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{
 "version": "1",
 "metadata": {
 "marimo_version": "0.23.3",
 "script_metadata_hash": null
 },
 "cells": [
 {
 "id": "Hbol",
 "code_hash": "e238d786bb62a06c07450dfbac87a566",
 "outputs": [
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 "outputs": [
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 "text/markdown": "<span class=\"markdown prose dark:prose-invert contents\"><h1 id=\"bayes-theorem-updating-beliefs-with-evidence\">Bayes' Theorem: Updating Beliefs with Evidence</h1>\n<span class=\"paragraph\">Bayes' Theorem is a fundamental concept in probability theory that helps us update our beliefs based on new evidence.</span>\n<span class=\"paragraph\">The formula is:\n$<marimo-tex class=\"arithmatex\">||(P(A|B) = \nrac{P(B|A)P(A)}{P(B)}||)</marimo-tex>$</span>\n<span class=\"paragraph\">Where:</span>\n<ul>\n<li><marimo-tex class=\"arithmatex\">||(P(A|B)||)</marimo-tex> is the <strong>posterior probability</strong>: the probability of event A given that B occurred</li>\n<li><marimo-tex class=\"arithmatex\">||(P(B|A)||)</marimo-tex> is the <strong>likelihood</strong>: the probability of observing B given that A is true</li>\n<li><marimo-tex class=\"arithmatex\">||(P(A)||)</marimo-tex> is the <strong>prior probability</strong>: our initial belief about A before seeing B</li>\n<li><marimo-tex class=\"arithmatex\">||(P(B)||)</marimo-tex> is the <strong>evidence</strong>: the overall probability of observing B</li>\n</ul></span>"
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 }
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 "console": []
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 {
 "id": "vblA",
 "code_hash": "c9e1e66d44b3c17a7882a8b80ef41e2e",
 "outputs": [
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 "text/markdown": "<span class=\"markdown prose dark:prose-invert contents\"><h2 id=\"medical-testing-example\">Medical Testing Example</h2>\n<span class=\"paragraph\">Let's say we're testing for a rare disease:</span>\n<ul>\n<li>Prevalence (prior probability): 0.1% of the population has the disease</li>\n<li>Test accuracy:<ul>\n<li>If you have the disease, the test correctly identifies it 99% of the time (true positive rate)</li>\n<li>If you don't have the disease, the test incorrectly says you do 5% of the time (false positive rate)</li>\n</ul>\n</li>\n</ul>\n<span class=\"paragraph\">What's the probability that someone who tests positive actually has the disease?</span></span>"
 }
 }
 ],
 "console": []
 },
 {
 "id": "bkHC",
 "code_hash": "f43af12daae0fc2b4b02e4a47de73c57",
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 "text/markdown": "<span class=\"markdown prose dark:prose-invert contents\"><span class=\"paragraph\">Given:</span>\n<ul>\n<li>Prior probability of disease: 0.1%</li>\n<li>Sensitivity (true positive rate): 99.0%</li>\n<li>False positive rate: 5.0%</li>\n</ul>\n<span class=\"paragraph\">Using Bayes' theorem:</span>\n<span class=\"paragraph\">P(Disease|Test+) = [P(Test+|Disease) \u00d7 P(Disease)] / P(Test+)</span>\n<span class=\"paragraph\">P(Test+) = P(Test+|Disease) \u00d7 P(Disease) + P(Test+|No Disease) \u00d7 P(No Disease)</span>\n<span class=\"paragraph\">P(Test+) = 0.99 \u00d7 0.001 + 0.05 \u00d7 0.999</span>\n<span class=\"paragraph\">P(Test+) = 0.0509</span>\n<span class=\"paragraph\">P(Disease|Test+) = (0.99 \u00d7 0.001) / 0.0509 = 0.019</span>\n<span class=\"paragraph\"><strong>Only 1.9% of people who test positive actually have the disease!</strong></span></span>"
 }
 }
 ],
 "console": []
 },
 {
 "id": "lEQa",
 "code_hash": "0945116d7539b44c0a5f8141266727b2",
 "outputs": [
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VVrFJZTTjClSpomQlM1Xsvrv6oeh9/GSNUmhXNV66Lx/hhVSNB4TlVpNc74hx9+cBOyafylHjvc2M3MUGUxGq8zwKuYKailNs7zSG/blnKcrrctTQyV2sRdKf8QT23/oz1+uEniPDpWjXNWtVX7ov/qYk69evXSfJ1C57x581ygUhBWhVSfI43jViiWaIFQUk6EpfCmqqXG2Pbv398FIc0CroqtxvRGm4TscNQJoIsMql5rIrNwugijC0UK5roloboqFJhUpdWFhyPZ3rH4PGaGuit0XJozQecitXkBjuRzeKxk5N+kzPKOW/MNpPZZ9/4tUneBqttffvmlu32cXqN5AtSRpDHsR/O9B4CTCQEdANKgiZ1E1WxRoFIoUUD2ZuoW/TEc7Y9J/YGvNmH9YaqZ0NV2Gf5HpsKAKuuabCo9k0apSqavJ5980v3xrTClCaHC721+vOkigiaPU4AMv/gQje5vrEnR9Id+eBXda4/W82nRRGKiAHK4bR1LXpDTe6Awq8qy3pP0ULVbFXh9qTNDM3LrtapY67OliqDCcEopuwt0oUYVS80aHl5V9oZFZJQmZ9O+qBKvCw4puxw007vamhWwFAY9CrIppXaRISXv/dZFi5T0mVC3iDcc5HjRMAVdnNDFlNRCaEY+hzpGr/IcLtoxp6TPmNrENawltXuCZ+TfpMzyhrroIk16fv90sUCTFupLHQWaHE6fdS+gp/dzkhE63/od0LCL8Cq6uh4A4ERAizsApEJ/FKvyo6qk14KtcK0/KsOrmZpNXeE7GrWzq/1SM7VHmxFeVSatS2N+o10c8IKa1pGyQuiFh+PR5p4WnRO1QisoqKU1JbXAe8477zw3q7XG4ocfp2btVuVNFdq0qNtA44oHDhzoxi+nta1jTRdHNNO+Wpr1mUjPLOwKuOH02VLlXe+tN7eAQpDahHUhw6NjVSUynHehJ/xzodcdaTDT2F7dYUDb8drGD7c9XWBQ1TYlher0tFcrwOlzrNvshV+U0OdIv3v6vByJjN5mLZwuduk9VXfK0fgc6hjU5aJZxcOfT61rJpx+r3Qs6tZIyXsfMvpvUmZobgx9PjWDunfRMtpxa19Svv86Z7o9X/i/V+