O8fHvABAcHMSkSS+cLT4BNm7cTHBw0NnPQ0PrExra4OxrAERHP0pS0rAy5Rw7dgrLl68jKWlYgdfMzNxOcvJcZs1aQXy8KjITEx8nLKw+8fETzhbFwhryS7IQbqkIJGPJWZIWKw9MBfroDlKSIRNVW6aiVD8IB6t7dMiDwdB7Fgx+D7IrwaDJsKE5XOOQ3zNWoto1fa47iPBpcXGjzxZueYYNe4CkpHkFblu+fAIHDqxk69Z5HDiwkl69OhS4PySk4PdvcHC1Ap8nJ88lPLxJgeLRVfHx77B8+TqWL594wfNDQxsQFdWC1NT1pX5d4T4pQIVw2804pNPmBcoDnwI9dQcpznPjIWzrhUVoxRNQ7jRsbQzvPO75cQ1IGgwt1sPmJnDNJlWEDpyEI44kOgjcA/QH9mvOInxPVtZhMjN3nL2cnSc8/CrGjp1yweODg4OKLCD37z903msfyffxYZKS5pGYWPrv8YyMLYwdO6XYmdPQ0AbExvYo9WsL90kBKoRHjALq6Q5RJhVQiwi89kdwtaOwthUMTSzYB/T50eqA90cnwPPWXSrLa0X64YMQmA2TYmF6PzXx6gTTgeuB5bqDCJ+SmbkDgJCQGgVuz/v8/E1ExWnWrGmRj4+Pf4fExLKd5zZ69McuzZz27t2h2PuFNaQAFcIjaqDavTtTBVShcofuIEWpdhRGjlTb1c+UV+9HjoRrN8GEx6F87jFG+0JgVi+PD3+sKjz8IdzzKRyuBn1nqg1KzR1y5W4H6gyvJ4FiFjMI4bK8mc/9+wv+Jpb3ef7bs7KOMHv2CmbPXkFy8lxmz15R4DmJiY+TnKwu22dmbj/72mpz0KEC60VLIzV1PVFRLUp8XFRUS5o1u7pMY4iyk01IQnhMD1QJt0B3kDKpCMxEXY5fpDlLmZwJgF6zIa2dmh197QUI8Oy18s/vgfUt1AxoRIZq1TRsNLz+L7WL3tu9DSxDLbuI0JzF560q5eOrUfAvJe/5kfluSweOUDqFPT8cCCr84a4KDg4iKqoFGRm/nrexZ8fZ96GhDQgJqcH+/QcL7F7v3ft5gLNrQfN2zc+evYLQ0PpnPx806DVWrHgXUDOqeWs1z19DWpSsrMPUrFmj5Afmfj3CXg74kSmEk0xA/U/iTBWB2cDtuoOURbkc6DtDrQsdM0wVo0c9v239j8Zwy7fwxlNQ4TSMfw6+6KpWBTjBFqAV8BpwWnMW4WxJScNISjrXGD7/ZfS8S/HBwUEXtE6Ki+txdld8nvDwJvTq1eFs8ZmcPJe4uB5nC8NBg16jV68O9OrV4YIZVOFMMgMqhEc1QLUFt2BTjE0qAXNQ87lfas5SaoOToNEfqvicdxe0aQgLu0ODHR4d5mQl+NcbsLI9fPwAdPkSvr8R7v0Uvmrv0aEscRp4EfgC1QkhTG8c3xRZ8kNK/Xx3p609PO0dGtqAWbPGnC0Ig4Ornb18fv7mpILPq09m5g6ysg4XOvOYt/EoPX0qoIrRvn2jz94fHFytyOfmFxwcxL59nl+s7crYomQyAyqExz2COpfGuSoD84Dokh7ojaJWqE1LYX/Ad+FqG/tGay44L4pRx3iubgP1dkFqFLzykpqEdYL/oM6Td8jGfuGFgoODzs5MRkW1PLuDPa9AK2xHfN7saN7l+vMNGvQakyadO+Bj+fL1BQraZs2uZuPGTSVmc7XFUmbmdjIytpT4uDwzZ8qWPk+QAlQIjyuH6g3q7AsMlVGrWR25P7TJr7CuJUSmwa56MMe6RlM7Gqjj6hNGqM9fehW+agcN/mfZkB51FIgFugN/a84inG/jxk1n12hmZm4nPv4dMjO3F3hM3galwmZJU1PXERJSvcBpSpmZOwr0Bg0ODirQqqkow4Y9QEbGlgvGP19Gxq8FxiuJK2OLkkkBKoQlrkedkuRsgcBCoJ3uIGVRcz8s6wgTHoVXX7R0qDPlYWSCKkR31IM2a9Ql+ZiFlg7rUYuAa4H5uoMIx4iOfpTk5LkFbktMnHK2bVJoaIMLTh8CtTs9PLxJoZex4+MnkJQ0vMBtoaH1L+gNen6z+sKEhzdh6ND7iIsbXezjzt/JX5ySilnhOilAhbDMy/jC6roqqKMdb9MdpCwqnoJH31UblAD21IZnx6njjSywqq06xvOL21X9u/AOePNJ1TPfCfai1v4+DLjexVH4q7yd8HnGjp1CXNxdBQrOkJAaBYq2vPWd+S+x53/+sGEPXHB7dHSLApfrN27c5HLbpMTEx4mObkl09KMXFI9ZWYcZO3ZKqc6X7917mEvFryiZYZqy8scJDMNIi4yMjExLS9MdRZRKKg5dSXmBI0AXYI3uIO7o9CUs6wS3fAPzesDF/1gyjJEDT70JY55XNXDGTWqD/h+NLRnOElcAU4DWuoN4oc2bpwBNadpUdxK9MjO3M3v2yrMbfcLC6hdazM2evYLMzB3s23eQrKzDxMffd8GsaGbmduLiRhc4Vz6/3r2fP3s2e3Ly3FIVjaB6io4e/TGgZlRr1qxBcHC1QnbojyI1dT2ZmTuIjT23Cz8zcwepqevJyjrM8uUTytyb1LtcCtQp9bM2b94MQFPXvgGKPKdaClCHkALUye5H/VfufIeBzsC3uoOU1Q/XQ0wK/O8yaPgnpMTAtb9YNlyzDapnaFimamD/yHvw2b2WDedxBhAPjES16BKKFKCel5GxhdDQ+kXuLi9LH1BREr0FqFyCF8Jy/wZq6g7hEUHAElQfSUe64UfVSb7FOth2hWroubiLZcNtbA7hGTC9LwQdgU8HwEcPQFWH7GEwgTGong7WlelCUOSa0Dz5d9sL3yAFqBCWqwW8rjuEx1RH9Qct+YA7L3XJ35DWFvpOh8PV1YzoW09YNtyhGtB/GgycBMcC4YFPYGMzuP4Hy4b0uO9RLSTfAHI0ZxFC+AYpQIWwxQAc2tCoUDWApUAz3UHKKjAbpvWHEQmQUw72WTxDbcAHA6H5Bvj5mnNdooZMxDENOE8A/0KtaHZIhykhhBeTAlQIWxjA+6jumr4hGHWueLjuIGVlAAkjVRf5hARbhtx0jeqLnxQLlU/AxMdUi9LgA7YM7xErgeuAz3FM7SyE8EJSgAphm0ao1ky+4yJgOXCj7iDuaLMGAnJLqR31oP0K+L2RZcMdr6JODO0zAw5Wh7vmqZ6h7VNhxAjVKepMgHo/YoR3rhc9CNwD9Af2a84ihHAmKUCFsNWzqHbfviME1Wzqet1BPGH4KHWYe8t18FVbS4ea1Uf1DF3XAi7/C1Kj4YVRUHuvqodr74X4sepUUW8sQgFmoGZDl+kOIoRwHClAhbBVBdTJ20V2pnCkmqgi1PGl9YTHoFsKHAiBjstg8sOWDrftCmjzNXxzs/oXUeG8M+QDsyFsq+qd7612Ap2Ax4FjmrMIIazlydadUoAKYbtWwKO6Q3hcbWAF4Nr5JF4q6AjMv1NVfKcrwKDJ8Mx4dU3cIqcqwpW/F31/YDYMec+y4T1mAmqn/EbdQWxgGKcBkxxpCSD8TF4BahjuT6JIAeqlDMNIMAzDzHsDIrdt26Y7lvCY14D6ukN43MWoTSqO7s9dLgfGDVWzn+VPwevPQI95kGPdrHXNfe7d7y22ADcDrwKnS3isk1WqtAM4ztGjupMIYa+juf/oK1Vy/zhjKUC9lGmaCaZpGnlvwKqGDRvqjiU8pjpqzsj31EEVoVfpDuKuhz+E5dEQsk81rA+wbs93SV2grO4S5UmngZeANsAfmrNYJShoPbCf3bvh8GHIyQE5VFD4KtM0ycnJ4fDhw+zevRuAoKCiDw1wVXm3X0EIUUZ3Aj2AebqDeNwlqCK0LVDM1WXv13YV/HwtXLL73G0nKkKlkx4dZuIQteEoMLvw+3fXgUrZcMJBXbzWAjegmtcPwrdWPYeELOPo0es4dgy2bw8BAvGtr1D4h78pSx+LKlWqEBIS4vbocha8Q8hZ8L5qB+qC9WHdQSyxA1WE+sxM2LbLIXIVjHke+k/32MtWPaJ2u4dtLViEnqgA5U9DORPWtoQ758Pfl3hsWNt0BSajfjHxFTk5ldi/vyOHD7fgxIl6mGYF3ZGEKCXXz4I3DINKlSoRFBRESEgIAQEuX0Av8jczmQEVQqv6qNO2fW9TEqiv7isgEsjUnMUjpvWHvy6Hu6fBliaqgb0HJr6OVoNWa9XepyHvqTWf+2rCu4/Aki4wsy+0WgcbmkP3hfD9Te6PaacvUO2aJqHm/X1BQMAJatVKoVatFN1RhCij14GntY0ua0CF0G4wame8b2qAKkIbas7hEc+PgTefhIAz8MoI6DcdjnvmuvjRajByJNTZA+XPqPcjR8L6VuoIzzW3wqXbYU1r6DHXI0Paai9qwclDwCHNWYQQ+kkBKoR2AUAyvnxB4jJUEXqZ7iDuMoAn34ZF3SDokJqabJsGu6y9uPzPxdBhBXx8P1Q9BnN7wguv4sizMD8CbgJ+0B1ECKGVFKBCeIXrgKG6Q1iqIZCGWnXkeF2+hG9vgYZ/wvqWcPN/4FigpUOerAQPfgTPjVUdoV59CT67Byoft3RYS2Si2jV9pjuIEEIbtwpQwzBuzP923n3PGobxe+7bDMMwGrozlhC+70XUefG+6wrUTGgD3UE84dpfYF1LuOUbePoNqGJDJWjA+OfgjgVwuJpaiprWFi7ZZf3QnnYcuBd4AjilOYsQwn7uzoBGAxnAMKCZYRjVAQzDGAMkog5G6YNae56Ud78QojCBQJLuEJYLQxWh9XQH8YSL/1EV4BNvn7vtv5dZfml8UYxqTfpnQ2i5Xm1OuinD2jGt8g7QHnBgDS2EcIO7BWgWEG2aZl/TNCebpnnIMIybUNcSk03THGya5nemaaaiCtFh7gYWwre1B+7XHcJyjVBFaF3dQTyhwulzO+F/bwQ3fQcDJ8NJa9vy/HwdtFynNic12KE2J901x9IhLbMGCAe+0R1ECGEbdwvQGqZprjjvtr6o3/8T899omuZBytLxVAi/Mx6opTuE5a5ENat3rQudQ/zRCLIrw4cPQ8dlsM/9Zs3Fyduc9NEDagXAnF7w4v/hyM1Ju1E9YyfgyPhCiFJytwA9WMhtUUCWaZrbCrlPfq4IUaJaqPNjfF8T1EzoxbqDeEqXL+HrNlBvB6xqq6Yot1h7KOnJSvDQh6qHaI4B//cyfH63MzcnnQYeB+4DjmnOIoSwlrsFaIGC0jCMGqgrKRuLeLyDTjQWQqd7UEusfV9T1Exobd1BPCUiA9a3gPB02NpIdZhP7WDtmAb8+1nVpP5wNXVI06pIqLvT2mGt8ilwCz5yeIEQolDuFqDB530elft+1vkPzC1O5RK8EC4xgPcABx3+7YZrUDsWfWbhQf2dsPo2tSjzYDDEpKgD3S32RTfVEerPhtBiw7k62Il+AJoBS3QHEUJYwt0C9E/DMNoD5O5wTwQOmKY5Of+Dcls0jTFNc5yb4wnhR8KABN0hbHMdkApYu2rSRlWPwazeMPw1eOtJuORvW4b95VposR5Wt1Gbk75uA70umBJwhgOoc+T/D8jRnEUI4VluFaCmac4B+hiGsR/1syKE3FlQwzBqGIbxnGEYy1CtmmINwxjobmAh/Mu/gOt1h7DNDaiZ0It0B/GUABNeexFiJ527bV0LOGhtR7q9tSEqFT58UG1OmtUHXnoFR67CN4GXUWfIZ2nOIoTwHLdPQjJNczCqv3Qz0zRDTNP8Lt/dqUA8EIG6muLQi0FC6FIB1UbXKOmBPuNG1A+O89f3+IRNTdXu+LwmnhY6VREe/gCeGa82J70yAqb1d+bmJIAUoDnwk+4gQgiP8MhRnKZpHswrPA3DqG4YRvW8285/88R4QviXFsBjukPYKhxYDtTQHcTTAo9Dg+2w6Rp1nXzNrdaOZ8Drz6glqIeCoN8MtTTVqZuT/gBaAdN1BxFCuM2Ks+BrAnGGYbxvGMZGwzA2GIax1DCM9wzDGGXBeEL4gdfwkQMsXdYMWAr41PFpV2xTZ8h3XqKuk3dYAVMGWD7s4q5qc1LmFdB8ozo5KaKoXiVe7hjQH7U4RY7wFMK5PF6Amqb5p2ma43JPQWoGxKE2t8ahLscLIUotCJioO4TtWgJfAtV0B/GkGocgJQaeeEs18bx/itqodKgajBgBtfdAwBn1fsQIOFLVI8PmTbqubnNuk37vmR55aS3eQG04sGdrlxDC06yYAS3ANM0M0zQjALn8LoRbugM9dYew3c2oItQzZZiXKH8G3noK3n0Eyp2G8c+o/qFj49XMqBmg3o+NV31EPVSE7qulNidNflhtTprZF0Yk4MjNSQCrUcs11uoOIoQoNcsL0HwG2TiWED7qbXzsorRLbkX1g/SpIhTgkfdhSRe1SHN7A8gOLHh/diBsDYNxz3psyFMVYdAkePp1OBMACSNhej8IdOjRQzuB21Bdcx1aRwvhl2wrQE3TzKDwozuFEC6rB4zRHUKLNsAioJLuIJ4WnQqrIy8sPvNkB8J7Qzw7pgFvPn1uc1LfmeqSfL0dnh3GLqeAIcBDgEM3+Qvhd+ycAQU5CUkID4hDHVTof9oCM4FymnN43L4STiku6f4yWnL7uc1JzdLV5qRmGywZyhYfA62BbXpjCCFcYHcBKn2EhXBbAJCM6hHqf7oDH+kO4Wk197l3vxvyNietug3q7VIzoX1mWDac5TJQjaeX6Q4ihChWiQWoYRie/FEkS3SE8Ihr8OemEgOAt3SH8KQhE4vuEF/hBDzyrqXD76sF0cth0kAIzIYZ/SBhBBgOPf9yP9AZGIUc4SmEt3JlBjTc8hRCiDJ4AWisO4Q2TwAJukN4ynPjIWxr4UXoqYpQ+x/LI5yqCLHJ8NQbanPSiFdgRl/nbk4yUd8hPYFDmrMIIS7kSgEa6sHxPPlaQvi5ykCS7hBavYwqRB2v2lFY2wqGJhbsA9puBWDA0HGwo571OQzVHarbInVcfe/Z8HUbqL/d+qGtMh91hOcm3UGEEAUYpln8VXHDMHKAA7mfurOJKBTANE2f2z9gB8Mw0iIjIyPT0tJ0RxFe5yF8cFWky3KAB4CpmnNYZuIQaLgNui62ddimm1S//LBM2FkX7pwPG1rYGsGjqqK+S3rrDiKE13gdeNrqQYwi73CxAPUUUwrQspECVBRtH9AUsP4yrbc6BfQCFuoOYocfr4Nrf4YA65fUh+yDOT2h7So4Xhke/EitD3WyZ4HRQHndQYTQTm8B6sol+CzUOtCL3HxrVub4Qohi1ATe1B1CqwrADFSbJp+WFqm2rN//CZy2/nf5/TWh4zJIHqQ2J03vD6+85NzNSQDjgY7AHt1BhPBzrhSg+03T/N40zYNuvmUAf1r9BQnhn/qj/lv1X5WBBagWPD7rTDkofxo+HQC9ZkO29W35T1WEuCR48k21OemlV2FmH6hy1PKhLfMV6t/Jet1BhPBjrhSgnuz1kujB1xJCnGWgDiMs4jQdP1EddWRnE91BrNJhJaRGQfABWHAndP3CY+fEF8uAt59Uwx2sDr3mOH9z0nbU6VqTdAcRwk+VWICapjnHU4OZpinf60JYJhT5HQ9qo5qQX6Y7iFVarVPd4i/ZBSs7QFQq7L/IlqGXdoZWa+GPMAj/Tp2c1GKdLUNb4iQQCwwEsjVnEcLf2H0SkhDCUo/iByshS3QpsBxVjPqk635WU5CXb4N1rdTUpE3HfGxpCi3XwVdtoe5uWBUJ/T+3Z2yrfICaDf1LdxAh/EiJGwENwxhD0T/atpqmOfm8x18BdAA2mqb5vfsRhRCuCwA+BK4HjmjOoteVwFJUOe6TjcgbbYU1rSEmBV55uZi9pp6XtzlpwmMQlwyf3wNXb4KXXwHTodMaG1HrQqej/gMTQljLlR8VSUAYai3o0Nz3Yajv11nnP9g0zT9zb69pGMb7hmHc5bm4QoiSXYHa6ytuAhahNij5pAY7YGMziE49d9txe77a0xVg8PvwxFtqc9KLr8Gs3s7enLQXtZVvLHJutBBWc2UN6J+mafZBfU/OAS4yTbOPaZpzTNM8WMRzDpqmucI0zcGAYRjGe56NLYQoXiz+vis+TxtgNj7c97Fcvp5IX3aCRn9Axk32jG3AO0/A7Yshqwb0nKsmZRv8z57hrZCDmmXpDRzWnEUIX+bSxZLcWcy9uYVnoUVnUXI3MSVLESqEnQxgMmpfuOgKTMHWq9R6TB4IO+tDu6/g69a2Dbusk9qc9HsjuOl7529OAjXb0hLYojuIED6qxALUMIwaQD/TNMt8Tc80ze/USxk3lvU1hBCldSn+3qA+v/7ARN0hrPb53dBnBhyqoRZpLuls29C/NlGbk1a2g0v+9o3NSZuBFsA83UGE8EGuzIA+jzq5zF2JQJwHXkcI4bIHgG66Q3iNR4BXdYewUsVTqggdOAmyA6H7Qphp3+nnB0Kg01J4bzBUPqE2J736grNPTjoM3AUMA85oziKEL3GlAI3KncF0S+7mJDmOUwhbGah9hPb0iXSC4cC/dIewUrkcSI6FZ8arnUL9psNHD9g2/OkKMORdeOwdtTnphVEwuxdUdXhThjFAZ9RGJSGE+xzaMEMI4bp6wDu6Q3gNA9Uj4EHdQaxkAOOeU9OPlbMhbKsZNsNMAAAgAElEQVTt4098DLosUZuT7poH394Mrz8Fe2qrwnRPbRgxwlmFaSqqVVO67iBC+ADDNItvNmEYxu+maTb2yGCGsc80zZqeeC1/YxhGWmRkZGRaWpruKMKRTKAnsprtnNNAH/zgT+SvS+EyfdvSr9oCi7pCo0y1wzz/rMfxyrA1TG1gOlpNV8LSqwS8CzykO4gQbnkdeNrqQYrc++nKDKhhGIbbW2lzNzMdcPd1hBBlYQDvA7V0B/Ea5YHP8YOm4/mLz5Ru8NQbkGNfP4Bfm8CcnmrW8/z/cAJzJ2efHWdbHI84ATwMDM79WAhReq4UoKmolmju6p37WkIILS5GzduIPJVRM6AtdAexQ1YNGDAV3noKHvgYTpezbeiHPirYrjS/wGwY4tAmfUlAJLBddxAhHMiVAjQZ1YTeXYnATA+8jhCizHoDfXWH8CpBwGLgat1BrBZ8UE1FVj0CU++D3rMgu5ItQ9fc59793mwdEA6kac4hhNO4chJSBpBhGMb0sg5iGMYM4E/TNFeW9TWKee1ehmEkGYYx1DCMxNyPQz34+sGGYbi85tzqPEK4byJQR3cIr1ITWAY01JzDch1WQmoUBB+A+T2g2yI4UtXyYfeVsPJ/X4jlESz1DxAF/Bs5wlMIV7m6Cz4O6GMYxpelWQ9qGEZ1wzCWAr1y3zzKMIwkINo0zTjTNMeaphmPOkVtuWEYUW6+drBhGEOBPwGXCkgr8wjhOTVRFw9FfvWB5fhBad5qneoSX2c3rIiC6OWw39o2XROHFH9E/cEaztoNX5gzwLNAP8DhX4oQtnCpADVNMxN1sHRHINMwjGcMw2hY1OMNw2hoGMazqOItCuhjmuY2t9MWHKNX7usWaG5vmmYWqmCeZRhGcBleNyp3xnMSkAFk6swjhDXuAAboDuF1GqFmQn3+G/X6n9Sh7Zdvg5+ug0xrL9KMf07tdj+/CM2uqJaiNt4KK9tDrX8sjWGLmUArXPyPQwg/5nIfUNM0U1EFaDnUmtCthmHsMwxjg2EYM3LfNhiGsQ/YmvsYA+iYex68pyWi1qcWlXU/6vCKUjFNM9U0zQjTNHvnex1teYSwzluoHqEiv+uBL4BA3UGs1mirKkIX3w7NrO1sebSaarWUOLRgH9Axz0OzDfBnQ2ixQcW57L+WRrHFL6gidL3uIEJ4sVI1os8tpBqi+jgbqONVIlA7G3rnfnxR7n1jgStM01zhwbwAGIYRjrosvqGYh2UAsZ4e2wl5hHDNRcBk3SG80i2o3fEVdAexWoMdcNvX5z5f0B02N7FkqKPVYORIqLMHyp9R70eOhB9uglu+hR+uh6t+g29vgWt/siSCrf4B2gILNOcQwluV+iQk0zQPmqYZb5pmABCNWuOYnPsWj1oDGWCa5vOmaR70bNyz8tZTFneVIxMItmkDkLflEcJFXVAdDcX5OgGfUkwXZV/zzS1qZ/xtqyHjJluH3l1XDZsWCfV3wtdtoPXXJT/P2x0HegATdAcRwgu5dRSnaZorTNMcZ5rm4Ny3cVbMeBaiee774gq+vMYe4RZnAe/LI0QpvA5cpjuEV+qDat/vF276DqJSYW9taPcVfN3a1uEP1YDOX8Kcu1THqGUdobsPTB+awOOoDUpFtEIVwi859Sx4V/YIZOW+t6PBh7flEaIUqgMf6A7htWKBMbpD2KHKcZh/J/SZoarBjstgSWdbI5yoDH1mQlKsalA/9y542EdWifwb1YH3uO4gQniJ8roDlFEInN1hXhI7NrS6lccwjDQXnnfjtlXbGGmMLPTObkndiIiNACA9OZ1FcYuKfKER5oizHydHJLMrY1ehjwsfFE5McgwAO9N3MqnZpCJfc9DGQdSLUBtaUmJTyJiUUejj6obXJTb93FLYor4ekK/J/q8pId/XtJPY9HN76kYaCRSlW1IKEbFqE0t6cgSL4mKKfOwI89zrJEfEsiuj8E1Q4YPSiUlOAWBnel0mNYsr9HEAgzYmUS9C/dmkxMaQMSmi0Me58zVlx8VQ1KMT8n1NsRGx1Cvia0oflE5K7tdUN70uccV8TUkbk9iV+zXFxMYQUcTXtDN8J8n5vqaEYr6mlKQU0nO/pojkCGKK/HvaQsKgZJgUC90XEnvpS9T7s/AtWVZ9TYM3JrOrLiSMhEsHJTD87wRGDcfx6yFmAzuAhcihuEL48gxonhJaIHuEt+URQoiyS4pTB7SfrgB/aVieYcDIBHgk9+TYR1+sy9tPgOED17D/A9wM/KE7iBCaGabpvHMbDMPYCoSaplnk78OGYcSium3nNYQv61jLgWamaRbZqdmOPIZhpEVGRkampaWV9qlClMJq1N5d5/1csMMZoD8wS3cQO5jA2KFw838K7pS3Wc/Z8Nk9UOkkzOgD902Bk/acIGqpWqiZ0Jt1BxF+7HXgaasHKbIucuoMaBao04pceKwdpwx7Wx4hyug24EndIbxWOWAqqiGyzzOA+LEFi8/vb7D9d5M5vdTmpENB0HcmfNEVgg7Zm8EKe4H2wFzdQYTQxKkFaGm4si7TTt6WR4jzvAY01h3Ca1VCFQ1+N3O1MAaabYQn3oYc+xZjxsTGEDQthshVsLsORK2Ar9rBxX/bFsEy2agzqt/UHUQIDZxagOa1OypuR3nebKSrJxm5w9vyCOGGKsAnOPfHg/Wqok5Luk53EDvlBEC5MzDhcXjgY3WGpg0iJkUQMSmC73Mb1v8RBhEZ8M2tcIUPnHdpoi6CPola4iGEv3Dq/zB5Jw4V19Q9LPd94VuXPcvb8gjhpptRnQtFUS4CllL8N71PuXOBuv5d9QhMvU81rc+2dzHmn6Fw6zeQHq5OEv32Frjhe1sjWOZt1GzoMd1BhLCJUwvQ1Nz3xa25DAWyTNO043dkb8sjhAeMBK7WHcKr1QWW5773C1ErIDUKgg/A/B7QbREcqWprhD11VJ/81A5wyd+w+jZo+5WtESwzH7UudI/uIELYwJEFqGmaGai1lNHFPCwKdTyo3+URwjMqoy7F23Op1alCgWWoGVG/0GodrIqEOrthRRT0nWF7hMPVoesXald89cPwZWe1W94XrENdf/hNdxAhLObIAjTXIKBPYTvPDcPohSoIRxf2RMMwkgzDmOXirnVwrc9nmfMI4b2aAcN0h/B61wKLUWtD/cL1P8Ga1nDNz/DS/2mJcLIS9J8G7zymWjTN7AOD39MSxeMyUUXoN7qDCGEhxxagpmnOBmYCBY59yS0AE4HehZ1MZBhGFOp0vV6oo55LEprvdT2epyiGYSQYhmHmvQGR27Ztc/XpQnjQS8D1ukN4vVaoS6gVdQexS6Ot8MMNakY0z/HKtkYwA9Sm/OGvQYAJ7w2BhBH4RBvb/UAH/KTnrPBLjmxEn1/u7GI059obBQOJxa21NAwjPffDDucXhYZhhKIaxoegis/8hWcG6udCUm7B6ZE8rpBG9EKv74HmwGndQbzeXKA34AOH9pTOrF7w7Hh1PbzpFo+9bGyEOuY2/5GjhXl4sjrAqVwOvB8Hj06EHB9ZPTIOeAbHn0QqvI7eRvSOL0D9hRSgQr//A17WHcIRPgQe1h3CTiYQvVytCa31DyztBOHf2R6j+wKY3g8Cs2HOXXDPZ3DC3klZyzwKvIWsyBaeJCchCSEc4XkgQncIR3gIGK87hJ0MYGF36LIY9tZW29S/bm17jIV3QMdlcCAYes5VdXANHzn6YyLQAziqO4gQHiIFqBDCRRVQu+L9ZpWjW54BhusOYacqx2H+ndBnBhyqoSrBJZ1tj7GmDdy2GnbUg8jVasP+Jbtsj2GJFKAt4AOHQAkhBagQojSuAV7RHcIxXgUG6w5hp4qn4PO7YeAkyA6E7gvVtXA3JBgJJBgJpXrOz9epU5O2XAU3/Kga1jf63a0YXmMjasOb51bZCqGHFKBCiFJ6FvVfoCiJAUwA+ukOYqdyOZAcC8+OgyrH4Io/tcT463JovQbWtYArtqmjOyM2aonicduAW4DVmnMI4Q4pQIUQpVQO+BjVqF6UpBxq4UIX3UHsZABjh8JP153bjHSkKowYAbX3QMAZ9X7ECEtPUtpXCzqsgC87wcX/QFpbiFpu2XC2OoBqtzJNdxAhykgKUCFEGVwFjNIdwjEqArOBW3UHsZMBXPY/9fGRqtBkM4x6QW1SMgPU+7Hx0GqtpUXo0WpqJcDUe6HaUXWcfT8fqdpOAnejGk1LPxvhNFKACiHK6Emgje4QjlEFWATcoDuIDi+PhB0N4HSFgrdnB8LWMBj3rKXDn6oI938C//6XWqY67W544i1Lh7TV88AjSJde4SxSgHopOQlJeL8A4CNUaSVcEQwsBRrpDmK3qfdRZDvA7EB1hJHFzAB49t/w3Fj1+VtPwWvD8ZmpwyTgDuCI7iBCuEgKUC9lmmaCaZpG3huwqmHDhrpjCXGeMGCs7hCOUgdYDtTXHcRO+2q6d78HjX8O7v8YTpeD4aNh8kAo5yNTh4uBSMBHuk4JHycFqBDCTY8A7XWHcJSGwDLAvrJLs5r7ynx/SlIKKUkpHo0z5X64YwEcC4SHP4S5d0HgMY8OoU0GqkfFL7qDCFECKUCFEG4KQB0+WU13EEe5GliCn/ypDZkIlY8Xfl+lbHjk3SKfmh6bTnpsuscjLe4K7VfCvhDongLLOsJF+z0+jBZ/oTa8faU7iBDFkAJUCOEBl6POFRal0RxYCFTSHcRqz42HsK0XFqEVs6HRH+p+Dda1Ur1C/7oUWn8Dq2+D+tu1RPG4g0An4FPdQYQoghSgQggPGQjYf/Si07UDZqD6hfqsakdhbSsYmliwD+jzY9Tt1Y7C6jZqYeZ5IpIjiEiOsCzalqZw6zfwy9Vw7S/q1KQmmy0bzlangAHAa/jMXivhQ6QAFUJ4iAFMAmroDuI4dwAf6A5htWpHYeRI2FMHzpRX70eOVLd/3h/apsGAqRcUoTFxMcTExVgabful0OZr+OYW1bp0TWtoudbSIW31IhCLKkiF8BZSgAohPKgB4EMNFm10P/Cm7hC6NNwG1Y7A9P6FFqF2OBAC0cshpRvU3A8r20OXxbbHsMxkIAY4rDuIELmkABVCeNh9qP/qRGk9CTynO4QOt/wHlnaCoENai9DjVaDHPPjwQahyHBZ2hwFTbI9hmaWooyN26A4iBFKACiE8zgCSgRDdQRxpDNBHdwgdbl5bsAi991MtReiZ8vDwBzD6eSh/RrVsekbPHilL/IBq0/ST7iDC70kBKoSwwCXABN0hHCkA+AQ/Ozc+T/4idEY/eHSinhyGalL/1Bvq0/HPqdNCjRw9cTxtO9AaWKE7iPBrUoB6KTmKUzhfP6Cn7hCOVBlYAFypO4gON69VTTkb/glxSVqjvPUU3P0ZnKygjvH85H4o7yM7eQ6helZ8ojuI8FtSgHopOYpTOJ8BvAfU1h3EkWqiGtX75Z9eq3Xw61UQ/t252zT1EZp2N3RbBEeqwoBP1brQKkf1ZPG008ADwEikTZOwnxSgQggL1UYVoaIsQoEUIFB3EB0qqqnGBDOBhCl/QP9pcKq8lijLO0K7r+CfWtDlS7VDvuZeLVEskQA8BJzUnEP4FylAhRAW6wn01x3CsVoC01DzyX4pqwY8+ZZaE3r359qK0I3NVcP6bZdDy/WqV+hl/9USxRIfA11RJygJYQcpQIUQNpiA2pgkyuIO/Li7avBB+LIz1MiC2b21zoT+fiXc8i38cD00+RW+uRWu+VlLFEukoto0+chppMLLSQEqhLBBCKo1kyirx4F/6Q6hQWxELLGP3KQ2JtXIgjm9tBahu+pB5CpYdRs02AFft4Fb12iJYomfULPuP+gOInyeFKBCCJvEoM77EWU1Dv/rK1Avox71MupBiw2wPPpcEdpvurYi9GAwdFoKc3vARVkqVsxCLVEssRM1E7pMdxDh06QAFULY6E2gvu4QjhUATAVu1h1El+YbzxWhaW1hW0NtUU5Uht6zICkWArNh3p0wvzvsqQ1nAtT7ESOg6hFtEd1yGLgd+FB3EOGzpAAVQtgoGPhAdwhHCwQWAo10B9Gl+UZIjVJvjf/QGiWnHAx+H0bHQzkT7kiB2nshwFTv48fC2lbOLULPAA8DLyFtmoTnSQEqhLBZJyBWdwhHq4XqEVpLdxBdmqXDTd+f+zy1g+oWr4MBJyoVPnxgNoRthWfH2R/Lk15FLZ6RNk3Ck6QAFUJoMB64XHcIR2uE6hFaWXcQ3T69BzouU2tCNRWhj757tm3pBQKzYYgPtMKdijo5KUt3EOEzpAAVQmgQBHykO4TjtQI+w497hAJcvQmCs2DeXdB3hpYitOY+9+53iq9QZ8j/pTuI8AlSgHopOQte+L52wGO6QzjeXcAbukNYKH1QOumD0ot+QPh3aj3oRfthfg/oM9P2InRfTffud5JfUG2avivpgUKUQApQLyVnwQv/MAYI0x3C8Z7MffNFKckppCSnFP+g/EXogjttL0InDoHjxayF+CMMn9rFsxtoC3yjOYdwNilAhRAaVUUdAujXF5E94t9AD90hdDq/CB38vm1Dj38OtoZdWISeqAg5wC1rYfQwfKoIPQR0RJ2eJERZSAEqhNCsNfC07hCOVw74FLUu1JfUTa9L3fS6rj04/DtY0QGu/FWdH2+To9Wg1VpIHFqwD+jo588dX/98Irzysm2RbHEMdX58CfPTQhTKME0f+pXMhxmGkRYZGRmZlpamO4oQFjgO3AT8qjuI4/2DalS/VXcQD0kwEtR7M8H1J50uB+XPnPvcROske8/ZML2fivTySPg/HytEy6N2yffTHUSU0uvY8Mt/kd95MgMqhPACgcAnyI8k99UGFgM+tO+l9PIXnx8+CHfOV9fDNZnTC+79VM2MvjICho3SFsUSp4G7kSMmROnIT3shhJdoCQzVHcInXIk6LamS7iC6HawO8Ymw8A7oOUdrETqjH9z/CeQYMOoF5zenP58JDATsW/ggnE4KUCGEF0kArtEdwifcgloT6tfbu2ocUmfHh+yDL7ppL0I/uxce+lAVoeOGwlM+2D/rKeA1fGq/lbCIFKBCCC9SCXUpvpzuID6hF+rMKb924w+wsj3U3OsVRegnD0Bssvr4jX/BoxO0RbHMi4CPbfoXFpACVAjhZSKAF3SH8BlPI+3+ueFHtTs+rwi9a67WIvSDgfDIu+rjCY9DnH0do2yTCDyOakMlRGGkABVCeKEXgBt1h/AJBvAm0F13EN3yF6HrW8Bfl2mN8/4j8Pjb5z5+eLLWOJaYCDyM2qQkxPnK6w4ghBAXqoi6FN8MOKU5i/OVA6ahDj9drzlLaSVtTPLci93wo7ocD9D4D8+9bhlNeBzKn1aX4pNj4VQFmHK/7lSe9TFwFLUeWd+cs/BGMgMqhPBS1wMjdIfwGVVQDcOv0B2klHZF7GJXxC7PveD1P6m3PIu7QLa+fgFvPg1DEyHAhI8ehLs/0xbFMrNQp3Qd1x1EeBUpQIUQXiweNQsqPOFiYAkQojuIt5gyALouhh7ztBah44bCC6+qInTKfdBnhrYollmMOjXpsO4gwmtIASqE8GLlUZfi/b6jpcdcBSzAOX+iMbExxMTGWPPiN30Htf6BL7toL0JHvQAJI6BcDnx2jzo9ydd8hTo//oDuIMIryBpQJ8k6DKs2uv74alUg4upzn+c9NzLfjFL6JjhyrHQ5Cnt+eFMIqqpu+20b7Npbutcs7PmNL4d6tdVtO/+B3/9butcs7Pl1a8GVDdVth49CxubSvWZhzy/qz9lV8vdUwt/T5ZCxpnSvWXceXJl73MzhJpAxFapthoj7zj1m1YbSvWZRz49sfu629ClwpGnpXrew54cPgKAt6rbfhsOuHqV7zcKe33gU1JsHQOudPcj+fXipXjK28Sgm5T5/0M4eJP8+nOS684jL/XMOP9yE9IyppXrNwp6fXm0zzfL9OUdMigBg4T2unV95/vPN3L8nI9+f88b0KUTk/T3N/i/wX6A2rCv631lhz48IH0BG7p9z0m/DiS3l39MFz2/Xgy/qjKLrkHlM6w+9Kqge+r5kLdAeWIqakRf+S2ZAvZRhGAmGYZh5b0Ck7kxCCCGsteAOSBwKFVI3sCB4A10X6U7ked+j/kPboTuI0MowTWkV6wSGYaRFRkZGpqWl6Y4ihCa/oVozyVYGTzFRPULf1R2kGAlGgnpvJlg70M/XQPuV8M/FcM+n8OkAa8crjgnmajVze6Jjc+5YAEs764tjlSuAFThvY5zveB3VKdhSRR7GJjOgQgiHuBIYozuETzFQZ3d30x3EG1z7C3zVDq75GZ7X/O8s33/ZlU7C/DuhQ6q+OFb5E2gDbNEdRGghBagQwkEeQ60gE55SHpiOOn/K712zCX68XhWjeXKKnMCxxXuDofIJSImBtl9pjWKJHcBtqMvywr9IASqEcJAA4COguu4gPqUqsAhoqDmHVwjItywteRB0WQLHK2uL8+hEmDQQArNhUTdos1pbFMv8gzokYa3uIMJWUoAKIRzmMuBt3SF8ziWoXo3BuoOcZ2f4TnaG77R/4ENBMGIkLOsE3RfaXoSmV9tMerXNmAEQlwQfPQBVj8Hi2+Hmb22NYossIArVqkn4B9mE5BCyCUmI/EzgLmC+7iA+ZzUQDZzUHcQbbGqqNib9fQlELVdb1Kvo2QQXcAY+fgAGfKpq4+jlsL6lliiWqgzMAW7XHcQvyCYkIYQoJQNIAmrrDuJzbkOd3y2AqzerjUl1dkNqtJoJPRaoJUpOOXjwI5jWD6ofhmUdIaKULYedIBu4E3V8p/BtUoAKIRzqYmCS7hA+qT8wWncIb9F0y7kidEUUxKRoK0LPlIcBU2F2T6hxCJZHw43faYliqVNAP+QXIV8nBagQwsHuAB7QHcInxQNxukOg+oDm9QLVpukWSGuritCfr4Ud9S0f0ly14ewpTvmdKQ/9p8H8O+CiLEiNgut+tDyO7XKAB4GJuoMIy0gBKoRwuDdRG5OEJxnABGQt3llNflVF6Mr20PgPrVFOV4A+MyGlG9TcDys6wNW/lPw8J3oMSNQdQlhCClAhhMPVQLVmEp5WHpgBhOsO4i2a/Kp6heZZ0B2OVrFkKCOyeYHz5893qiL0mg1LOkPtvaoubrLZkijaPQ+8iNp6KHyHFKBCCB/QHnhSdwifVA3VI1TmmM/z8f1w5wK1JtSiIrQkJyvBXXNheRTU2ZM7OfubliiWew21X1uKUN8hBagQwkeMBproDuGT6gJLUHPNItfN/4G6O+Gr9tBtkbYiNDsQ7lgAK9tB3d2qCA3dqiWK5d4CBgFndAcRHiEFqBDCRwQCU4ByuoP4pKuBeUAF3UG8xVW/qd3xdXdCWjvovASGvwq196imnbX3wIgRcKRqmV5+Y/oUNqZPcemxx6uoidjVbaDBDhWr4Z9lGtbrfQDci9opL5xNClAhhA9pDrygO4TPaoesti3gqt9yd8fvgjW3QeLzsLc2mAHq/dh4aLW2TEVoxJGmRBxp6vLjj1WFrl/AN7fAZf9TM6GX/lXqYR1hOtAT1TNUOJcUoEIIH/Mism3GOveg1uPZJSUphZSkFBtHLKUrf1e7gchR3eLzyw6ErWEw7llbohwJUkfXr20JV2xTM6H1t9sytO1SgG7AUd1BRJlJASqE8DEVgKlAJd1BfNYwYKBNY6XHppMem27TaGU0ox9F/neaHQjvDbEtyuHq0PlL2NAMwjLPrRLwRSuATsBB3UFEmUgB6qUMw0gwDMPMewMit23bpjuWEA5xNXKWj3UM4F2gs+4g3mJfTffu97CDwdBpKXx