n9nGSEOhr0u6Q7Jnh0QVBzjADAiYAKOgD8P90WzKvkqtqj6qgqX7o1kipGolsWqZ1Y9wBWINNy+sNP7azhgcpTv359d+suTQankK8KUjgFUoV33TJKEzBpAjJVyrRdvUbt9brNkwKMgpDG/+oPZE1MpT9AtV9HGmKOpmeeecZVrVRZVpeAQqcm0lL7szoE9L3odmkKNZoUbMqUKe4WWmrd11hq3e9clfjD0fk+66yzrHbt2m5bqmZqbP/vv//uJmDT+OHjQRdb1OqtWzipAyLavctT0vurYQ5aXsMfdMsphS99rrxj17hntYzrvdbkeQqZGk+s+2CHT/qldSnga3I+7wKQPhMKQtFCY1o038IHH3zgAqE+x+GfZV040cSGus+2gruGMWi/FAp1a7ZoreUKcroIo9uxNW7c2K1D+xmNWp9VUW3atKmbuM+7zZrGuWvc8pE4ktushVdg07Pd9H4O77vvPnee9G+GbpPm3WbN6yZJi+ax0Pui86iAr5ZxjcnX75Sq0pqLIqP/JmWGuio01lzvl4b8aI4J3WZOczHoXOvfI3V26N8n3e9d/3bVrVvXvf/aZ02OGH7hIyOfk/TSZ1Vj3vv06eOq5hoCoi4T79+gY1G1B4CjKqunkQcAP95mTbdI0+2f3nzzzYjbCcn//vc/d6sh3YatevXq7vXRboHlee6559xzTz31VKr78Pbbb7tbBeXJkycQFxfnbt903333BVatWuWenzp1aqBr166BsmXLuu3qtlS6DdbkyZOP+W3Wot0qKdrtmtauXeuWLVOmTCA2Ntbdskq3otKxpVzuuuuuCxQpUsTdwk3HmvLWR95tlp5//vmo+7Vo0SJ3Cy5tQ9vS7c10Pr744ovQMtFujSXee7V+/fqIx3U8ugVeRjRu3Nita8CAAVGfT3nbLN2arUWLFu62YHofK1WqFLj33nsDW7dujXjdjz/+6G6TpfNTrVo1d1u6aJ+xb775JlCnTh33eS1fvnzg2WefDd2aK63bd6W8jVVqtxrUV/htsH777Td3Ozl9TkuVKuU+oz/88MMhnyHdRvDKK68MFChQIGIdqd3e7aeffgqceeaZbr26tV7Hjh3dbc7S8755+x5+vEdym7W0pPZZSs/nUGbOnOnOv94nLaNbuenfkcO9T94tzB588EF3GzPv9+rSSy91287ov0mZvc2aZ9q0aYHOnTuHPsdab5cuXQJjxoxxz+/evdt9ruvWrev+PdPvlb5P+XuSkc9Jar+f0Y5TnxGtV9vW7d6uvfZa99nVcp988km6jx8AskKM/ufoRn4AQDhVwXv16uXaTqPNiA4AOLbU8q+ulAkTJrgOFgDwKwI6ABxDugaqFs/ChQsf8eRdAID00zCJ8Ek3NSZeQ0ImT57s5sBIz4ScAJBVGIMOAMeAxolq3KNC+axZs9w4ZQDAsXfHHXe4kK55DTQpne48MHHiRHvqqacI5wB8jwo6ABwDamevUKGCu2WVJnNK7y24AACZowk+NRmdJonbtWuXmzDv1ltvtZ49e3JqAfgeAR0AAAAAAB/gPugAAAAAAPgAAR0AAAAAAB9gkrhTzIEDB2zVqlUWFxdnMTExWb07AAAAALLwbjPJyclWqlQpy5aN2q0fENBPMQrnZcqUyerdAAAAAOATy5cvt9KlS2f1boCAfupR5dz7JYyPj8/q3QEAAACQRZKSklzxzssIyHpU0E8xXlu7wjkBHQAAAABDX/2DgQYAAAAAAPgAAR0AAAAAAB8goAMAAAAA4AMEdAAAAAAAfICADgAAAACADxDQAQAAAADwAQI6AAAAAAA+QEAHAAAAAMAHCOgAAAAAAPgAAR0AAAAAAB8goAMAAAAA4AMEdAAAAAAAfICADgAAAACADxDQAQAAAADwAQI6AAAAAAA+QEAHAAAAAMAHCOgAAAAAAPgAAR0AAAAAAB8goAMAAAAA4AMEdAAAAAAAfICADgAAAACADxDQAQAAAADwAQI6AAAAAAA+QEAHAAAAAMAHCOgAAAAAAPgAAR0AAAAAAB8goAMAAAAA4AMEdAAAAAAAfICADgAAAACADxDQAQBIh1atWtndd9/tm/Wkx0MPPWQ33XTTcdnWyeTRRx+1evXqpXv5DRs2WLFixWzFihXHdL8AACc/AjoAwNeuvfZai4mJcV85c+a0ypUr2+OPP2779u0zPxs7dqzb5y1btkQ8Pnz4cOvXr98x3/6aNWvslVdesQcffDD02K+//modO3a0UqVKuX376quvDnldIBCwhx9+2EqWLGl58uSxtm3b2oIFCyKW2bRpk1111VUWHx9vBQoUsBtuuMG2bdsWsczMmTOtefPmljt3bitTpow999xzdrIqUqSIdevWzR555JGs3hUAwAmOgA4A8L0OHTrY6tWrXVDs06ePq3A+//zzdiIqVKiQxcXFHfPtvPvuu9asWTMrV65c6LHt27db3bp17Y033kj1dQrSr776qr311lv2559/Wr58+ax9+/a2a9eu0DIK53PmzLHRo0fbt99+64J/eKU+KSnJzjnnHLftKVOmuPdK79nbb79tJ6vrrrvOhgwZ4i5eAABwpAjoAADfy5Url5UoUcIFvltvvdVVdb/55hv33ObNm131smDBgpY3b14799xzIyq+gwcPdlVeVYurVKniKroKnMuXL4+o0l900UUR21QbutrRU/Phhx9ao0aNXNjWvl155ZW2bt0699ySJUusdevW7nvtl6rV2ka0Fvf07v8PP/xgNWrUsPz584cuWKTlk08+cdXycFr3E088YRdffHHU16h6/vLLL9t///tf69Spk9WpU8c++OADW7VqVaja/s8//9ioUaPcBYAzzjjDzjrrLHvttdfc9rScKKju2bPH3nvvPatVq5ZdccUVduedd1r//v0P23EwcuRIt129T02aNLHZs2dHLDdhwgRXmVd1X5V5rVcXHjJ6PtP6PESj49X51/LVq1e3AQMGRDyv41RnwpdffpnmegAASAsBHQBwwlE4UwAUBd/Jkye7wP7777+7kHneeefZ3r17Q8vv2LHDnnzySRc2f/vtN9d2rtCYGVq/WtVnzJjhwp5CuRfCFRyHDRvmvp83b54L02o3jya9+//CCy+4iwKqVi9btszuueeeVPdNVdy///7bXUDIiMWLF7vWeF0A8SQkJLggrn0T/VcBN3zdWj5btmyu4u4t06JFCzckwaMQrHOhAJ2We++911588UWbNGmSFS1a1F1k8M7FokWL3MWJSy65xLXQf/rppy6w9+zZM8PnMyOfB11wUNu/XqMLFE899ZQb3//+++9HLHf66afb+PHj03WuAQCIJkfURwEA8CGFrTFjxrhq8h133OEqowpiCllq5/bClAKyQvNll13mHlM4e/31113QFAUrVUP/+usvF6qOxPXXXx/6vmLFiq4tvHHjxm4stqrcamUXTR6mQBtNRvZfLeeVKlVyPyuQahx+ahTgda5U0c0IhXMpXrx4xOP62XtO/9UxhcuRI4c73vBlKlSocMg6vOdU3U6NxnG3a9cu9D6VLl3aVaW7dOliTz/9tGuv9zoQVAHXeW/ZsqW9+eabrgp+LD4P2iddNOjcubP7WcemCyADBw607t27h5bT+Z42bVo6zzYAAIcioAMAfE/jnBV6FawOHDjg2sk1pllhXeHQC1pSuHBhq1atmqt0erSMwrNHLcoKzVrmSAO6xlZrH1RBV1VY++WF45o1a6ZrHdp+evZfrdpeOBdN4Oa100ezc+dO91+1Y59omjZtGvpeoT/8XOhcq3Ku0O3RhQide1X/dcHjaH8e1D6vyr0mwrvxxhtDj2uSQnUXpOzsUHUeAIAjRUAHAPiexnOrQqqWaVUpFbCOJrVnK+iFC2+JTkmhTS3b+lJYVCu2grl+9lrvj6bY2NiInzVWO+X+ppxVXHThQPuWXhpLL2vXrnUXATz62bvtmJZJeXFAYVVt9d7r9V+9Jpz3s7fMkVB3ws033+zGnadUtmzZQ2abPxq82enfeeediOAv2bNnj/hZ5yAj5xsAgJQYgw4A8D3NJK7bqymEhYdztSUrHHpjn2Xjxo1urHN4FVvLaFyyR89r3LFeLwpVKSddmz59eqr7M3fuXLedZ555xk1YpgpsytDqjb/ev39/qutJ7/5nlKrtugWa2rAzQq3bCtDqTAifkV3751W29V+dO3UQeH7++WdXxfYCrJbRWPnwixya8V2V7LTa2+WPP/4Ifa8LDPPnzw+9Tw0aNHDHpM9Cyi+d76P1eUjZmq+LQv/+++8h20zZxq8J7erXr3/Y8wwAQGoI6ACAE5bGIGu2cbUea7IwtUBfffXVlpiY6B4Pr0BrzLqCm4KlJhLTDOFeO3ObNm1cYNOkYarCasxxytnDw+lCgQKhZi9XcNO455T3NteM86p0qz1//fr1h9wnPCP7fyQdAZq4TesMp33QhQfv4oPawvW9qv+i/dX4bs30rmOaNWuWmxFdAdWb5V4hVhO1aZ81ZlvjvTUmXpOseWPeNQRB50dt4bodmyZz0yR5vXv3Puy+a2y9LhDo/Ot9UjeAt+2+ffvaxIkT3fa033qvvv7669AkcUfr85DSY4895sa/a7y7LhjovAwaNChiVnq1tmtdur0cAABHLIBTytatW9UT6f4LACeC7t27Bzp16pTq85s2bQpcc801gYSEhECePHkC7du3D8yfPz/0/KBBg9xzw4YNC1SsWDGQK1euQNu2bQNLly6NWM/DDz8cKF68uFu2V69egZ49ewZatmwZel7f33XXXaGfhw4dGihfvrxbX9OmTQPffPON+/d12rRpoWUef/zxQIkSJQIxMTHuOKKtJ737H+7LL79020rLd999F0hMTAzs378/9Ngvv/ziXpfyy9s3OXDgQOChhx5y50LHdvbZZwfmzZsXse6NGzcGunbtGsifP38gPj4+cN111wWSk5MjlpkxY0bgrLPOcuvQfjzzzDNp7q+3byNGjAjUqlUrkDNnzsDpp5/u1hPur7/+CrRr185tO1++fIE6deoEnnzyyaP6eXjkkUcCdevWjdjukCFDAvXq1XP7VbBgwUCLFi0Cw4cPDz2vz0O1atXSPEYA8Buygf/E6H+OPN7jRKNWRU1qs3XrVtf+CAAnO933WlVhtTCfSvR/72o579Wrl3Xt2tX8TvdB11wDamtPbdZ7P38eVIHX2Hh1DwDAiYJs4D+0uAMAcBJSu/rbb7/txlvj2NqwYYO7BduJcCEEAOBvzOIOAMBJSjOve7Ov49jROPn77ruPUwwAyDRa3E8xtLEAAAAAIBv4Ey3uAAAAAAD4AAEdAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAPkBABwAAAADABwjoAAAAAAD4AAEdAAAAAAAfyJHVOwCcCBo1amRr1qzJ6t0AAADAYZQoUcImT57MecIJiYAOpIPC+cqVPThXAAAAvvZYVu8AkCkEdCBDYiwuLo5zBgAA4DPJyclZvQtAphHQgQxQOO/duzfnDAAAwGf69+9vZHSc6JgkDgAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD5AQAcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENABAAAAAPABAjoAAAAAAD6QI6t3AAAAvylf3uzaa4Pfv/yy2ZYtdlLJnt3sjjvM4uPNXn/dbNOmrN6jE4M+E/psTJ9u9tVX6X9dvXpmF11kNmuW2bBhx3IPAQAnOgI6AMAXoUfGjDEbPz74fZEiZj17Br9XGFIoygwFJAUlOXDAbN8+s23bzFatMps82WzJkoPL7t5ttmJF8Hstd7KpX9+sQAGzf/6JDOdly5q1aGFWsqRZzpxma9ea/fqr2fz5B5fJls3s9NOD6yhYMHh+Fi40++kns6Skg8tp/a1aBd/b/PmDFzmmTTObONEsELBTioL52Web1aoVPJ/r12f1HgEA/IoWdwCAb5x5plmePMd+Owrl27cHQ+RppwUvEihMelavNnv33eCXQvzJpnHj4H9nzjz4WIUKwfNQuXLwAsbWrWalS5t17WpWvfrB5S680KxDB7PixQ92FtSpY3b99Wa5cgV/zpvX7MYbgxdE9H5u2GBWqJBZu3Zm7dvbKWf/frO//w5e3GjYMKv3BgDgZ1TQAQC+kTt3MKSrGpuahASzNm3MKlUKhj8F7XnzzH7+2WznzvRtR8FbChc2u/TSYMVYAX3ZMrN//43e4q5lzzknGFoVRHfsCFaYx441W7nyYNW/devg63Usqk7/+WewQu9p0iQYXHUcqlLv2hXcro5548bgMnpcYbZqVbN8+YIVfT03ZYrZjBnBZbQP2pbCc1xc8DzMmRM8D3v3pn7sRYsGw7VCoyrfnkaNggFSVfBXXgk+37lzMHxrX+bODe6XfpbffjMbPTp4nL17By92qLKuDghVirXf3rlWxbhBg2C41zKqoodX26N1OqijQcejz4Mq8IsXm40YEfk67csZZ5gVKxa8qLB8efA8rlmTsc9LRraZUnrfB3UhaF91QWjUqNTXBwA4tVFBBwD4ggKogqhCjIJONAp9N9xgVrduMBjqNXpMFWEF6hwZvOys14ePJU6ruqkgX61aMMQqcMbEmFWpEgy8ogpxjx7BcKrnVDVWYL/gArOWLQ+uR+Fdy6oyr2UUGmvUMOvW7eD+K/DpmHRs2taePcELA6pye2PIdbwK+94yWk/TpsGKd1rUxi56TXiA1D5LePu5970uTijoapmUy4UvX7Fi5LqiLafz5x1HWnS8uiCifdRrdK6vuOLg8wrRuoCQmBis9uuzo+q/Kvk670fyeTncNlPKyPugrg1R8Nf5BAAgGiroAABfUDVTY3VVyVag/eOPQ5dRsNLEZqqW/u9/wVZ0VS4VolQVVnUyo2PVVQVXuFMl1Avb0ShUy9ChwUqtqGrsad48GAK1PlWNFfJ0seHcc83OOsvs99+DQVvj7D/7LHgMXqhVOFcALlMmWLX1tjVu3MEx+Qp+OnbRcarqr/Hfb74ZrNTr+G+9Nbg+BWCtJxovHKac+E5V35o1g/tx993Byn74+dBFEwVhVd0VXHVM+q8Cpyrr3jKyYMHBc6pW982bD13X4SjkDxwYDL26cNKxo1mpUsEQvnTpwYsev/wSPE8K1ArjCux6L778MuOfl7S2Gd5t4MnI+6DPt3dO9P563RIAAIQjoAMAfEOtzwpVmoAsfGIyj8KXKNwobIlarxV8FRIVpjI7mVxqtD+1awcrpgpiCnFqh9fEZ+H7poD24IORr42NDT6uYK8ArOCnn7XP4dVmL7hqW6rWqzVbQVGVdr1WLe7h21IF+M47D91XVYJTC+jeOHGds5QBXetT9VcBUqFTF0x0zOJdUNAs5Nov7Z8miVNlWGFf++Qto0D+4YfBidEUYHVcel/U5q7j9ZZLy7p1BydTmz07eM5E7ewaXuBdFFC3gb5SHv+RfF7S2ma0gJ7R98EL6LqQAwBANAR0AMfMx/b/f90CaTjXnrLyVts22Fx7f8+9FjOhkz3QvofVaaVEVNkt84e9bF/aGGttj1gVa2RbbZl9bLeH1vEfG3HE57hEiYOhNa3ZtVWR1dhltairGqzqsSrOCm/ffXdwOY1BVkBNSS3eCrSq3irQKawp3KryqxAr+l4UxBXKFYK1fq+Kq/b5AQMOrlMhOny8tUfV79Rou+IF3HAa3+6NcRdVyRXQFai9iq/WreMNP2Zvtn3ts0ez4L//fmRY9YYQhC+XWXrPvGPyKMAfT+l9H7zPWcr9BQDAQ0AHAPjKkL9GWvcmney0UsFwHm7WygXWskojq1A40WqWrGR/r15kZ1dvEgqb3jjf9FKluFOngz9PnZr22G3dlkyVVS+8tm1rVq7cwW0rTCt8DRlycAIyzWiuVmcFVo0198Y9q8Ksx9QmrfHtKSuzquaqldsLtxrfrvWr1d07TgX6kSMPVoe1bl04SK16Lt5t1VTJD6fXqqrvTXinixCqpouqx16o1OO6COGFYI0F98Z8e+fGO1+q+uvChCrGGtstem1a++fRsWq9CvO6MJGyyq0hBOpM0L798EPkBRc9LjoWnQ+19esiiNfintrnJa1tRpOR90HvmxfQaW8HAKSGgA4A8JW9+/fZG2M/tic7HdozPGTSSOvS8BwrFlfYPrnhOVu6abUL66Kx3+EBMS0Ku5rUSyHVq1prNvZFi1J/jSYkU8jSOGyFQ4U5b7uiseIKfwr9vXoFQ5g3blyzgKuFXMFS1Wht8+qrg+vSGO6UNHZdAVGvU9D3xqR7P6v1XBOTKYxqjLcCpdapMfEKh5p5PrUquhf6tf9a1rvPu0Kr1qVtKIxrm5oETYE6fNZxBU+1rivoK3B64+J18UK3EvNocjy1tmt96hzQ+nXs336b9izzHs0if/PNwW4E7wKAArDXaq5x57pAoosIOle6YKB90QURvZe6ODBpUrBqr/3Q+HTtszcGP9rn5XDbTCkj74O6IESTAxLQAQCpYRZ3AIDvDJ8+xv7dsOKQxzdt32pd3r3XvprxsyXt2u7C+cbtW1wQGzz4YNg8HFWoFdAVkBWc9VqFurRorLkqqQqAqiIraOn2aV6rt0KXJiLT+rwAr/HWCne65ZYowH39dTAAKvwqVGpMd0oag65br3lj13Vcaq9XZd4LktpnTaSnAKzQ6VXWNQldWvdu10UChVNtX23zHu2zJndTwFQ414UAjc9+552DVXfROdCXF4b1/Y8/mn3+eeR2dLFDQV/7pmCu86CWdwX59NCxfP/9wWCv13/yycHnJ0wIDjtQlVzHrn3WxQR9Frxt6GdN2Ke2fQVl7Yu3TLTPy+G2mVJG3gfdMk/SexEJAHBqigkEwm+QgpNdUlKSJSQk2NatWy3eK3vgsEqXLm0rV/awuLh4660b/iJdGIOO46VrJsagn4p0z3NVuFXx1ozyfhJ+T3KF35Nhm7oYoq4KXdDQbO9pzXUA4Mj179/fkpP7WGJioq3QGCIcFtnAf6igAwBwilE3gGZeV0u+2s9xbNWpExzKoOo54RwAkBbGoAMAcIpRa7bGR+P4XRDxbscHAEBaCOgAAMA3vvoq+HWybxMAgGhocQcAAAAAwAcI6AAAAAAA+AABHQAAAAAAHyCgAwAAAADgAwR0AAAAAAB8gIAOAAAAAIAPENAR1eDBg61AgQKHPTsxMTH2FfemAXxh6/TltvCZUYddbv5j39q2uWuOyz4BAAAg/bgPegYpkKblkUcesUcffdSOh1atWtm4cePc97ly5bKKFStaz5497bbbbsv0ui+//HI777zzQj/rmBTEp0+fHrHc6tWrrWDBgpneHnAsKZCmpVDLKlakVbXj8iYsHzzRdi7d5L6PyZ7NYgvmtQKnl7cCjctnet1xtUpZvirFQj9vGDvPts9da+VuaRGxXMU+bS1b7thMbw8AAABHFwE9gxRIPZ9++qk9/PDDNm/evNBj+fPnD30fCARs//79liPHsTvNN954oz3++OO2Y8cO++CDD+z22293gblr166ZWm+ePHnc1+GUKFEiU9sBjgcFUk/y7FW2cex8K9+zVeixbDlzRPzeWiBgMdmOXYNRQoOyVrh1VTuwd78lzVhh676b7QJzfO3ETK03W2x293U4OfLnztR2AAAAcGzQ4p5BCqTeV