3o2pZurK96qHvi75B9cDYqzuIKDUpQL2UaZoJpmkaeW/AqoYNG+qOJYSDPAlE6g7hsyoAM4EbLR4nIjmCiOQIi0dxU8197t1vgQMhEJUKP16n2peu6KD2RfmiDNR3uo9O9PosKUCFED4qAHWadDXNOXxXEPAFcKmFY8TExRATF2PhCB4wZCJUPl74feVPwSPv2psn1/6a0GEF/HyN6p+fGgU1fXSqcBNwG/Bf3UGEy6QAFUL4sIao7oHCKvWAxUB13UF0em48hG0tpAg11bmZdf7WEgvUZvwOK2BzE7j+J1geDRft1xbHUluB1oCP9uL3OVKACiF83IOAl8+gOdy1wFzU0Z1+qdpRWNsKhiYW7AN6+xfq/ifeUWdmarKnDrRfCb81hpu+h2UdoUaWtjiW2o6aCf1RdxBRIilAhRA+zgAmAbV0B/FpHVBNwv1WtaMwcqSq9s6UV++/iIFho9TnvWbDRn1rWXfXVUXo1lBolg5LO0F1H90+/jfQFlivOYconhSgQgg/UAd4X3cIn3cf8IruEN7mtRfgvk9Up/gHP4IcQ1uUHQ2g3VfwZ0NouR6WdIFqh7XFsdQB1C9Fq3UHEUWSAlQI4Sd6og7xE1Z6EXhIdwhvYgCTBsGgZJjXAwJMrXH+d5kqQv97GdzyH1h8O1Q9ojWSZY6gWoUt1R1EFEoKUCGEH3kHqK87hE8zUHPN0bqDeJOKpyA5DhptPXebxpnQ/zZUl+O314c2ayAlBgKPaYtjqeOoFeBzdQcRF5ACVAjhR4KR08ytVwGYDVzvgddKMBNIMBM88Epe5PWn4a65cLpckQ8xIptjRDa3LEJmmJoJ3VkX2qXBwu5Fd5JyulNAH+BT3UFEAVKACiH8TDTwqO4QPq86qkeozDef5++L4dUXYcGd8NgE0HhF/o/GaiZ0dx2IWqFWCFTK1pfHSmdQa5STdAcRZ0kBKoTwQ4lAY90hfF4DVI/QIN1BvEmdPeqad+XjkDQYRg3XGufXJqpP6J7a0HkpzO4FFU9ojWQZExgM/Ft3EAFIASqE8EtVgSnIj0DrXQ/Moew9QmMjYomNiPVgIi9w67fw+d1g5MCLr8HH91/wkI3pU9iYPsWWOJuuUcd27q0J3b6AGX2hwklbhtbiWSABrZPPAvnpK4TwW62AYbpD+IVoVCfWsqiXUY96GfU8Gcc79JgPb3kYlCoAACAASURBVD+hPh40CZZ2LHB3xJGmRBxpalucn65XRej+i+DOBTCtvzpF1FeNRBWiUoTqIwWoEMKPvQzcqDuEX3gAGKE7hLd5bCLEj1HHdT7xdoFNSRHhA4gIH2BrnB9uhOjlkFUDes6FT++FcqdtjWCr14FHgBzdQfyU356cJoQQUBGYCkQAPnzN0UuMQJ3XLbuR8xk1HMqfVrOg5c+cvTkjaIuWOBkR0GmpOjO+70w4XR7umwI5RW/Yd7QkVL/Qj5GCyG4yAyqE8HPXAq/qDuEXDCAZsK65kAMFmPDqS3D5X+duO1lBXx5gfUvo/CUcrgb3fA4fPqSOt/dVnwG9AR/de+W1pAAVQgj+BbTWHcIvBALzgLq6g3gjE/i/F6HdVyRteomk3/TtkP/PLXD7YjhaBe6fAsmxas+Ur5oPdAd8tB+/V5ICVAghKAd8gtodL6xWH1WEVtIdxNtkBcPkgfDtrcT+053YXT20xlnTBrp+AccC4eEPIXkQjBihWjadCVDvR4zwnaM8l6GO7jykO4ifkAJUCCEACEVtSxB2aIm6HF+S9EHppA9KtzqOd7goC5Z0geAD527TvE17VVvovhCOV4KBH6quUbX3qpUDtfdC/FhY28p3itCvgShgn+4gfkAKUCGEOGsQ0EV3CL9xH2rxQ3FSklNISU6xI453uHqzOhczT2K8viy5VkTBnJ6qFi5/3lrQwGwI2wrPjtMSzRIbgHbAP7qD+DgpQIUQ4iwD+AAI0R3EbyQCnXSH8DZt1pz7eNgYmHqvviy5Oi1T3x2FCcyGIe/ZGsdyPwEdgL26g/gwKUCFEKKAuoCP/W/qxcoD0yj6YNS66XWpm+7nW5ZeeVn7zviaJVyTLul+J8orQn3wS/MKUoAKIcQF+gD9dYfwGxcBC4HqhdwX1yyOuGZxNifyIm89Aatvg4p6jyXaV9O9+53qR9Sa0P26g/ggKUC9lGEYCYZhmHlvQOS2bdt0xxLCj0xAmgXZpwlqJrSoy7x+64l3oO7uc58f0dOpYeIQOF658PtOVoB3H7E3j52+R4pQK0gB6qVM00wwTdPIewNWNWzYUHcsIfxICPCh7hB+5XZgjO4Q3irHgOdHQ/MN6sB2m41/DraGFV6EVjgFf11meyRbfQd0BA6U9EDhMilAhRCiSJ2BwbpD+JXngHt0h/BGx6rA4tthS9PcvkhFTEda5Gg1aLUWEocW7AOa2j73hKs4uHOerZFsl47aMJelO4iPkAJUCCGKNQ4I0x3CbxjAJKCZ7iDeptpRVYA2+B980xru/VRVgTY6Wg1GjoQ6e1Q7pjp7IHoFvDZcfT69H3Rcamsk221AFaEHdQfxAVKACiFEsaqhTkmSH5d2yTuu8xLdQbxNgx3wZWfVqH5uT3jqTe2N6gFefFXtlap0Eub1gDardSey1nrkxCRPkJ+oQghRoltRF4eFXRqgilBxnms2wfw7oeIJmPA4jPOCf5cGPP0GfPAQVDkOi7pBsw26Q1lrLaoIPaw7iINJASqEEC4ZCVynO4RfaQVcsjGJpI1JuqPYLiJ8ABHhAwq/M3I1TM2974OH1WHtmpkBEJsM0/tC9cOwtBNc96PuVNb6D+rcNClCy0YKUCGEcEklYCqgtyG4v4mL2EW/iF26Y9guI2gLGUFbin5An1kwrR+saa2mHb1ATjkYMBUWxkDIAVgeDY1/053KWt+gujcc0R3EgaQAFUIIl90AvKI7hN8ZC0TrDuGN+s2A2rmHRZrAP7W0xgE4XQH6zITUDmqT0ooOcPk23amstQboChzVHcRhpAAVQohSeQ64WXcIv5ESG8OS2BhmAI10h7FR0m/DSfptuGsPPhOgNiTd+D38dam1wVxwojLcsQDW3AqXbofUKKi7U3cqa60GuiFFaGlIASqEEKVSDrUrvoruIH4hY1IEGZMizh7XGaQ7kE1id/UgdlcP1x58ujz8cAPsrA+dv4QDwdaGc8GxqtD1C0gPh0Zb1eX4Wv/oTmWtNCAGOKY5h1NIASqEEKXWGBivO4TfaQp8jn8c1xnbeBSxjUe59uBKJ9XO+Gt+hs1Xq+nH7ErWBnTBoRrQaSn8crXavL+0E9Tw8S7uXwHdAe9YlevdpAAVQogyGYxqSS3s1A1wsSxztEn15jGpXikaUQUfhCVdoP52+Po2uG+KOr5Ts321ICoV/giD8O/gi65Q1cd37KwA7kCK0JJIASqEEGViAB8A+i93+pt4oL/uEN7o0u2qCK1+EGb1gX+97hWN6nfXhQ4r1PLUW7+FBXdApWzdqay1HLgT8PEv0y1SgAohRJnVBybqDuF3DGAyEKE7iIUG7ezBoJ0urgHN77qf1eX4CifVwsvD3rFq9q/LVRG6uw50WAmzekP5U7pTWWsZ0AMpQosiBagQQrilP9Bbdwi/UwWYD9TRHcQiyb8PJ/l3F3fBn69dmjqOaE1r1RXeS/zRWF2O3xcCMYvg03sh4IzuVNb6EugJnNAdxAtJASqEEG4xgHeRk8utUTd8J3XDC+/h0wCYC1S0NZFDdFwOF+Xu+DGBzCu0xsnzy7VqY9KhIOg7EyYPBCNHdyprLQZ6IUXo+aQAFUIIt9VCXRQWnhabnkxsenKR998CvGdfHOc5XU6dkXnTd/DTtbrTAJDeDG5frE4QffBjeOtJvGKtqpUWAX2Ak7qDeBEpQIUQwiO6AgN1h/BLDwFP6g7hrQJyICtY9UTqsgT+10B3IgC+aa26RZ2oCI9PgNde0J3IeguRIjQ/KUCFEMJjXgca6g7hl8YDUbpDeKMAE6YOgDarYUcDVYRm1dCdCoDUaHVs5+lyMHw0DPOD/loLgH6Aj++/cokUoEII4TFBqFOS9Pdf9BUjjQRGGgklPq48MAMIszqQE1U+oXbGN92kFmHeOV9NPXqBhXfAgKmqZemoF+CJt3Qnst481NZFfy9CpQAVQgiPug14RncIvxSCmmHyjsZDXibkAHzZGertgFVtvaZRPcD0/mqZKsBbT8FDH+jNY4c5wD3Aad1BNJICVAghPO7/gGt0h/BL1wCfIXPQhbrsf7D4dgg6BL83hoPecSke4IOB8NQb6uNJg6DvdL157DALuBf/LUKlABVCCI+rDExFXRgWdosBXtUdwlvd8COs6ACrIs+1afISbz0F/9/evcdHVZ37H/8sLnIRawDRQr2GVtvzsl6SYLW1gjWhVVGrAlqttyqJqLWWKgGtBeoFg9ZLq4UEW61WrYLiBfUo8RSOHus5MCm/X1/W82sb6uVUWhWMhyqIwPr9sfaGYZiZTEhmr71nvu/Xa5yY2bP3szNh8sza63nWNddvm7Z60pO+Iyq+h4FzKc8kVAmoiEhRHA7M8B1E2ZoOnOE7iLgatQJ2CxZk32Lg/xziN540N14