0JCgquoez/PnTvX4uLi7Pvvv7eGDRu6qvaECRPs2muvtYsuuihiPXfffbergHsOHDhgTz/9tFWoUMEF47p169oXX3xx2P3Jmzev27aq56pyV6lSxb755hv33LJly6xTp07uokF8fLx16dLF1q1bF3rtjBkzrHXr1m6f9bz2efLkyYe0uOv7xx57zC2v49WXHkvZ4t6sWTPr27dvxP6tX7/eYmNj7ddff3U/79692+655x5LTEy0fPny2RlnnGFjx47N6NsAZIgCqfflVY69n/ds2GYLnx5l2xess6Vvj7cFT3xnO5dtsjVfTbeVn0yKWM+6UXNcBTw8zG8av9D+fWWMLXjyO1vy1jhL/nvVYfcnJja723bOgvlc5T62UD7bPn+te27v1p1uuwue+t7t16rPp9i+bbtDr929JsmWv/+7LXg6+Lz2edeqLYe0uOv7TeMW2O61Sa6DQF96LGWL+7L//WbrR/8TsX/7tu+2+f1G2o6lG93PB/btt/U//m2L+o92+7Xs3Qm2Y8kGPoUAAABHGRX0Y+D++++3F154wYXm9LZ/K5x/9NFH9tZbb7mQrUB79dVXW9GiRa1ly5bp3rbC/Z49e1zg98K52uD37dvnquvXXXddaNmrrrrK6tevb2+++aZlz57dta8rTEdrd589e7aNGjXKfvrpJ/eYLk6kpPU999xz9swzz4SGAqjLoFSpUta8eXP3s1rw//77b/vkk0/c419++aV16NDBZs2a5Y4byCrrx/xjRdvVdC3n2fOkr/1b4Tx51korfn5tiy2cz7Wurxk+3bLnzWV5yxdO97ZjYrNZYP8BF/hXfTLJVfTLXNvUAgcCrrq++ospVubaZm7Z1cOnWa6S8Vbu/OZmMcHAHq3ar3b3PeuSbfvC9Va62xnusWy5Dj0uVe03TVxkRdpWD/3eJs9ZZTnicluesoXcz9oHXcgoeUkD97jC/cqP/rJyt7awnIUPdg0BAAAgcwjox4Baztu1a5fu5VVVfuqpp1z4bdq0qXtM4V7V94EDB6YroKuV/uOPP7aZM2faTTfdZGPGjHGhd/HixVamTBm3jFrga9WqFXqNKuz33nuvVa9e3f2cWkBW6FfQV6t+Wi3tqtCrM0D77QXyoUOHunZ7/eGv7Q0aNMj9V+FcVE1X8NfjOgdAVlElO1+louleXlXlTRMWWulrmlieMsELcaqIq/q+dcrSdAV0BfDk2Sttz9pkK9CgnO34d4PtXptsFe5qY7EJwSEmJS6uZ0sHjLNdK7dY7sQCtm/rTivYrKLlLBIMxqkFZLW6x+TMbjHZYtJsac9fq6St+2GO2++85YL7nDxrlcWdVsr93qqinzR9hVXsdbYL51KoWSXbsXC9e7zI2cF/PwAAAJB5BPRjoFGjRhlafuHChW4MecpQr0q4KtxpGTBggL377rtuWVXBe/XqZbfeequ9/vrrLph74Vxq1qzpKt9bt251P/fu3dt69OhhH374obVt29Yuu+wyq1Spkh0pVfvPOeccGzJkiAvoujjw+++/u4sMogsGupBQtWrVQy5QFC6c/mojcCzkKnVoV0ha9m7aYYG9+23Fh39EPK5KeO6Saa9ry6QltnXqMresAnSBJhUsoXE52/LXEsuRkDsUzt1+FY1zbfmqYCugF2hawdaOmGnJM1da3opFLH/NkpazUD47Ujny5XIXJtQJoIC+d/MO27VisxW/oLZ7Xi3yGpO/+LVfDjnObHmZaA4AAOBoIqAfAxpbHS5btmzBiafC7N27N/T9tm3b3H9HjhzpxmaH0zj2tKit/MEHH3RV7pIlS7ptpZfGrF955ZVuuxo3rxno1Xp+8cUXp3sd0fbnzjvvtNdee81Vz2vXru2+vOPURYQpU6a4/4YLn1wPyArhE8U5Ue7YoFDqObBnn/tv4pWnW474yAq1ZmdPS3ydRCvUvIrF5MjmqtKHuztEykq/2tK3z19n2xeucxPelbikvsXVKGlHKq52oq37frYVO/c0S5q10nIWi7NcxePdc4E9+925KHdTc7NskfuZLefhJ6QDAABA+hHQjwNVljWGO1z4eG9VthXE1fqdkfHmoop45cqVD3m8Ro0atnz5cvflVdE19turnntUzdaXKu9qRVerebSAnjNnTlf9PhyNe1eLvdrWFdC7desWek7dAFqHJqrzWuABv8qeN6ftXpcU8Ziqyap4e5VtBXG1nGdkvLk3Fjxa1Vtt6/u27nJt5V4Vfff6ZDuwa6/lLHrwIpba2nM2zW8Fm1a01cOmulbzaAFd+5fy4mA0+asVd1V5jVdXy318ndKh5zTeXRV0TRzntcADAADg2GAW9+OgTZs2bnZ0jQFfsGCBq1SHB3bNoq6x2ArJ77//vi1atMimTp3qqtD6+UioZV2Va1W0ta6//vrLheWzzjrLPb9z5043YZtmUF+6dKn99ttvNmnSJBfsoylfvrxrWdeFhQ0bNri29NS6BzRj/UMPPWT//PNPxO3edCFA+6P9GD58uFuf9ksT5KmKD/hJ3gqFbfeqre42aHs2brMNv8xzk655suXK4caCa/y2Zkffs2m77Vq91Tb/uTg0W3qGt1mxiOUqHmdrhk9z69q5crOt+XK65SlXyHKXKuBuy7b2u1luBvW9W3a4ceMam+6NR08ptkDeYMv6mq22f8ceN24+te6B/NVL2EYd4/ptrqIefjFAP2tW++R/Vrv1ab80Qd62/595HgAAAEcHFfTjoH379i6w3nfffbZr1y67/vrrXUjVmGxPv379XKVdYfXff/91tzhr0KCB/ec//zmibapl9uuvv7Y77rjDWrRo4VrfNVu6JmLTZHBqMd+4caPbj7Vr11qRIkWsc+fO7nZq0VxyySUuVOu2bFu2bHGVdt0+LhqF8PPOO89tt2zZshHP6XVPPPGE9enTx1auXOm226RJE7vggguO6DiBYyVf5WJWqEUVdwuywL79Fl+/jKssh1fVC7eu5irtmixOwTV77ljLVTLBCjU/tKslvb+3pa5o7NrNlw+a6H7OW7moaz13z2eLsQM797rQvn/7HjcGPK56SXdP9Wjy1yhh2/5ZbSve/8NV4Yt3qmsJ9Q7OSxFObfMrh/7lLgaEj4GXEp3q2sZfF7hbre1L2uWOOU/pgpavarEjOk4AAABEFxNIT/8jThpJSUmhieJ073OkT+nSpW3lyh4WFxfvJtdD+nxsHTlVOC662gjONACc4vr372/JyX3cnE4rVqzI6t05IZAN/IcWdwAAAAAAfICADgAAAACADxDQAQAAAADwAQI6AAAAAAA+QEAHAAAAAMAHfBvQdQuwYsWK2ZIlS+xE9fbbb1uZMmXcLc5efvnlTK1r8ODB7tZrJzLdlk33SPdcccUV9uKLL2bpPgFZQfckX/T8j+5e5umxfeE6W/rWr8ZNNwAAAE5uvg3oTz75pHXq1MnKly8femzMmDHWrFkzi4uLsxIlSljfvn1t3759Ea/77LPPrF69epY3b14rV66cPf/88xHPT5s2zerXr2/58+e3jh072qZNm0LPaV0NGza0v/7666jcsqBnz55uH3W/75tuuinqcrrPsfeVL18+d49yBdkpU6ZELHf55Zfb/Pnz7WTy3//+173PuuUbcCrZOH6B5atW3GIL5HU/677nS98ebwue+M4F8Wj3ZLfsMZY8c2UW7C0AAABO6YC+Y8cO+9///mc33HBD6LEZM2bYeeedZx06dHAh+9NPP7VvvvnG7r///tAy33//vV111VV2yy232OzZs23AgAH20ksv2euvvx5apkePHtamTRubOnWqC4ZPPfVU6DlVc88880w7/fTTM30My5Yts71799r5559vJUuWdBcMUjNo0CBbvXq1zZkzx9544w3btm2bnXHGGfbBBx+ElsmTJ4/rKDiZnHbaaVapUiX76KOPsnpXgOPmwN79ljRtuSU0KBvxeEK9Mpa/VslUX5dQt4xt/mvxcdhDAAAAZBVfBvTvvvvOcuXKZU2aNAk9pkBep04de/jhh61y5crWsmVLe+6551ygTU5Odst8+OGHroVaAb1ixYouHD/wwAP27LPPhlpD//nnH7vxxhutatWq1rVrV/ez/Pvvv+6igCq66Q3gqvCrEh8fH29dunSxtWvXhtrRa9eu7b7Xfqg6nlarvlrX1RGgboFzzjnHvvjiC3ehQRX4zZs3R21x1wWL1q1bu24CbV+V/8mTJ4eenzBhgjVv3twFe7XZ33nnnbZ9+/bQ85988ok1atQo1I1w5ZVX2rp160LPa7vah6JFi7p1qLKvCwme5cuXu2PWPhUqVMidi/Bj3L9/v/Xu3ds9X7hwYbvvvvuitueqi0H7Apwqti9YazHZs1me0gVDjxU79zQrcHp5iy2Y+oU8Vdx3r9pqezYd/D0GAADAycWXAX38+PEucIbbvXu35c6dO+IxBcddu3aF2sFTW2bFihW2dOlS93PdunVt9OjRrp1dLfMK/aJQr8CvwHo4Bw4ccIFU7fHjxo1z61PAVxu66L8//fST+17t8qqOKyRnRK9evdyFB607GoXn0qVL26RJk9zxq5MgNjbWPbdo0SLXaXDJJZfYzJkz3cUNBXYFfo+q+/369XNB/6uvvnLhWq31noceesj+/vtv15WgixhvvvmmFSlSJPTa9u3bu3Ol9+q3335zFyq0zT179oS6EXRR4b333nPb1rn68ssvDzkOdSvoHOm9A04FO5duslylEjL8utiEPJY9Xy7buezgsBwAAACcXHwZ0BWmS5UqFfGYAuHEiRPt448/dtVZjet+/PHH3XMKwN4yw4cPd8FbIVpjtr1JyLxl3n33XVehVmt1zpw5XYVdlXe1oDdu3NitQxV6jY9OjdY/a9YsGzp0qLuQ4LWjK6wrMOuigKrGogq0KtTZs2fP0DmoXr26+29qlXdV8Nu2beuWU3X7sssucxcf5Omnn3YB/u6773bPadz+q6++6vZRFzTkmmuusXPPPddV+NWpoOcVxtVe761fY/VVZVdlX9tStVsU+HV+dS7VKVCjRg1XXddrxo4d65bRpHg6t507d3bPv/XWW5aQcGgo0fusUL9mzZoMnR/gRLV3607LkT/yQmJ65YjLZfu27Dzq+wQAAAB/8GVA37lz5yGVcLV+a8I3VbrV/q4WdY1JF82SLmpdV5X4ggsucOFbwVMzhYcvU6tWLRekdRFAAVvV4EceecSNU7/jjjtcmFVVWUF/xIgRUfdPFWVVxMOr4jVr1nTt3F7LfGZ57eBqj49G7eMaT6/g/Mwzz7iquUf7r+q1qtrely48KFR7nQQax6/AXbZsWVcJ15ABUciWW2+91bWea8I9tafr4kj4+hcuXOhe561fbe4K/9oPje3XBRFduPDkyJHDhf2UdDHDm3cAOBUE9h2wmBxH9k9vTGx2N4YdAAAAJydfBnS1Untjr1OG0i1btrgQuWHDBtdmLqoCe2FW481VBVYQVVXWm/DNWybaOlVpVru4qr+qRGs2dY1f96rBWcEL+hUqVIj6/KOPPuomldN+/vzzz+4CgddCruO/+eabbfr06aEvheoFCxaE1qfKtsauDxkyxFX9vdd6LeqqruscqtV+1apVdvbZZ9s999wTWr86B8LXry91LGgse0Z4s+ir0wA4FWTPG2sHdu09otce2LnXsufLedT3CQAAAP7gy4Cu1mqNf45GIVxt0aq8qt1dVewGDRpELKN28sTERFdF1zJNmzaNGgDVqq4g7I3NVuu8Kuqi/+rnaNSyrUnS9OXR/urigYLy0aAWcQVoVchToy4CBegff/zRBW5vEjedD+2PWvVTfumceMFYlXdNJKc2+fAJ4jw6Z927d3ezrGt/dF93b/0K+5pVPuX61cauL81c/+eff4bWpTH/KW8dJ5ptXxdHvPHtwMkuV4kE27M+OJQkIw7s2+8miMtdIuPj1wEAAHBi8GVAVzu2qsMpq+hqcdfYbz2nCc4UMDV22hvfraq6xjrPnTvXVXTvuusu+/zzz124TEnt2ArmCp1e+7tusaZZ4VVtHjZsmPs5GoVmjb3WOG/drk2TnHXr1s21iUdr4z4cBXtV+1Wx1qRwl156qWu/18Rs4TO3hw8B0L6rwq/XaJI2VcF14UB073W1pGsZnQeF6a+//jpikjgF9ddee81Nbqfb1el8htNs+XqNWtl1vr/99tvQ+nXcCtTqYNAkcYsXL3b7opniNSGf6Nzr/dEEdHo/brvtNnecKen1Gr4AnCryVSpqu9cn2/6dwW4VUfDetWar7d+22wVxfa+vwP4DoWV2rdjsWuNzlzk4+zsAAABOLr4M6Aq/qtJ+9tlnEY9rEjNVfBWCR44c6QKkbqsW7v3333fPK1wrWCo4Rruv+WOPPebawzXG2qOwr0DbokULNz5bs6CnVsXXtgsWLOiWVWBXC70mTzsS1113nas4q5Ktsd8a063Qn1q7uC5IbNy40V0UUBVdtztTS7qOSTQzvcbZq+Vc50sdCQrc4RPvKfzr4oUq/grSL7zwQsQ2vAn0tC4do7bp3Q5NE+r9+uuvbvy6Nwmc7lmvix6q+kufPn3cRHSqwKuDQePVL7744ohtaHkFeM0dAJwqchWPt9wlEyx5TnDiSln7zQxbNnC8bZ2yzPZu3O6+19e+5OCkjpI8a5XF1060bLEZm3ASAAAAJ46YQLSbU/uAAvi9997rWqC9CjcyLykpybWgayI3L0xnFV0k0Nh3tej7ndrwV67sYXFx8W7eAqTPxxac+R+Rts1faxtG/2PlbmuZ6kSQ4fbv2GOLX//Fyt3YPM17pZ/Kulr0ST0BAKeO/v37W3JyHzfU1evqxImTDRCUw3xK1W21Zut2ahm9hzhODLpvu9rsgVNN/qrFbe+m7bYvaZe7v/nh7N2yw4qfV5twDgAAcJLzbUAXza6Ok5duEwecqgo2iX5niWhylyrgvgAAAHByo3ccAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAPkBABwAAAADABwjoAAAAAAD4AAEdAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8IEcWb0DAE5eXW1EVu8CgDS0avUo5wfwqbFj+f0ETkVU0AEAAAAA8AECOgAAAAAAPkBABwAAAADABwjoAAAAAAD4AAEdAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAPkBABwAAAADABwjoAAAAAAD4AAEdAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAPkBABwAAAADABwjoAAAAAAD4AAEdAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAPkBABwAAAADABwjoAAAAAAD4AAEdAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAPkBABwAAAADABwjoAAAAAAD4AAEdAAAAAAAfIKADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAPkBABwAA8InWrR+zCRPmZsm2p09f4ra/bduuNJe74oqX7Ysv/jhu+wUAp5IcWb0DAAAAfqOgmpbu3Vvatde2ivrcmjVbrGvXV+ydd262ypVLHNX9euaZr+yHH2a473PkyGbFiiXYOefUtauvbm7Zs2eu7lKrVhkbNqyP5cuXy/08atR0e/31Ufbtt/dHLPfWWzda7tw5M7UtAEB0BHQAAIAUFFQ9P/882wYPHmsffNAz9FiePFkXUE8/vbL17dvJ9uzZZ3/+ucBeeeU7F9avuqp5ptYbG5vdChXKf9jlChTIl6ntAABSR0AHAABIITyo5s+fO+KxAwcC9uGHv9q3306xrVt3WNmyReymm9q64CyqnsuNNw50/61bt5y9/PK1NnfuSnv33Z9twYLVtn//AatUqYTdfnt7q1q15BEH6U6dGruW+IkT57uAnpy80157bZT9/vt827t3n9WtW97uuKODlS5dOFTdf/XV723WrGW2b99+K168gN1ySztr0qSKa3Hv1et9GzGiry1cuMaeffbriG4Cr2tALe6XXtrEffXrN8ydj0ceuTS0f1rvJZe8aLfd1t7at6/rnv/44wn27bdTbdOmbW5funVrYS1b1uRzBwApENABAAAyYNiwP+zzz3+33r0vcC3s338/zR588GMbNOg2Fz7ffLOH3Xrru/bCC9dYhQrFLEeO7O51O3bscYH1zjvPtUAgYJ999rvdf/8Q++ijOyxv3mBb+ZHImTPWtm7d6b5/5pmvbeXKjfbkk1e4db799k92//1DbfDg29x+qNquAP3KK9e6NvWlS9dH7QZQu7suHoR3DkRbrm3b2vbYY5/bzp17Qs9PmrTIdu/ea82bV3c/Dx063kaPnmW9ep3vzs/MmUvtySeHW0JCXqtXr/wRHzcAnIyYJA4AACADFKyvuOJMa9PmNFc9v/nmdi6oexOneS3gCqCqdMfH53E/N2hQwdq1q+NeU65cUevTp6MLsjNmLD2i86+QP2XKvzZp0kJr0KC8rVix0SZOnGf33HOh1alTzu3Tgw92tg0bkkITz61bt9VOO62MVaxY3EqVKmhNm1Z1Ff5oVfrwzgF9RQvo6hpQ0B8//p/QYz/9NMuaNavmLhCoDX/IkAl2330XumW1zQ4d6rnzMGLElCM6bgA4mVFBBwAASKft23fbhg3JLuSG08+LFq1N87Vq737vvZ9t+vSltmXLdtfmroC+du3WDJ1/ta+fe+5T7vVqHz/77NrWvXsrmzp1sZsorkaNxNCyukhQpkwRW7p0g/u5c+cz7KWXRtqkSf9aw4YVrEWLmlapUvEjfv+1vVatarpQrsnqVEnXRYKHHrrEPb9y5SbbtWuv3XPPhxGvUxW/cuWMtfYDwKmAgA4AAHAcaAb2pKSd1rNnBytePMFy5sxht9/+PxdWM6J+/QquXVwt60WKxGVo9vbzz29gjRtXsj/+WGCTJy+yoUMn2K23nuOC+5Fq27aO3X33YNu8ebtbp47LG4+vwC5PP32lFS0af0iVHgAQiRZ3AACAdNItyBSKZ89eHvG4flbbunhjzlXhTrlM586nuwnZNDZdAVWTzGVU7tyxlphYyIX88HBerlwRt81//lkZekzrX758g5UvH9w30a3ZLrywkT3++OXWpUtTGzlyatTt6DhUoT8cdQ8UKxZvv/wy28aMmeUq6t450HZ1nGqt1z6Hf2k/AACRqKADAABkwOWXN3OTp2k8tcZ5637hmvVc472lYMF8litXDjc2XFVjVZQ1nrt06UI2evRMq1atlGuVHzhwtFvuaNEEbGeeWc1eeGGE9elzgRsz/s47Y6xIkXj3uOi+5qpulylT2JKTd9m0aUusbNmD4T1ciRIFXAVc49x1nLlyxbqLA9Gozf6bb6a4cfAvvdQ99LjGoet8vfHGDy7s165d1h377NnL3HMajw4AOIiADgAAkAFqB9++fZe9+eaPbiy5KudPPtk1dCszVbXvuONc++CDcTZo0FgXSnWbtXvvvdBefPFbu+mmt13FuUePs906jibdH123WXvggaGudV6TxT3zzJWhivaBAwfcTO7r1ye5boDGjSu72dpTq4xfeGFDe/zxL1xrvnebtWg0m/tHH413Vf2U4/Ovv761GwuvdvrVqze7ixVVqpTM9H3bAeBkFBPQFKA4ZSQlJVlCQoJt3brV4uMjx4IhdaVLl7aVK3tYXFy89e7dm1MF4KTQqtWjWb0LAFIxdiy/nxnVv39/S07uY4mJibZixQo+W+lANvAfxqADAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8wSRyAY6ZrqY6cXRwXH68awZkGAAAnPCroAAAAJzndKq179zcOuTd7Zt1227s2btzfR3WdAHAqo4IOAACQCa1bP5bm82ndniw96+7X73I766zqlhkDB/5kV1/d3N0CTqZPX2K9er1/yHLDhvWxQoXyu+9nzFhqn3460ebPX2UbN26Luh/XXNPC3eO8efMali1bTKb2EQBAQAcAAMgUhVrPzz/PtsGDx9oHH/QMPZYnT84sPcOzZi2zVas2WcuWNQ95Tvup+6F7ChTIF/p+1649VqlScTv33Hr28MOfRV336adXtuef/8b+/HOBNW1a9RgdAQCcOqigAwAAZIJXcZb8+XMf8tjIkVPts89+t9WrN1uJEgWsc+cz7KKLGrvn9u7dbwMG/GC//vqPJSfvdK/r2LGhXXVVc7viipfdMg899Kn7b/HiCfbJJ3fbwoVrXNV63rxVFhNjlphY2Pr0ucCqVSsVdf900aBRo0qWM+ehf/YVLJgvtM8pnXFGFfeVFlXktcwvv8whoAPAUUBABwAAOEZGj55pgwb9YnfeeZ5VqVLCFixYYy++OMJy5461Dh3q2fDhf9rEifPskUcutWLFEmz9+iRbt26re+1bb91oF1/8gvXt28lVqr0W8iefHG5VqpS0Xr3Od48psHut69HMnLnM2rY9LepzPXq85S4SVKhQzLXi165dNsPHWKNGog0dOiHDrwMAHIqADgAAcIyo3f3WW8+xFi1quJ9LlixoS5eut2+/neIC+tq1W10FXME4JibGVdhTtpurwh1ekVeAv/zyZla2bBH3c+nShdPch7Vrt1jhwnERj2l9Cviquiugq8qvMekDBvSwqlVLZugYtW5dWDhwIMA4dADIJAI6AADAMbBz5x5btWqzG6P9wgsHbwWomdS9tnKF9Hvv/dC6dXvdGjeu7NrEGzeulOZ6L7usqVufqvMNG1Z0Y8sTEwuluvyePfsOaW9XuPcCvpx2Whm3r1988Yf95z8XZ+g4c+XK4cL53r37LFeu2Ay9FgAQiYAOAABwjAK69OnT0WrWLB3xnNeurmr10KF3uUnWpk791x577HMXuh97rEuq69WM8GefXdv++GO+/fXXQlelf+ihS9xM6tEkJOS15ORdh93fGjVK2axZyzN4lGZJSTtdyz7hHAAyj4AOAABwDKiNvEiRODc5XLt2dVJdTrOot2lzmvtq0aKm9e07xIXe+Pg8liNHtqj3Li9TprCVKdPUVdP79Rtmo0ZNTzWgV65cwrXVH87ChWutcOGDrfTptWTJOjcmHgCQeQR0AACAY0TV7tde+97y5cvtJnpTG7hmX1dFu0uXpm52d4ViBVyNQR837m8X7L0WeI1Jnzp1sRujHhub3bWqv/XWaNfWruc09nvu3JWhMe7RqGX+hx9mRDymVna9XpPDqQVeY9CnTVtszz13dUQHwMqVm0I/60KDJqSLi8vjZpQPn4SuUaOKR/nMAcCpiYAOAABwjJx/fgPX+v3ppxNt4MDRrhW8QoXidumlZ7jn8+bNaZ98MtFWrNjoZmLXpG3PPHNlqAVeE8wNGPCjC9Cqxn/44R2uuv7001/a5s3bXft68+bV7brrWqe6D23b1rGBA3+yZcs2hMada2K4N9/80TZsSHb7VLFicXvhhWusfv0KodfpQoImjvNoP6R9+7p2//0Xue91gWDOnOX24IOdj9EZBIBTS0wgEAhk9U7g+ElKSrKEhATbunWrxcfHc+rTqXTp0rZyZQ+Li4u33r17c97SqWupjpwrHBcfrzo4ARfSr1WrRzldp4i33vrRtm/f7cbDH0266KBugHvu4d/7o23sWH4/M6p///6WnNzHEhMTbcWKFUf9PTkZkQ38J/WbZiLTBg8ebAUKHLxdyolGrXZfffVVmstce+21dtFFwavowMlk+MTl1vjuUXaiqn7zt/bT9DVpLnP/4Ol2+4BJx22fAGSdq69uYcWLF3CzrR9NBQvms+uvT716DwDIGFrcD0MB9P33D7Z3eRYsWGCVK1e2rL4AcN1114XCdKlSpaxdu3b27LPPWrFixTK9/tWrV1vBggXd90uWLLEKFSrYtGnTrF69eqFlXnnlFaMJA36lAPrV74deQf+hX2srVyx4f+GsvADwn/eDY0JjYsyKJeS2ZjWK2D2da1jh+FyZXv/459paQt7g7Y5WbNhhbR/82b78b3OrUebguNEHL69l9FABpwaNab/66uZHfb1dujQ76usEgFMZAT0dOnToYIMGDYp4rGjRouYHalOfN2+eHThwwGbMmOEC+6pVq+yHH37I9LpLlChx2GXULg/4WfNaRe2p7nUjHisUl/kAfDTkz53Dvn+8lamgNW9Fkgvs67butv/dFRybmhlFE4ITTKUlLg/3KwYAAPATWtzTIVeuXC6shn9lz57djXOpXbu25cuXz8qUKWO33Xabbdu2LdX1KEC3bt3a4uLiXLBu2LChTZ48OfT8hAkTrHnz5pYnTx63vjvvvNO2b9+e5r6pcq79UfX83HPPda/56aefbOfOnS60P/744278tI5BlW8959mzZ4/17NnTSpYsablz57Zy5crZ008/HbXFXdVzqV+/vnu8VatWh7S4v/32224/tN1wnTp1suuvvz7089dff20NGjRw26xYUfd6fcz27duXnrcCyLCcObK5sBr+lT1bjA0a/a91fGyc1b/je2t1/0/22NBZtn1X6p/DucuTrNuLv1uDO7+3hneNss5PjrdZS7aEnp+ycJNd9fxEq9vzO7e+Jz6ZbTt2p/25VuVc+1O8QG5rcVoxu7p1efv9n/W2a89+14b6xrfzrWXfn6z27d/ZRf1+tfGz14Veu2ffAXv841nW/N7RVuf276zNA2Ns4PcLo7a4q3ouFz8x3j1+zYsTD2lx//TXpdb8vtGHtL/eNmBSqNIvY6avsc5P/Oq2qfW+PmK+7YtyCygAAABkHAE9E7Jly2avvvqqzZkzx7XB//zzz3bfffeluvxVV13lwvKkSZNsypQpdv/991tsbLCCtWjRIlepv+SSS2zmzJn26aefusCuAJ0RCvcKyAq8aj9/8cUX7YUXXnDrbN++vV1xxRWhZbXv33zzjX322WeuCj9kyBArX7581PX+9ddf7r8K+Gp9Hz58+CHLXHbZZbZx40b75ZdfQo9t2rTJRo0a5Y5dxo8fb926dbO77rrL/v77bxs4cKBr1X/yySczdJxAZmmC5AevqGUjHmlpz1xbz/6Yu8FeGP5Pqsvf+940K1Ewt33xn+Y27D9n2U0dKlls9uA/ocvWb7cbX/3Tzqlfwr5+qIX1v7GBTV24yfp9PDtD+5Q7Z3ZXTd93IGAf/LzYXUS479Iabp1n1SzqwvKStcGLgB/+vNh+mbHWXrqpgavCP39DfUssnCfqej9/4Cz330F3N3Gt76/d0uiQZTo0LGlbtu+1P+dtDD22ZfseGz9nvXU8PdH9PHnBRus7aLpdc3YFG/loS3vsqtr25e/L7a3vDl4YAAAAwJEjoKfDt99+a/nz5w99KYjK3Xff7SriCrVt2rSxJ554woXd1Cxbtszatm1r1atXtypVqrj11K0bbL1V5VohVuvUc82aNXMB+oMPPrBdu3al683UuPi33nrLGjVq5Kr0CuZ9+/Z1obxatWpubLoq/uH7o22dddZZrnqu/3bt2jXqur2W/sKFC7uKfaFChQ5ZRuPVVcUfOnRo6LEvvvjCihQp4s6TqFquCxPdu3d31XONme/Xr58L6sCxMHbWOlf19r7uGjjFPd69bUVrUq2IlS6S15pUL2J3dapm309elep6Vm3aaU1rFLGKJfJb+eL5rUPDUla9TPBOCG9/v9AuOD3RrVPPNahUyB684jT7+o8Vtnvv/nTtp4L3J78utdPKJbjW9/dGL7Ie7SvZ+Y0T3TbvuaSG294HYxa75Vdv2unG0TesXMgSC+d1/9U+RFMwf0733wL5Y13FvkC+4M/hEvLltBa1itq3k1aGHvthymormD/WzqhW2P38xrcL7MYOle3ipmWsTNF8dmbNonbXhdXs0/FL03WMAAAASBtj0NNB4fLNN98M/ayWdq+arGA9d+5cd4sCVa0Vpnfs2GF58+Y9ZD26PVePHj3sww8/dEFdAb1SpUqh9ndVuVXF9mjyNVXDFy9ebDVq1Ii6b7pdmi4aaDltWyH73XffdfujsehnnnlmxPJNmjSxqVOnhtrTFZAV3lW9v+CCC+ycc86xzNBFhhtvvNEGDBjg2up1PLpAoG4D7zh/++23iIr5/v370zxvQGYoXD5y5cELU3lyZXf/nfjPehes/127zbbt3Gf7DwRs994DtnPPfsuTM7hMuGvbVrCHPphp3/yx0gV1VZzLFg3+WzB3RZLNW5ls3/51MNxq8jVVwzVBW6WScVH3LXnnPnfRQG3lu/cdsIaVClm/bnVs2869tm7LbmtQOfJCmIK/tiUXNytj17/8h3V4eKwbZ9+qTnFXZc+Mjmck2kMfzrRHup5mOWOz24i/Vtp5jRJD92PWtqcu2mQDv18Qes3hzhsAAADSj4CeDgrkKWds16zmCrS33nqrC5uqKKsl/YYbbnBju6MFzUcffdSuvPJKGzlypH3//ff2yCOP2CeffGIXX3yxG7t+8803uzHkKZUtWzbVfVOlXIFbAVhjydXiLgroh6Nx4Ar/2hddbOjSpYu7cKCq95Hq2LGju7CgY2zcuLFraX/ppZdCz+s4VUXv3LnzIa/VmHTgaFNoTDlju0LzLa9Psq4ty9ndF1W3hHyxriX9wQ9m2t59B6IGzTs6VnMV6nGz1tmvs9fZayPmW/8e9a1d/ZK2Y/d+u7x5WbumTXCuhnAlC0VvO5d8uXPY8Aebu3Z7VbbV4i4K6IdTq2yCjXmyjf06e739Pne99Xp7irtw8OrNh7avp1frOsXdhQV1HdQuX8CNq3+gS63Q8xpTf0fHqu6YU8qVg4YsAACAzCKgHyGNIVfVWmO8vepwWu3tnqpVq7qvXr16uXZyzQ6vgK6wrDHZGb11m7Yd7TWahE4Ttqla3bJly9Djf/zxxyHLXX755e7r0ksvdZV0jRtP2cKeM2fOULU7LQrZCt+qnC9cuNBV53VsHn2v8e5ZfYs6nNrmLNvqLiT1vbRmqDo8avLqw76uQvH87uvathWt97tTbfjEFS6s1iwbb4tWb8vwrdu06WivyZ8n1ooVyOUuGpxeNdheLqpeKziHL3de41Lu65wGJe3GV/9y48ZTtrDH/n94VrU7Lblis1u7+iVc5Vzj6nWsuhDgqVk2wRav3Z7lt6gDAAA4WRHQj5AC5t69e+21115zVWMFYY3/To1mVb/33ntdCNaM6CtWrHCTxWlSONFYcbWfa1I4tcGraq/APnr0aHv99dePaB+1PVXp1UavGdx1MWDWrFmh5zULvarumpldQf/zzz9348sLFDgYADy6r7qq85rwTRPdKYindos1tbmru0CT51199dURzz388MPuOXUF6Fxou2p7nz17thvDDxwP5Yrms737A/bRL4td1Xjqos1u/HdqNKv6c8P+tvYNSrox62s377LZS7bYOf9fSb6xfWW7/JkJblb1y84q6yrwCuy//bPeHu56sL0+I25oV8lV6dVGr7HnX05c7maSf/76+u55TSBXNCGXC82aDV7jxYvG57L4KLdOKxyX03LHZrMJc9ZbiYJ5LFdstlRvsaY2d3UXLFyVbBeeUTriudvOr2K3vj7JShbMY+0blnQXGNT2vmBlsutEAAAAQOYQ0I+QJndTwNXEaw888IC1aNHCjUfXDOXR6LZsmuFcz69du9ZNnKZKs9q9pU6dOjZu3Dh78MEH3a3WVN1TsFZl+0ipXV5j1Pv06WPr1q2zmjVrupZ676KA2uOfe+45N7mc9k8t6d99912oIyBcjhw53KR1um2bQrb2cezYsVG3qwnzVIFXpVwt/eE0k7wm3dN6dO40i70mzdNFCeB4UeC9/7Ka9s4Pi6z/l3OtUZXC1vvi6m6G8mhUZdcM5/cPmm4bkve4idPa1Stpd1xY1T1frXS8fXhPM3vpq7nuVmtSpmheO7dhqSPeR7XLa4z6s1/8bZuSd7tx7ANua+wmoZN8ubPb/35cZEvXbbdsMTGusj7wjtNDHQHhcmTP5iatG/DtfHv1m3nWsEoh+7BPs6jb1cR5avlXpfyC0yP3v3mtYvZmz8Y2YOQCe/eHhW69msDu0rPKHPFxAgAA4KCYgJIgThkam67Kt4K72tuRPuoaWLmyh8XFxbvJ/pA+XUt15FThuPh41QjO9BFo1epRzhvgU2PH8vuZUSqeJSf3scTERNetisMjG/gPs/oAAAAAAOADBHQAAAAAAHyAgA4AAAAAgA8Q0AEAAAAA8AECOgAAAAAAJ3pA123DdH/sJUuWmB+9/fbbVqZMGXfbsJdfftlOdOXLlz+hj0Ofk5iYGJs+PXgrK93nXbOjb9++Pat3DTimNm/bY83u+dFWbNhx1NbZ+52p9t7oRUdtfQAAADjBA/qTTz5pnTp1csHRowCW8kv33vZMmzbN6tevb/nz57eOHTvapk2bQs/t27fPGjZsaH/99ZcdjVsG9OzZ0/r27WsrV660m266Kepy2r/cuXPb0qVLIx6/6KKL7Nprr7Vj7dFHHw2dJ91rXPdH1z3VFcR3794dseykSZNSPY4Tke7L3qRJE3dLDOBk9tZ3C+zsusWtdJG87ufqN397yNfISSsjXvPnvA3W+Ylfrfbt39k5//3Zhk9cHvH8LedVtoHfLbTknXuP67EAAADAhwF9x44d9r///c9uuOGGQ54bNGiQrV69OvSlsOvp0aOHtWnTxqZOneruxf3UU0+FnnvxxRftzDPPtNNPP90ya9myZbZ37147//zzrWTJkpY3b/AP42gUjh9++GHLKrVq1XLnSfv8yy+/2GWXXWZPP/20NWvWzJKTk0PLFS1aNM3jOBFdd9119uabb7qLM8DJaOee/Tbst+V2yZllIx5/qntdG/9c29BX23olQs+p0n7L65Ps9GpF7Kv/NrduZ1ewhz6caePnrAstUzUx3soUzWvf/BEZ7AEAAHAKBvTvvvvOcuXK5SqgKRUoUMBKlCgR+lKF2vPPP//YjTfeaFWrVrWuXbu6n+Xff/91gV9V+fRQmFX1XpX4+Ph469Kli61du9Y9N3jwYKtdu7b7vmLFii6Ap9WGr0r7Rx99ZLNnz051GVWz77zzTtfSr+M566yzXEXbM3bsWLedMWPGWKNGjVyQVsCeN2/eYY9FlXOdp1KlSrn9vuOOO2zcuHFuf5599tmoLe6BQMBV38uWLeveB71W+xe+v/fcc48lJiZavnz57IwzznD76FHngs6/nte+arsff/xxxH598cUX7vE8efJY4cKFrW3bthHt6O+++67VqFHDnY/q1avbgAEDIl6vTgh1S+h5nRN1T6TUrl07ty86XuBkNG7WWssZm83qVSwY8Xh83lgrmpA79JUrNnvouU/GLXXV9vsvq2mVSsbZ1a0rWPsGJe39nxZHrKN1neL23eRVx+1YAAAA4NOAPn78eNeOHs3tt9/uWrVVCX/vvfdcmPTUrVvXRo8e7SqmCrN16tRxj99yyy323HPPWVxc3GG3feDAARfOvWCn9SngX3755e55/fenn34KhURVpzUWPTWq2l9wwQV2//33p7rMfffdZ8OGDbP333/fVf8rV65s7du3j2jRlwcffNB1AkyePNkF7+uvv96OhALvueeea8OHD4/6vPblpZdesoEDB9qCBQvsq6++Cl2U8C46/P777254wcyZM11VvkOHDrZoUXDM6q5du9z7N3LkSHchQK3z11xzTWh4gc6ZArz2XxdRFO47d+4cei+HDBniug50QUXPqxPioYcecudHtm3b5s6p2tinTJniLibogkFKOXPmtHr16rnPE3AymrJwk9Uqm3DI449/PMua9P7BLnt6vA37bVnEv5PT/91sTasXiVj+zJpF3ePh6pQvYDOXbLE9e/cfwyMAAADA8ZLjSF+oMduq2qb0+OOPuxZ2VWV//PFHu+2221xY86q7qrrqsRdeeMEF4wceeMA+/PBDt3zjxo1d6FWIvOKKK+yJJ56Ium0F+1mzZtnixYtDwfuDDz5wreKqams9qvh6beGqTh+OWsp1sUBBsXnz5hHPqWqsNmxV5hWa5Z133nEXBlT1v/fee0PLKrC2bNnSfa/ArxZ7heHwLoKMhHSdw9Q6CHRcqmrHxsa6Sro3NEDPaZiB/uu9RwrHo0aNcp0CosfDA7Oq9j/88IN99tlnbj0K6LqIolBerlw5t0z4BYBHHnnEXYjQ81KhQgU36ZsuGHTv3t2GDh3qLqTo/OjY9d6sWLHCbr311kOORfuScg4A4GSxauNOK1Yg8vf/zgurWpNqRSx3zuz229/r7bGhs2377v3WrU0F9/z6pN1WOD5XxGuKxOe0bbv22a49+93rROvdu++AWz6x8Mk1/AUAAOBUdMQBfefOnVFDp6qoHrU3K9w+//zzoYCuoBbezqyZ4BX2fv31VxcS1RauqrFCttqyNZFcSqrYKpiHV8VVqVVrvZ7TazNKr+/WrZsL1b/99lvEc7pgoPHsuqDgUShWkPVa9D1eR4Bo7LusW7cutA3Pf/7zH/eVFlXU1DYfjSriandXC78q4+edd547V6ra6+LF/v373TCCcGp713AA0fP9+vVzgVyT6O3Zs8c9741xV6fD2Wef7UK5Lpqcc845dumll1rBggXde6pzovkHNFzBo0CfkBCsFOq86FyEf0aaNm0a9VjUQq85DYCT0a69ByxXjshmpdvOP/i7WbNsghun/t6Pi0IBPb1yxQbXq9AOAACAUzigq4V98+bIdstoFLIVBBX+NFY6pd69e9vdd9/tbrelNmpVzTVmWpVn/RwtoB8rjz32mAu1ahc/UgruHi9cq5Ks4/NuLyaFChU67LoUclWZjkYXJzS+Xa38quSrK0EXQnTxQx0L2bNnd63l+m/K0P/ll1/aK6+8Yq+//roL+QrhOud6HxTURa/TeidOnOiq+K+99ppr3//zzz9DIV5dBHp/w6XcXnpomEClSpUy/DrgRFAwf6xt3ZH2TOt1KhSwASMXuFb1nLHZrWh8LtuYFHkXhw1Jeyx/7hyh6rl46y0Ud+i/rQAAADiFxqCrOq6W5sNRKFXVNVo4V6u6QqjGS3tVXVWqRf/Vz9FoYrLly5e7L4/2ZcuWLRFV6oxS6NW+qLIdvm2FR42VDq+sa//UTp/e7amyrXHr3tfhAvrcuXNdS/oll1yS6jKqPOsCxquvvuouZmjMuarnem+0/6rch29TX8WLF3evVdDWOP6rr77aVctViZ8/f37E+nWBQV0DunChCd50DhTutQ61pWvcf8r1excU9B5p7Lva+z1//PFH1OPQGHjtM3AyqlEmwRat3pbmMnOXJ1lC3lgXzkUTyv0+d0PEMhP/WX/IRHMLViZbiYK5rWD+nMdgzwEAAHDCVNDV9qzx46qiK4DLiBEj3Ezqmtldrc2qwGrysGiTgym4KQxr5vBs2YLXCRQG33jjDTfJnCZBS+3+2Bp3rarvVVdd5SrAaq1WBVljvzVbeGbomFQZ1vh2b9I5VZc1dlpjzRWsNd5bE9qpLTvabeYySvu/Zs0aV2lXy7/XSaDJ08LHt4fTeHiFcFWwVdHW2HIFdo0X1/h7nRu17GucuMLv+vXr3QURhWjvosM333zjKuR6/3Su9d55FxwU4LW8Wts1c71+1joUvEWhXcMW1NKuFnt1SGhiPH0e1BVx5ZVXuoq7WuB1TjWLvuYdSEmPq8Ve7ylwMjqrVlF76cu5tnX7HkvIl9N+nrHWNibvtroVCriZ2xW8B36/0K5rVzH0mitalrMhY5fY88P+drdn+2PuBhs1ZbW91TNy+M7khZvc5HEAAAA4xQO6AnKDBg3cGOabb7451N6tgN2rVy/XSq0wqOAXPk7Zo4CnNnaFUI8qwQp2LVq0cAEzteqxKrtff/21G7OuZRXwFRLVhp1ZCuB9+/Y9ZHz4M8884wK0ZjrXvcl1IUCTqnkXJzJjzpw5bry62sMVeBWSFWp1USBa54FovL32SWFYQV3vhy6QeJPjaZI4hfw+ffq4AKwhCbpw0qpVK/e8Lppo0jZdaFHA1yzuul+97k0vGquueQF0ASQpKckFf4V9b5I83c9er1NbvS4i6CKG9kFt8qLb32l/NDu/LhDomHTLuJTvqS7Q6CKANxEdcLKplhjvxpl/P2W1XdGinMVmj7GhY5fY058Fb1lYtmg+63tZTety1sH7pOsWawrjz3z+t33w8xIrUSC39bumjjWvVSy0zO69+23M9DX2zp2Rw0wAAABw4ooJhN/bJ4N0iy6FM7Uoe1Vw+JvCti4CKIh7E8ZlFY13r1KlipvxPXwCPj/SHAIrV/awuLh4d1EE6dO11PGbQ8LPxs5aa88P+8dGPNzSsmWLPvFjRn08bomNnrbG3ru7yVFZ34nu41UjsnoXTkitWj2a1bsAIBVjx/L7mVEqDCYn97HExERXiMKJlQ2QyQq6qAKue3CrQpvWfcaBaHQbOHUq+D2cA5nVqnZxW7p2u63dsstKFspzVE5ojuzZ7L9XnHZU1gUAAICTIKCL19IMZJQ3sRxwKuje9uAY86PhsrCWeAAAAJwc6EsHAAAAAMAHCOgAAAAAAPgAAR0AAAAAAB8goAMAAAAA4AMEdAAAAAAAfICADgAAAADAyXCbNQAATnT16plddFHw+0cftZNOnjy6LWrw+/79zXbvtpNWq1bBN3Du3K9szZrp6X5d9eoXWYkS9WzevBG2evWUY7iHAACkjoAOADgpXXutWfnywe8PHDDbu9csOdls+XKzv/4yW7364LLbt5utWGEnrTPPNMuVy+z33w+G8xw5FEovtvj4RMuTp7DFxMRYUtIKmzr1XTsVLV/+uwvo5cq1sDVrplkgcCCrdwkAcAoioAMATmr79pmtWWMWH29WuLBZkSJmdeqYjRxpNnVqcJkFC4JfJ6Ps2c0aNAh+P3PmwccV0EuUqGu7dyfZ/v27LUeO3HYq2759rW3bttby5y9uhQtXtQ0b5mb1LgEATkEEdADASW3bNrN3/78oXKqUWZcuZgUKmJ1/vtmyZWYbNkRvcS9d2qxNG4VYs5w5g+tR0P/hB7PNm4PLJCaqpdqsTJlg4F2/3mz8eLO//z64/bZtzapWDV4giI0127HDbNEis59+Cq5T8uc3O+ccswoVgu3ou3YF1zVx4sELB3Fxwf2pXNksb16zpCSzadPMJkwIdgikpmLF4PLqHgjvGlAlfeLEF2zPnm1Wr961VqDA/7cbpEOTJndb7twFbNmyCZY9e04rVqy2q8CvXTvLFi4cZYHAfrdcTEx2K1euuXtey+/bt8s2bpxv//472vbu3RFaX0JCWVe5jo8vbdmy5bCdOze7Kraq2maBDG0zmrx5i1j58q3dMepCxM6dm2zlyj9t1arJEctp3xTQtW4COgAgKzBJHADglLFqldn33x+sLNevH325mBizK68MhluFX4Vlhevq1RUmg8solF9/vVmVKsH2+S1bzEqWDF4AqFv34LoUqBXOt24127QpGMZ1QaBr14PL6GKBqvq6ELBundn+/cH2fF0AEIX2Hj2C+6tltD9apwJ7x45pH3PZssH/rlwZ+XggYC6cZ0bp0k2sWLHTXPBW8E1MbGwVK7YNPX/aaZdb+fKtLE+egrZjx3rLli27lSxZ310QUBAXhea6dbtboUKVLRAI2K5dWy1fvqJWqdI5VrXqBRneZkp58hSyBg16WLFitVyg37FjgwvsWne5ci0jlk1OXhm6YAAAQFaggg4AOKWoau4pWjT6MrlzB6vOMnBgsPrsLa8KuCgcK+SrGj5kSDDIt29v1rRp8LkZM4LLDR8eDNQKxKJ28wsvDIbvggWD1fhChYLPffut2axZwe8V5LUfcvrpwQsDqrgPGBDch2rVgiFfYV9Ve4X/aNTWL7qAcLQpTE+ZMtD2799jNWpcYsWL13aBecmSsZY/fwnXKi7Tp79vW7cutZw589sZZ9xl+fIVc1VqVckV4BXcd+3aYpMnv+WCd+XKHVwQL1mygauY79q1OV3bVKt+SmXLNndBXu3rGl9/4MBeS0w8w6pUOdfKlj3LVqz43a3LW7fkyhVn2bLFumUBADieCOgAgFOKquOHs3NncDI5VcnvvDMYflXZVru5F6C96nalSmYPPxz5eoVptaQr2KtFXu3zGvuu6nc4LaOAPn++WfHiZhdfbNa6dbDtfskSsylTIrel0H7ffYcej55PLaBrcjjZE8ygR5Vawr1wu27dbBeWVRnPm7ewm3zOU7/+dYe8Vu3sCuhxccHlNm5c4MK5qG1dAV0V77i4khEBPa1tJievirKd4PrVut6ixYMRz2XPHmv58hW3pKTl7ufwgK9Qv2cPAR0AcHwR0AEcMx+vGsHZhe94Ld+iynZq3n/frHbt4PKqnNesGfxZIVljwz0aC66vlLJlC75WoVshWlVvbU8h3avcaxkZMyZY2Vc7fLFiZuXKBcetq8196NDIcePR9lkt9qnxZm1PeXFAxo4NDrjXdjQuPympdOixtKhqr+r+ihVNbezYpu4xVfR1fmTKlJvcOnXxQqLNkL9oUUMbO7ahm2FenQirVjW2sWMbu+d0waFhw+Byc+Z0cWP607NNDWHQnAAyd+5FNn36Re59y5cvOFO/N3dAuKlTbwjtn4YonHGGd276HJOLGgAApIWADgA4ZWiSuA4dgt+rJX16GrfJVvVcz2siNrngArNGjYLhWQFdYVAhVK3jH3wQnC1eNDZcQU9jzhUOvYq9WtPVon7WWcGJ48IpyC9denBCuNNOM7v00uC2RNtSYNc+f/HFwXZ1he4aNRRGUz8Or7LujZ0/mjT+/pdfgtX5WrWCj+k8b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 "id": "PKri",
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 "outputs": [
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 "text/markdown": "<span class=\"markdown prose dark:prose-invert contents\"><h2 id=\"why-this-matters\">Why This Matters</h2>\n<span class=\"paragraph\">This example shows why Bayes' Theorem is important:</span>\n<ol>\n<li><strong>High false positive rate</strong> combined with <strong>low prevalence</strong> leads to counterintuitive results</li>\n<li><strong>95% accurate tests</strong> can still give misleading results when the condition is rare</li>\n<li><strong>Bayes' Theorem forces us to think about</strong>:<ul>\n<li>Our initial beliefs (prior probability)</li>\n<li>How likely we are to observe evidence given our beliefs</li>\n<li>How to update our beliefs in light of new evidence</li>\n</ul>\n</li>\n</ol>\n<span class=\"paragraph\">This same logic applies to:</span>\n<ul>\n<li>Spam detection</li>\n<li>Financial risk assessment</li>\n<li>Scientific hypothesis testing</li>\n<li>Machine learning classification</li>\n</ul></span>"
 }
 }
 ],
 "console": []
 },
 {
 "id": "WyvZ",
 "code_hash": null,
 "outputs": [
 {
 "type": "data",
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 {
 "id": "IAFF",
 "code_hash": null,
 "outputs": [],
 "console": []
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}