NNzVC301utaTjWn1HVHwPAecDJd6TfwdKQEVEimYacITvIMqSAX6J+xggOWzq7eaCHvFfsOwY39E4BqbPhjsvhX4b3brxX3nJd1DF9wBwAeWVhCoBFREpmj7AfcAA34GUpYG4oqQ9fQcSV703Q0UHbOznKuNf/RffETkGLv8p3HM+7PoRPH0iVKV8B1V89wMXUj5JqCYoiYgU1UFAE3C570ASaVzzU916/j645TqPJVltb+o/F0FTTINbhujtEbDoNPjGv8LvjoK9/1b8Y3fC9oKL7oZdP4SJC+D5sTB6mesiVcp+hRsZvJvSHyE01pb4+lclwhizdPTo0aOXLl3qOxQR6bItwFjgBd+BlK1foHWqclrfH2pb4eWvwBf/L7z4Vdj9f31HBUDfjfDYaTDuaVj9aTjm3+Evn/MdVfFdCLRQ7CT0VuD7RT0CeRpSlHqCLSISA72Ae4D4tL0pNxcC3/UdRFwN2ABPngwH/Tf84RA4dVFsGtV/sgtMWAAvfA2G/x1aa2GfN31HVXy/AC7GfXQtVUpARUQisQ/wM99BJE6qpZpUS3WP7OsnwNd6ZE/FN+ntU5n09qnRHXDoWteo/tOrYf0A+GhgdMfuxIYBbt34l4+C/d50XaQ+vdp3VMU3H7iE0k1ClYCKiETm28BpvoNIlMUNJ7G44aQe2Vdf4BGgskf2Vlwtf76alj9fHe1B938Dlo5xGV7MeoR+OAhOeAZ+fxh87i+wpA6GrPEdVfE1A5cBpThZUgmoiEhkDDAP1WX7MxRXGT/IdyCdaBm+iJbhi6I/8EF/goHr3debe8HS0dHHkMMHFTD2efjjF+DgV+G5r8OnPvAdVfHNxZUwlloSqgRURCRSw3DlBeLLwcCvfQfRiYYDb6ThwAgq4XPZYuCMh+Fr/waPxmfU/r1hrl6qvRJqUrB4HAz80HdUxXcncAWllYQqAY0pY8xMY4wNb8Do119/3XdYItIjTsG1nRZfTgGu8x1EnPWyUJ1y/ZDOfgBePNp3RFutHgHHvQBv7Q1ffQkWnQr9NviOqvh+CkyhdJJQJaAxZa2daa014Q1Ytv/++/sOS0R6zO3Afr6DKGvXABN8B5FD1brPU7Xu836DmHYTTP45fNzfVQG95jmeNG/s70ZC/7EnjF0CvzkT+iSp0etOuh24ktJIQpWAioh48SngXt9BlDWDa451mO9Aski13U+q7X6/QRjgZ9+FUx6H94fA2Odgyi0w7B3otdndz5gB/9zVS3h/OgjqlsDawfDNJ+BX57mwSt2twFSSn4QqARUR8WYMbmaX+LIrrihpmO9A4qr3FnjwLDjiFfiffeH277uJmLaXu5/TCEe+4i0J/cMhbgGndYPgrIdg3sUkPzMrwC3AdJJ9qkpARUS8uhGIz6XNuJlhZzLDzizqMfYFHsW1aZIsBq53SxCZLS7xTLdhALSPhJuv9BMbsPwIOPFp+GgATLobbvs+yc7MCtSEm0aS1FNVAioi4tUA4H6gt+9AytpXgbt8BxFn916wY/IZ2jAA5l4SbTwZXjzGLeC0sS9ccQf8+Edew4nMbOBakpmEKgEVEfGuBvdnRHyaBFzqO4i4WjO0e49H4Pmvu85Rm3rDtdfD1CbfEUXjBmCm7yB2ghJQEZFYuBromSUnS0lLdT0t1fWRHe824NjIjpYgQztZdqizxyPy+Klw/r2ujWnTNLikTIa1fwzM8h1EFykBFRGJhb64qni9Ladb3TaC1W0jIjteuFznAZEdMSEuuQv6r8/+2C4fu3ZNMfHAt+Hiee7ruy6D8+71Gk5kZgLX+w6iC/ROJyISGwcD5/gOouztgauM91PXHVNX3QIj27MnoZ/0dSsmxcj8epjyE/f1Ly6E8Qv8xhOVa3FljUmgBFREJFZmonps/76IKw2TwKAP4ZUj3cTK9D6gh/7eFSdNWOjWx4yR26bAj2Zt6yR1wtO+I4rGNcBNvoMogBJQEZFY2R+42HcQApxK8ubVFdWgD2HWLHhnL9jcx90vP8I1qH93Tzj+WXjPfzFSuuuudR2i+m6CR0+HY+M1UFs004GbfQfRCSWgIiKxcw26ABwPPwTG+w4izvpuggUT4LDfu0v0/T72HdH2DEydA3Mvhv4fw5Mnw5G/8x1UNKYCP/EdRB5KQEVEYmcvtEJSPPTClYYd6jmOWPvUOlhS57K73f7pO5odGbj0LrjvHDeI++zxLl8uB1fiOjvEkRJQEZFYuhIY7DsI76ompaialPIaQ7hc5x4RHrNl+CJahi+K8IjdtMcaNxoK8PEu8OuzY9Ud3faC7/wSFp4OFR/A82PhC3/0HVU0pgB3+A4iiz6+AxARkWwqgGlAo+9AvDqp5SnfIQCwH265zuOATREcr+HApNQyZ7DANx+Hfz0e3tkTpsRn/G1zHzjrQRj4TTjhWWitha++CKtG+o6s+K7ArbV2me9A0mgEVEQkti4DhvsOQgLHAHf6DiLuDHDer9zXP7gVHpngNZxMn+wCpz8Kvx0DI1bDC8fB3m/5jioa3yVey80qARURia2BQJksap3D26nhvJ2KTxLeAEyO4DhV6z5P1brPR3CkIjjzYWia6r4+53548Wi/8WTYMABOfhJe+RLs/4YbCd3zH76jisZlwDzfQQSUgIqIxNqFQBlcI8xhfk0D82safIexnTuA0UU+RqrtflJtCe5EetXNcOmdsLEfnPIEvBavZPqfu7muUSsPhYP+5GqoBq/1HVU0JgMtvoNACaiISMz1xa30LHHRF1iA69haLKlBr5Ea9FoRj1BkBrjje3DK4/D+EJft/X0v31Ftp2MwjH0e/vsgOOQP8NxYuHEavDMMNvdy9zNmwK4xLOzvrgbgJVZ5jUEJqIhI7J0JHOI7CEkzjOIu11lTfS411ecWae8RCZcg+tIrUNUGu3/gO6IdvLsn1LbC6/vCqBRMvRmGvQe9rLtvnOMWgCrFJHQ5fie/KgEVEYm9XsANvoOQDIcA9/kOIu4Grofnvu6a1Q/Y4DuarP62NzxxCmzB5czpBmxw/fWvjPuyQgmkBFREJBFOBL7sOwjJcBow03cQcbf7/27L7Nb3h3kNseoRCnDWQ7kTogEb4JK5kYZTFpSAiogkggFm+w5CsrgWOL2H92mXLccuW97De/XM4srPJ89zi7THyNA13Xtcuk4JqIhIYhwDfMN3EJIhXK5Ts3Q7YYDv/gx6bYYZP4Z7zvcd0VZrhnbvcek6JaAiIomS0BVydtKkFc1MWtHsO4xODQIeB5SndOLkp+DOYD2e+hZ4vs5vPIG7LnGzA7LZ2Bd+HkXz1zKjBFREJFEOByb6DiIyI6pXM6J6te8wCnIAsBC35KHkMXkeNN4Em/q6ZYlWHuo7Im65CtpHZk9C+3ziKuGlZykBFRFJnOtQmhNPY4D4rH4eYzdeDWc94DrCn/AM/M9nvIbz4SA48hW3gFN6H9D/PMIlSg+dBV/4o9cQS44SUBGRxDkQuMB3EJF4qv4knqo/yXcYXXIZcL7vIOKul4VffgfG/BbGLIVh7/qOiA8HwaxZsNc70Gezu//yy/DYqTC4A549Hoa/7TvK0qEEVEQkkWYA/XwHUXRt86tpm1/tO4wuMcBcYJTvQOKu30ZYPA5+/W33dQxt6Q1nPwC/OxL2exOePhEGrfMdVWlQAioikkh7A5f6DkJy6A88BuzpO5C42/UjNxoKsG4Q3PID2GL8xpRhwwDXPerPn4XDV7qe+n0+8R1V8ikBFRFJrOnAbr6DkBz2Bh4F+vgOJAnCHqFX3QLTbvIdzQ7eG+aWs393D/jGczDvYmLXTD9plICKiCTWHsAPfAcheRwN/Mx3EElggKtvdEOLN0+FO+M3ut/+WRi3GD4aABf+Eq69zndEyaYEVEQk0abgElGJqwZgku8gkqCuFe6+yH19+U/h8VP8xpPFf30JvvWQq5L/8Qw4717fESWXElARkUTbDbjadxCSh8GNgh7lO5AkOO8+uO6HYHu5TO+VL/mOaAdPnuLyY4D5k6Dueb/xJJUSUBGRxJsM7OM7iKIYXvU2w6uS3/umH65J/fACt08Neo3UoNeKGFGMXXMDXDTfVf+c9BS8sa/viHbw80thzlXQdxM8ejocutJ3RMmjudEiIonXH9eW6SLfgfS4+lSL7xB6zAhcZfxooLOmQzXV5xY/oLgywNzJ8PYIGL4aRsTzA8i0m2Cft+Bbv4FnTnCN7N+KX64cWxoBFREpCecBB/kOQjpxJHCX7yCSoM9meOw0d4277ybf0WRle8H598LS0TBitUtCd+/wHVVyKAEVESkJfXBLdErcXYSbNCGd6LfRjYYCdOwOM2fApngtQbuxH5y6CF79Fzj4VVh0Kuzyse+okkEJqIhIyTgdqPIdRI+aZWYyy8z0HUaPux3XoikXu2w5dtnyqMKJNwuc8gTMmumqf2LWf7NjsFvOfvWn4dilboVRs8V3VPGnBFREpGT0Am70HYQUYBdcUdJnfAeSBAa44RrotwHmXgJzpvqOaAdv7ueS0HWD4OwHXbiSnxJQEZGSMhZX5iJxtxewCFchn8mMHoUZrdXktzr6P9ya8WYLTGuCB7/lO6IdrDwcxi90swSm3wQN83xHFG9KQEVESooBZvsOQgo0CiidOv8iG/8o3DrFfX3+vfDbMT6jyer5r0N98ILedSmMe8pvPHGmBFREpOQcBZzkOwgp0LnA5b6DSIor7oArboNPdoFvPg6rDvAd0Q7u+Q7M+hH03gK/ORNqNJU3KyWgIiIl6Qa2lRBL3N0CjEn7/xWp+1iRus9TNDH3kx/A6Qvh3Ptgvzd8R5PVzJlwz/mw60eweBwcsMp3RPGjRvQiIiXpi8BZwAO+A5EC9AUeAWqAN4Hqf37Bb0Bx1su6ocXem+P7Gcu4S/Gf+RuMXQLPHg9ffhnWDvUdWHxoBFREpGTNIunjDOOan2Jcc3lMpBsGPA4M8B1IEvRJSz7fGwpX3gwb+3oNKdOmvq4oaeWhcNCf4MmTof9631HFR7LfmQBjzHigDmgHhgIVQJO1tlsD3t3drzGmAnjBWlvdnThERHbeSGASMNd3IDutuj7lO4RIHQ7c7TuIJLHAaY/Bi8fAu8Pg3vNjNSq67lNw4tPwypHwlZfh/nPgjIdhS7z66XuR6ATUGNMMYK1tSPteBZAyxjRYa1uj3m+wXT0wfWeOLSLSs64F7gU09JIUZ/kOIEkMrjJ+9DK47zzY90247ke+o9rO25+B45+Fl452hfy3XAlTbvMdlX+JvQQfjFBOTE8SAay1HUADsCBIBiPZrzGm1hiTAuYDbYCmHItIDAwnyTXWqZZqUi26kCR51KTgkYnQazNcfy3Mv8h3RDt49WC3ZOfGvvD92+F7t/uOyL/EJqBAEznapwUjlGvZuVHIndqvtbbVWlttrZ2Qtp2ISAw0Arv7DmKnLG44icUN5dtSKn5NhmLqxGdg7mT39eS58MzxfuPJYumxcME97utbp8Bpj/qNx7dEJqDGmCqgEsjXXasNdync+35FRPwaDMRv+ULp3OPAQN9BJEX9fLjmetjcByYsgL+M9B3RDh48G6bf6Ar5HzgbvvwfviPyJ5EJKFAb3Oe7zL0KqDDGVMZgvyIinn0Pt/ijJMkhwD2+g0iS666Fc38Fl/8UKuM5E+6maTCvAfp/7CrjD/x/viPyI6kJaLhAbr7frjXBfVUM9isi4tmuwA99ByE7YSIwzXcQSWGAey6A2Ve7YcY4MnDZnfDUOBi61vUI3fMfvoOKXlIT0EKKizqC+yEx2K+ISAzUA/v7DkJ2wvXAN3wHkRTpieff94LJP4f1/f3Fk8XmPnDmb2B5DVT+1a2WNPBD31FFK6kJ6BDYWpnema5UwhdrvyIiMbALrjm9JE1v4EHgs74DSRILTHwE5k2Gc+6HLTFqEAp8tCuMW+yWsx+1IljcaZPvqKKT1D6gXUn+urLwVbH2m5cxZmkBmx21cuVKxowZ01OHFZGyZHFlLR/5DqQgrwczIH87xm8ckesIOgFm/FWqwI0cbYk6nqRafzz0Phwe7QP7VsJn231HtJ13gIP3gMPfgr6LoXJf+POB0Rz7Ll7iCcYU9RjLli273Vp7RbbHkpqAlqONH3zwwbvLli37SxGPcVhwv7KIx5B40mtfvmL+2r/h/rvMcxiRa4viIDF/7XvCR0BQav634BYz64GXw/9ZHdyK6zCAdtasbMffP6ykJqAd4FYdKuBy+ZpOHo9iv3lZa8f01L66IxyJjUs8Eh299uVLr3350mtfnuLyuid1DmhXFDKfM077FRERESlpSU1AwzZJ+SrRw5kzXVmRqFj7FREREZFAUhPQcKWifM3gwyUQujKRplj7FREREZFAUhPQ1uA+X9V6JdBhre3KUgjF2q+IiIiIBBKZgFpr23BzMOvybFYLtMRhvyIiIiKyTSIT0MAkYKIxZofRSmPMeFwiOTvbE40xzcaYBdme2539ZqFm9SIiIiIZEpuAWmsXAo8A89O/HySOTcCEbK2UjDG1uPXoxuOW2O2R/WZRmfY8EREREQkktQ8oANbaBmPMeGNMM9vaIlUAdbnmaFprW40xYQHRIz21X2NMJdCMq6CvZNvo5/vB8dYCzUGCKyIiIlK2jLXWdwwiIiIiUkYSewleRERERJJJCaiIiIiIREoJqIiIiIhEKtFFSNIzgvZSdUA7MBRXQNWkZvvlI+jW8IK1ttp3LBINY0wTUMW2ld/agNlBP2QpYcaYqcCo4H/Dgtkma21rjqdICTPGpHy89ysBLXNBpT/W2oa071UAKWNMg96QSlvwWtcD033HItEIXvP5uGSzMe17Tbh/9y3p7wdSOjJe+zlp368FlhhjFlprJ3gLUCIXfBip8nFsXYIvY8HI58TMPzZBn9MGIFezfkk4Y0ytMSaF+2PUBmi0u3zMBxrTRzqttR3B+0ALUG+MqfcWnRTTfGvthMxR7mCgYQ4wXq99+QjaR3obfFACWt6ayLGsaPCGtBaNjJUka22rtbY6+GMUvtZS4owxVcDyPNNrGoP7Zn34LC3B6zneGLMkxybh9zUCWj4aAG9XOZWAlqngD1ElsDzPZm24y7MiUhrOAHIuhhFc/QhHx2ojiUiiMiS4r8nxePghtDLH41JCgiugD+Nx8EEJaPkK/7jku/S6CqgIhulFJPmqcPM8x+fZJnxPGJJnG0mYYNR7JHBAjk3Si9GkhAWj4ZW+Cw6VgJavsAIyXwK6Jrj3MkFZRHpcB67qeVSebcJL75oXXGKstauCUe5s6oL75qjiEW+mpxeh+aIq+PJVyPyu8I1KIyEipWES0NxJd4vwEu2KCOKRGEjrhtGizielLZwH7jsO0AhoORsCW+d8dUbFCCIlIKh2z5lgBO14KoDWAt8bJOHCHsDAHLXfKgtnWGtzzgOPkkZAy1dXksqhRYtCROIkrIJXIlLCglGwM3DTq2qASXFJSqR4gp6fs33HEdIIqIiIhFWxtcAErYJW2qy1bdbaRmttnbV2MDDEGNMejIBLCQqKiTvidGVDCWj56oCtl186s6bzTUQkqdJWyGnUSFj5sda24PpCL1Ej+pLVGLzOsaEEVAoRG/Lu4gAACRlJREFUm09MIlIUL+AKULxXxoofQXLSgVuEQK33SkjwoSJ23Q2UgJavQnr9haOjWiVHpEQFK+O0huvCS1kLOx/k6xMrCRJc3Rjpu+dnNipCKl/LcW8yleTu9zcyuI/dL66IdJ8xphloU/JZ+owxC3BzfI/Lk4yEfwvy9YmVZKkFavMswVoDYIxJEQw2WWvrcmzbo5SAlq+wFUu+OaDhpGUVJIiUmKAitiNb8hmXlVKkR4WjmjXkHlQIL73Hok+kdF8wpzvnvO4gMa211lZHF5WjS/BlKvjD0sG21S+yqQViNWlZRLovqHgfmWfkswYtQFFqWoGGTgpRatK2FSkqJaDlbRIwMVslfPAHqoMY9QyTotOCA2Ug6AE5qpOm43VoJaRS08S2aVU7CN7zK4CFGvmWKBhrre8YxKNgDtgQa+2EtO9VACncp2V9Ei4Dxph23OW3wXHqEyc9K6huTpE/uRwCVFlrTTRRSVSCJPMMXEueVWnfrwUWACuimv8n8RDM/azCw3u/ElAJ35Tq2NZuqQJo0tzP0hUkIs24ZKOS7Uc/23CT0ZvVE7K0hPO9Cti0zcecMCm+YIBhOtvme4b/9vXvvUwEHziacIlnulW4EfBIihKVgIqIiIhIpDQHVEREREQipQRURERERCKlBFREREREIqUEVEREREQipQRURERERCKlBFREREREIqUEVEREREQipQRURERERCKlBFREREREIqUEVEREREQipQRURERERCKlBFREREREIqUEVEREREQipQRURERERCLVx3cAIiIiXWWMGQ8MASqANmttaxeeWwtUBs9dZa1dWJwoRSQXjYCKSMkxxkw1xizJuNWnPd5kjKnwGWO5McZUBIlfTxkFNABNQFUXn1sHTAieO6oHYxKRAikBFZGSESQ5KWCotbYu/RY8vsQYUwlM9RtpWZoPLDHG9MjP3lrbCBy3s88NfydExA8loCJSShYArUFysh1rbQtuxCwVeVQCsAToANp6aofW2o6e2peIREsJqIiUhODybm225DNkrV0F5Hxcisda22KtHdyVuZoiUrqUgIpIqagCVnW2UTASKiIiHikBFZFSMRJX2VwIjcKJiHikBFRESkUKXAV8Adsu0PxBERF/1AdUREqCtbbFGNMINBljsNbOybdtrseCdk3VuIKZNcBQoDmYP5q5bQVQH2xbgWvp05xrnqMxZgmud2Ul0GKtbQz6WYYjtyOD+Bo6O98s+24KYgnbS3UAkzJ7XBpj2tOO1wEcYK3t2MlzqQzOpzH4+YfJ/yjg4fDYQWxVwfYLs83T7erxc8SUfv5DYWu1/E4J4oZtvwcVuHPVhxeR7rLW6qabbrqVxA2oBWxwex9XFT8eqCzguRW4Su0FWR5rBqqybN+cZdtUtn2kPac+iK8J1w4qc79LgFQ3fgZLgv1X5NnmfaC+m+cStrOywTk1h8cMvteese3W887xc+nS8dO22fqzzPLYeKA982ec+dwc59aOK2rL3N/7hfw+6aabbvlv3gPQTTfddOvJG26kLUzC0m/tQaKSNTELktX2PPtdkPH/zdn2FSQvNj3By7KNDWIcn+Wx8cHjWZOmAs6/toDj98i5BImjDX52tWnfr89M3tLOO1vC192fZb7XrQl4P89zs8XTni2hDR7r1gcE3XTTzd00B1RESoq1ts265vMGt+LNHFx1fDhi91djzHYr5wQtnMbjkpUdBJetx2esnjQR+GuW46/CXUau7iTUGpt9CcjwUn+hBVWZx28N9pH1Mn5wrs0Z396pc7HbLkVX2bRL5da1XOpKoVd3f5b5ltKcDVSkXU7PK5hGUAnkmqbRDFRl/g6JSNcoARWRkmWtbbVu1ZuRwGBcUlEBvJCxaZis5Uqa2nBrhqfP/VsBrM2x/Vo6TyBX5Ph+eIwhnTw/nzBJyhbDhCzJYXfPpbvN5bt7/JyC12wVblS2EA1Ah809zzP8gFCzszGJiIqQRKRMBAlFQzCa2WSMmWq3FSpVBdtk7SNqrZ2Q5Xtbl3IMRsPS1zkfQuc9STvtWdoNLbjR3EbSRkKDEdz2zI19n0sPHL8zq4BKY0xFnsQyVAmsCgqasqnAfVDJlTCLSAGUgIpISTDGNNkCKp6ttXOMMdNxVdahSraNPHblmFNxCd5C0irljTFdrmLvSdZVtS/Ejfqlx1JPjkvL3TyXNd2LOLKfZSV5RmvTRow7bP4FC3J2WBCRwigBFZFSUdH5Jlu1sv1l3bD1T8GCNkQ1QHWukVPPmnHzVuvTkqmR2UYAfZ9LBMcPpzN09iFDo5oiEdEcUBEpGUFPzUKlJzorgucXNNcwuDxbi+sJ2WnCFBT+RCqzGCmIYUHmdr7PJaLjV+JGNfPuP22+6E7PORWRwigBFZFSMr3A7cJWTaGwKjxncmOMqUhLfsI5obmKlsIG7aG6HNsVW3oxUl2OynTf59ITx885eh2cewWuGr4QTbiq+ZxV7saYyi5+2BGRDEpARaSUVBljMlsMbScsLkmf4xe0Q1pIjjZMgelsq1wPL+XucMk2SFK7fEm/SMJzbCL3PE3f59ITx883KtqI62BQ0LzN4Peijfy/Cw05WmiJSIGUgIpIKWkElhhjUtlGqIJCl0ayj6JNAlYYY5Zk9PsML+0vT5s/GSa5TRnbVeJGV2cTXMbNVXlO7jZLFRn3Oy2IdyGux2m+vpawE+eS9nMa2YWwMs+rJ36WE7L1+Qw+bNSQf9Q228/5OGBItg8zwe/Qw3n2JyIFMNZa3zGIiHRbehV82rriYeIxBDfC1tZZpXyQtNQF24cJ58PW2raM7arYdsl/eXC/tXraGLMAlzitsMHa7saYVPC9MOlZhav4nhMkXAsIWkIF2nBzI7vS1D3zfKqA6dlaSRXhXFalt1RK239YZJS+bUN4Xjtz/LR9L7DWTkh7zYfiRntH4lZI2mHkM0c8TZmV7zl+F5oLmasqIvkpARURERGRSOkSvIiIiIhESgmoiIiIiERKCaiIiIiIREoJqIiIiIhESgmoiIiIiERKCaiIiIiIREoJqIiIiIhESgmoiIiIiERKCaiIiIiIREoJqIiIiIhESgmoiIiIiERKCaiIiIiIREoJqIiIiIhE6v8DJIaPvSGML+QAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from collections import OrderedDict as odict\n", "from matplotlib.ticker import ScalarFormatter\n", "from scipy.interpolate import interp1d\n", "import matplotlib.lines as lines\n", "hep_spt.set_style('singleplot')\n", "\n", "# Define the background, the effect of the alternative model and the observation\n", "bkg = np.array([25., 16., 9.])\n", "eff = np.array([3., 2., 1.])\n", "obs = np.array([29., 13., 10.])\n", "\n", "dct = odict([('x', np.linspace(0., 4., 10))])\n", "for v in ('y', 'y1sl', 'y1sr', 'y2sl', 'y2sr', 'yobs'):\n", " dct[v] = []\n", "\n", "# 1 and 2 sigma intervals\n", "sig1 = chi2(1).cdf(1)\n", "sig2 = chi2(1).cdf(4)\n", "\n", "null = hep_spt.cls_hypo(norm, bkg, np.sqrt(bkg))\n", "for i in dct['x']:\n", " a = i*eff + bkg\n", " alt = hep_spt.cls_hypo(norm, a, np.sqrt(a))\n", "\n", " cls_mgr = hep_spt.cls_ts(alt, null)\n", "\n", " # This way we calculate all the values at once, using the same sample\n", " # for the test-statistics for each hypothesis\n", " values = cls_mgr.evaluate(\n", " np.array([\n", " null.median(),\n", " null.percentil(1. - sig1),\n", " null.percentil(sig1),\n", " null.percentil(1. - sig2),\n", " null.percentil(sig2),\n", " obs\n", " ]),\n", " size = 1000000)\n", "\n", " # First item in \"dct\" is \"x\"\n", " for dv, v in zip(list(dct.values())[1:], values.CLs):\n", " dv.append(v)\n", "\n", "# Plot the predicted and observed CLs lines, together with the 1 and 2 sigma regions\n", "r2s_area = plt.fill_between(dct['x'], dct['y2sl'], dct['y2sr'], color='yellow')\n", "r1s_area = plt.fill_between(dct['x'], dct['y1sl'], dct['y1sr'], color='lime')\n", "(pre_line,) = plt.plot(dct['x'], dct['y'], color='blue', ls='--')\n", "(obs_line,) = plt.plot(dct['x'], dct['yobs'], color='red')\n", "\n", "# Add the 90% and 95% CL lines\n", "xmin, _ = plt.gca().get_xbound()\n", "\n", "x90 = interp1d(dct['yobs'], dct['x'], kind='cubic')(0.10)\n", "x95 = interp1d(dct['yobs'], dct['x'], kind='cubic')(0.05)\n", "\n", "line_90 = plt.gca().add_line(lines.Line2D((xmin, x90), (0.10, 0.10), color='purple', ls='--', ms=0))\n", "line_95 = plt.gca().add_line(lines.Line2D((xmin, x95), (0.05, 0.05), color='pink', ls='-.', ms=0))\n", "\n", "plt.gca().add_line(lines.Line2D((x90, x90), (1e-2, 0.10), color='purple', ls='--', ms=0))\n", "plt.gca().add_line(lines.Line2D((x95, x95), (1e-2, 0.05), color='pink', ls='-.', ms=0))\n", "\n", "# Change the scale settings\n", "plt.gca().set_yscale('log', nonposy='clip')\n", "plt.gca().set_ylim(1e-2, 1.9)\n", "plt.gca().set_ylabel('CLs')\n", "plt.gca().set_xlabel('Scan variable')\n", "plt.gca().yaxis.set_major_formatter(ScalarFormatter())\n", "plt.legend(*zip(\n", " (pre_line, 'Predicted limit'),\n", " (obs_line, 'Observed limit'),\n", " (r1s_area, '$1\\sigma$ region'),\n", " (r2s_area, '$2\\sigma$ region'),\n", " (line_90 , '90\\% CL'),\n", " (line_95 , '95\\% CL')\n", "))\n", "\n", "print('Limits:\\n- 90% CL: {:.4f}\\n- 95% CL: {:.4f}'.format(x90, x95))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }