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@karino2
Created February 2, 2017 13:41
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{"cells":[{"cell_type":"markdown","metadata":{},"source":["# 8.4.4 Belief Propagationとsum-product"]},{"cell_type":"markdown","metadata":{},"source":["factor graphのツリーに対して適用出来る、マージナルを求めるアルゴリズムを考える。\nマージナルはランダム変数のノードかファクターノードに繋がってるランダム変数のサブセットに対して求める。 \n元のネットワークがツリーか有向ポリツリーの場合を考える。(ここでツリーの定義)"]},{"cell_type":"markdown","metadata":{},"source":["## ある確率変数ノードのマージナル\n\nまずある確率変数ノードxについてのマージナルを求める事を考える。\n観測値が無いケースから。\n\n定義から同時確率はファクターの積で表せて、それはさらにxの回りのノードで分解して以下のように表せる。(ノーマライズはされてるとする。されてない場合は最後にすれば良い。後述)"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\n+NNbsVh03X7SK4S3llt23ZTa8kZ2uAxVwSFIIHH/ALVv/By3/wAExv2Z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bfs2/t26R+wL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\ntP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8uwTvONrX1iqjXNKc11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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["さて、この同時確率をマージナライズする為に和を取る。\nこの時、和を取るランダム変数は各サブツリーごとに直交している事に注意(ファクターグラフがツリーだから)\n\nそこで和はこの$F_s$ごとに別々に取れる。\nこの$f_s$からの寄与をメッセージと解釈して8.64のように置く。\nこれはファクターからランダム変数へのメッセージ。\n\nこうして、周辺のノードからのメッセージが分かれば、それを掛け合わせればそのノードのマージナルが分かる(8.63)"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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30FvJcWbHlbW7ilMpXkbkjZQC8hfyL4q/wDBwT+0X8QP+DhLw/8AE6X9q7xd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\nfjR/wcm/8G89x+1xZ3//AAUC/YQ8HpD8V9Lg+0eM/Cmlx7H8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K/AjQv2Pv+Dzz9t26Nh8c/2o0+EGm26krdXHib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\nOP2+Yvail6y/yTPta/8A26/2GdKna11T9s/4V20kf345/iBpqMv1Bn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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["メッセージの実際の式は8.64と8.67。\n\nここで、青のメッセージの積だけで同時確率が表せている事に注意。\n緑のメッセージは、その青のメッセージの構成要素。\n\n青は「ファクターからランダム変数」で、緑は「ランダム変数からファクター」となっている。 "]},{"cell_type":"markdown","metadata":{},"source":["青は一つ前の緑の積と自身のファクターの積の和を求めて、自身に繋がってるノードで和を取った物になる。(8.66)\n\n緑は一つ前の青の積となる。(8.69)\n\nあとはこの2つを交互に葉まで戻れば良い。 \nこの2つの式が重要なのでここに2つ並べておく。\nまず一つ目のファクターからランダム変数へのメッセージは以下:"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAs0AAAHmCAYAAACIzLPpAAAABHNCSVQICAgIfAhkiAAAIABJREFU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\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uvowTNNu7EswSv/h6NE8IwitPf4LHL+N/w64f1aNl6CRaBttRN6BEff9RNAwcM5vWsZIn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u56EU2yXC4aRyQdE0WcJUmSZOwuGYZhmP5GRwddOEPV2LpcwPAU5fJ0fj61fuZGJ/HJxKuUeuY9\nRUB5ubKjoI/8fODZHRSETrwq8L7Jk4C3Diu7ynm9VGD21DaaYL1YFFqhmNNJS/ynTwOjRpEud3QG\nMG5caB3sGhuBy/PFAd+DK0N3v6ivBy7xmzDa7cD/tUQ2EXI6ga+NCNxmsQB/awse0E+aLJ7IWCzk\nGT1zRvjj8ue8YeqtyLVISQH+3h7eaxbvp9bkcv5y2viaAA6aGYZhmKgybbo4c7mnCFgw3/zxMMGR\nB83p6cCH9RSI1tcDbxwkiU1XF2VQJ0wI9B4u3k/BcGcnLfv/eHP8tmFubKSCQpEue+oUCvbDmdx9\n54pAN4lwgm85F45WSpsOl2i39gaAhYuUk52UFODnB42zgmtsBP57XHjPtduBf3aG99zycmDSNcrt\nvz2lT4MeCizPYBiGYaLKkiXioPm+5VT5HusucIyStWuAm2aR04LNBry8ty/ozcpSNvCQM+92+ot3\nGhuBKwvEjT4yM0kmE+5qyIrlgW21t2yljG4kQeqEPGXQfOxY8KD56e0kY3izhOQp102l71hesxAJ\nIveMWKLWuTESONPMMAzDRBWvlyrkRYVlFgvw7M6+yn0mfmhrI/u3MWOMDa7ihfp6yjCLAuaMDNLz\nR/K+Rce9wwH8oTZ8rW3RHmDxksBtVivwj47YauAB4NsTxG4mkyeRjl3LHs/hIDlFONTWAt8SFCee\nOB66r3ww2D2DYRiGiSoWC/CzYvHyvNdLQUDxfvPHxWjjcFDQ0R8DZgC4Z4k4YHY4gF8ei/x9Wyyk\n0fbPVLe1AQ/r8HpW45rJysy32x2Z+4QRlL6tbv+3dg3puU8cBw4dBH5doXwPdwk0yXoRtXMHgJ4w\ntNXB4KCZYRiGiTrZ2eQQocb8BcCatdSNrexE+HZnDKOXdkHhWUYGFaga5eySl6f0PH5pr3axnNtN\nGWWRpCk9XeyH/Njjgfpps9myRbx95gyaeKWk0L8zZ9Bn8vI+ei8OB7B5U/it0wHSzYeyPRJYnsEw\nDMOYRvF+4IGV4gyfD5uNLL5YssFEk7ITwG2307Fos1Gh3v+sNr5gUSTTUCveq6qirnttX3aIFBWz\nVVVRkaEcux34TVVs2q+LChQB4P33jCs0VENNnhGNQmPONDMMwzCmMe924M/NVCQlX6K1WoHVq4CP\nGjlgZqLP5EkkG/i4Cfi0izLC0XD4sFgCm50A4mYnJYdJY93m11JdVMyWlyduPNLdDVw71djujHoR\njTM/P/oBs9lw0MwwDMOYis0GbN1CWbHCderFNd4AACAASURBVOSesWI5FUht3tR/NbRM/GG1mtNk\nR0136+PgIWDW7MBiuQXz1YPOnzwhzii3tAA36WhnbTQ3TFduM8sVR80lI9hnHg5sOccwDMPEhOxs\n431UGSbeKC8HntkRuM2/9XNzM3CnTEaQnU02cWrYbMBbJWK7vKoqkkGZafn39HYKXg8eosz6/Sto\nImwGpwWyEABIjoKbCGeaGYZhGIZhokB9PWmU5XZrV/hlkO9coLz/xaLgFnKZmRQ4ix534EB44w0X\nmw147QDg/QL4vDfyJi6hoFY0PGqU8a/FQTPDMAzDMIzBNDdTa255JnjRwr4VlspKpeuF//3ByMsD\nfn5IWR/Q2iZ+fH+kokK5zWIBRo40/rU4aGYYhmEYhjGYOxcoreWmTqFmPj7kra2B0ItgJ0+iffoH\nziI7vf5Idzc1TpEzYUL4nRy1YE0zwzAMwzCMgYgyyFlZ5E/sH8wdLwt8THo6MF5gnxaMRQuBMZnA\nps2AxxPePhKR42Vk6SfnKoM7Afpgn2aGYRiGiZDqaqC9gzq2RcO2jEk8LskhTTMAzJ1D2WB5+2zL\nYOXzfI9JSgK+OxP48WZqDsIomXgVTVDkiPytjYCDZoZhGIYJk44O4O6Ffd3bHA7gV+Xm2Jgx8Y3b\nDZw8SdpatYYj/zUq0JdZRMFE4ESZ9mMGImpNXhwO4C+no/OarGlmGIZhmDDo7KRCL/92x21t1AKZ\nYaxWah2t1aFP1KRETvn7YgnCQMbrBe5ZIr4vmlZ3nGlmmASjpaUFR48exdGjR9HV1QUAGDNmDMaN\nG4cbbrgB6Zzi6te0tVGwNmaMUgbQ0gIcKaX7R46kLmRZWbEZ50Dg6DFg+g3K7dnZ1LglGoVITP/C\n7QZunEEtvbX4tCu4Bd1AYsNGYOOjyu1WK/C3NqUMxig4aGaYBKKwsBCPPio4U3zJkCFD8MILL2De\nvHkmjooxgx07gV27+zSSdju1/fVlVVY+SA0U5BmpzZuoNXWoOJ3AS3tpCXTECGqUkJcX/Hn+eL3A\nmyXAsWN0e9HC0PdhJh0dQEMDkJOj76Lb2Ql8ewJNVuQUrqPvh2G0aGwkl43qavXHTJ4EvHPMvDHF\nO+XlwKRrxPc9uDK6HtEcNDNMAvHNb34TH330UdDHHTlyBNOnC/qaMgnJ0mUUMIt44nEK2nbsFN8P\nAL+vCS3j3NgI3DiTfGb90RuAe73Ac7uAbdsD92GxUAY23roAulzAQ6v6PuP0dOB31foC5zNngF8c\nBebMDdxusQB/biZ9JcOIKDlMnQDltnT+FEwkH+ZoZU4TjcpK4NqpymYwAH1GHzVGt2iSNc0G4/V6\nUVtbCy8LkJgocOuttwIARowYgbvuugtPPfUUnnzySVx33XUBj7vhhhuwY8cO0S6YBGPvPvWAGQC2\nbKUAVYu7F9G/LldwbWRbG12U5AEzAKxZK94u557FwPIVysd6vTReM6ivp+z7t8YD8xcAtbXixzmd\n1IrY/zNuaQFOVokfL2foUOCG6UrdqtcLrONMM6NC2QngljnqAbPFAqxdQwWAHDATJYeBqyeLA2aA\n3Emi7jIiMYZx6tQpacyYMRIA6Yorroj1cJgBxlNPPSUB+OovNTVV6uzsjPWwmAjo6pKk4SmSNCgp\n8r/L8+nfc+2SdM9iSerpUb5eT48kXZytvZ8nt2iP+XhZ8LFE+7B8pViSzrEpX/dHm5SPvXaK8nHn\n2CSpqSm013zsceV+Blslqb3dmPfE9B9aW+l3qPb7uGmWJNXVxXqU8cWPNmmfU+6cb844ONNsELW1\ntbjuuuvQ0NAAAKioqIBLa82FYQxmxYoVuP/++7+63dnZiWeeeSaGI2Ii5Y2D1PHKn7S04M8T+QT7\nGi24XOTu8JBAZrFhY59m2n9f/pKMYJnmkyeDj++9cu0laX/cbmrYMGky6YcnXgWsWq2uAW1upky3\nKBsl93MtO6EswLJagXfLtB0PRHxvkfJz93pJosIw/rxZojz+LRZg9izyFz50kAt4fTidwIyZQOF6\n9cfk5gZ2WYwq5sTm/ZvW1lZpxIgRAVm+CRMmxHpYkiRJksfjkXp7e2M9DMYkent7pXHjxgVkmz0e\nT6yHxYTJU9sCsynDUySpoSF4JveBlfqyzxUVfa9VUyN+zJsldP+RUsrKBsuAyTNCd84X7/f8NEl6\n46D2vpqaJOmyPO2MXFdX4HNEmeNBSZJ09SR6j/6IxibKRutFtL+LMsPfH9M/8Xgk6YUiSbp7oSQ9\ntIr+zysSSl4oCr7Sdlle9Feu/OFMc4R4vV7ccccdaJc1ev/+978fk7HU19dj27ZtuP7663HBBRdg\nyJAhGDJkCIYPH47rr78epaWlrLfux1itVtx8881f3e7s7ERNTU0MR8REwsiRgbc9HnKy0CI3l5wu\n9OCv4xVpjZctBWbOoP9Pn0YV/MEyYN+dGXi7t1f8OKcTuO129cy100nFiFquAiWHgXuX9t2urBRb\nd73/HmlD5QWIFYJOYtdMDt5sQo25c5XbmpvF7hpGU14OfHMMcOFooPTt6L8eEz4WCznJ7CmiQt5F\nC/WtIA0UqqpoRWnxEuVKmz/p6cDrB0zulmhefN4/eeaZZxQZ5hp5OiOK9PT0SEePHpXuuOMOKTU1\nNWAsan9jxoxhrWs/5uTJkwHf90svvRTrITFh0t6u1Oa+tFc78/L/2Tv/uKiq/P+/cEZAGARlzClI\nUFBwoZUWSlJUTFxppRULN1rpK1u00kapG21UVlja6oYfsbRwF1v8hBsWFvTBXUzYMMEgscaEQAUb\nDHJQEEYYZGCu8/3jOuPM3HPnFzP8sPN8PHjonHvvOWdmYOZ93+d1Xu/cvaw2ebyL+UzzBHeNpr9f\no5HJuOcPRY+btZ3NsI4TajQP/Mb0HFb9jtzHk3+0LFs+Tngz+521nXtswSJy/zIZua/1GzSaO/1s\ny1719pL7zNtnfV/W0N3NZu71VyToAiNlLKFWazS1tezqkSV/8wsWDW+GWQvNNA+BlpYWpKen6x4L\nhUJkZ2djzjD4KR09ehSrVq2CWCxGbGws8vPz0dHRYdG1jY2NyM3NdfAMKSOFr1F6srKycoRmQhkq\nU6cCRw4b7p6XyfjP9/QEklazRRDCwsz3r1IBTU2sdtp4ASp5DTv+wU+AXy9js5f19Ww2d/e7rMWa\n1pnCOBv03J/ZDBAALFtmeg4HP+Fmh0+e5FbV8/EBzjcB39cBj/zO8FjtjWw0ySEjehF53ONfkdvf\nfofNNOfvNz1vEu7uZC20sU7c3pSVs5l5LQoF6zdNoYxmjh4F9v+L3aMwM4jds1D8mfnrnv4T+7k4\nrBnmGwiHf8hbh6ysLPTrrT1mZGRgroOd+0+ePInk5GTU1dVZdL5QKIRarea019bW2ntqlFGCWCw2\neN+1VQMpY5P589kgVLsRxpR0QH8zmsjC6mHSU9wNcgBb3vfMmZv+w3wVy06dAoRCdqlZn+BgdunZ\n39/8HLZsYQs4aDH+4hQI2M152mKXQqNvLu2veGsrt29juy6FAtjwZ9bKzxS2SjRCQ7iSk4qjtvVl\nKYdp4QvKGGTf/5r/O9QnIADY8T+sVGykoJlmG+ns7DTI1opEIgPnAkeM9+ijjyIiIsJswCwWi+F/\n45uKFDADgFQqRb2j0x+UEcHFxcXgfW+kKacxz/Hj7L8uLmxWkY+1f7S+b5kMqDP6KPD2ZrXRlnoV\nk7LfLi5ssF9jQR9HvzTMEpcaBYH6PsgMwx+EygjaYWMN+O9XW/ZFPX+++XNIkPImMpl5f+yhYLSl\nBgAgEjluPArFHrzzNqvnNoenJ/A/24GG+pENmAGaabaZgoICgyxzSkoKvB20VlBcXIzk5GSzGcPY\n2FgkJSVBrVYjOTnZ5LlNTU2IiIhAYWEhrRx3CxIYGIimpiYA7HvNMAwEAsEIz4piK2vXsv8+/ji3\n8pyWJfdbb5MGsKWjjT9atNnhqPlsltdcwMf3EdLeDmRtt2weW94EProh6bjxq6tjyZKb/y85xM0C\na+fb28vt19/P8HGTBcVZFi28uQHSWkgbNTs72bkNtUhFezsrpRGJ2Ix2eDjbTrpZoFBGO+7uwN/3\nAOueZeVYdXVAxw2ZkUgELPs1uzE3IoL9HBoN0KDZRoqKigwex8XF2X0MhmGQkZGBrKws3nNEIhFS\nUlKQmpqKoKAgAMDKlSst6r+/vx9JSUmQSqXw8/MzfwFlzODv768Lmvv7+1FXVzcsWnuKY/jtg+yP\nsc5XnyeeMHzs789mcPXx9jbUvgKspMF4QcrVlf03IAD44H+BPXsM+xIIWK2wRAKsWMH6y5LI308O\nuN3duT61JYfYto4Orkba15cNGNVq4MWXuM8pehF7rfFzI/HwQ8C2v/EfDw8HPv7IfD988GV4u7uH\nFjTvfpf11tb3n/7bNjabT9rO0tFh200UhTLchISwmeSxAJVn2EB7ezsqKip0j0UiESIjI+06hlKp\nRExMjMmAWatt3rFjhy5gBgCZ0Vqpq/YbkEB3dzdSUlKoDd0thvFmQP3fV8rY5SiPLCEoCEh42LDt\njdfZzXP6RBKkAx2dgJeXYVtd3c2g9pHfsXZtV7uBCzL255qStZ/73338ATPD8Af5EeHcNpWKK8vQ\n8tDDwB2+wDR/VmetT+IjbDDKtw/aOIh9cwurj854gXuuuzvwVdXQNhjxfdzq67Db29n30pSdlj47\n32bLkhsXbPnLC+wGTdIiJJ/VH4VCsR0aNNtAaWmpgWY0MjIS7u4W7rqxgLa2NkRHR/MGOr6+vigo\nKMA///lPYobYWMaxfv161NXVISkpiRhAl5WVmQzOKWMP45u4akvKtFFGNQzDr2d+7VXu8qWPD6sB\n/OgAm8X5phYQi7nX9vZyg1iFAsg12tjn7s726eNj2VJpySFugKvF2H9aS3Gx+X718fRkM60AOXAE\nuJsGAWDhQmDWLPK5Q10G5tlGomsv/gyYHgDcH8M6BpjbWqJQcLPr+mzfTq5+SKFQ7A8Nmm3A2MLL\nntIMpVKJuLg4XneL6OhoSKVSPEJy0b+BvvWcSCRCRkYGQkJC8MEHH6CkpARCwrdIZmYm2tvbh/4E\nKKMC40wz3Qw49qmuZjOUxvj4cLPMWtzd2UzwumfZwh6kALK3lyvtAIA/P8f+6AdkCgWbIbXEWWLL\nm/zHQkK4WXCA3eBH0iWTEAjY0rl8jhpajLPoprB0bFPwBe/a9g1/vvmadnYCr7xqur/Ll00HxcYS\nHC3WPG8KhWIZNGi2AeOsXUREhF36ZRgGcXFxvBXc0tPTUVpaanbDYa/eJ39SUhI89YR0S5YsIWaV\n+/v7R613c2dnJ8rLy1FebsI2gGJAaGioweO6ujqoaDpqTNPBo9d9+SXLs6OkLKhIxG62CSdIJna+\nDdw1h63M9ew64O5wNkM6O8R0hrSz03Qlv+hF3MqBABuMk4JfPfUZAHaux44a+jWby/AaQ8q6Mwx/\nhUJL4QuavbzY18W4OmCrmRsQPz92I5SW0bIhikL5OUKDZivp7Ow0sHwTCoV2C5o3b97MK8nIy8vD\nW2+9BRetCasJAgMDdf+Pj4/nHE9LSyPOubS01PLJOoCqqio8//zzePLJJ/GHP/wBK1euxOLFiyGR\nSBATE4OYmBg8+eSTDp0DwzCoqqrCSVPf+GMA40yzWq2m2eYxTnAQty08nPVmthRSQKeVJLy3+6bH\nsz7Nzaw2efe7NwM+pRIoMiGlMKWn9fNjbdn4tL+TJ3Pb4pazhU3ON7Ga6q+rudZupjbgkQjj2RfL\np6u2FD6LPVKQDrA3F6ZuQMaPZzXYh0qAmq/YGxwKhTIy0KDZSoyzzKGhoRYFsuYoLy9HZmYm8Vh2\ndjbWrFljcV8pKSkA2MBpGaEcl0AgQFpaGqd9JItgbNmyBVFRUcjKykJubi7y8vJQVFSEiooKA/24\nIze07du3D6GhoYiKikJERITDA3RHIhAI4GW0PttKqvxAGTMEBbHaZG2mMSgI+HC/dZlHUtZVa8kW\nHg58+C/LHR707s05aLXPJJJWs//ybQNxduZuxKuuYYNtPz/+fvnkCHwZeh+fm9IOfXa/y3X2sAZj\nz2uAfT7u7uy/JBMbc8VP3NyA2GVsxtnSHA31aaZQ7A8Nmq3E2Jki0NQ3h4WoVCqkpqYSj6WmpmLd\nunVW9bd+/Xps3boVu3bt4j1HRPhE7bWHoM8G9u/fj40bN1p0Lt/rNBRUKhVWrlyJ5ORkg2xsbm4u\nqkil0sYIYqPUlvHvLmXsse5Z4GIbcLySLSdtraUY6U9cf1FixW+Bb0+SC3To4+dHllfo88/3uYFx\nQAD7HMxh7PJRVWW+SIq3NzlTTir8oUUbwOtz5gzw6O+5VnltbazG+9l1/BKO9nZy1jg4+Ob/SWW9\n+VxRSFj6Mc232ZJCodgODZqtxLganz2C5qysLJ2nrj7R0dEmA18+XFxc8MILL2DFCv5vNVIAZbyk\nPxzU19frMuPmiI2NtXvVxc7OTsTExHB8t7UUFhbadbzhxPjGqIPPk4sypvD2Nh/U8kHSCxu3+fmx\neuG3d7JFPvQz2QIBW5Hr/4rJAao+S+5n3Tte+Atb9evd3WxAbomdG2GBzKSDhBZSYRH9SoPGrP0j\nOVN/6N/AY//v5uPOTmDBIlbjvftd9v8kl04+dxN9dxJSpcGDn3C1ziQYhi1uYg5PT/PvD4VCsR4a\nNFuJceBhvOHKWtrb27F161ZOu5eXF/Lz8x1SxU2lUhE3A2pLbw8XSqUSiYmJBpUVtYSFhSEpKQm5\nublwdnZGaGio3V8PhUKBqKgojhuKPiSnkbGCsTyDBs2U1UaZVYHAcDOdfvvTf2L9ma8pWY/m801A\njwL4rJh1v7AEHx/WF/nve9gA1VJnzoSHuUHf0S+B/f8in9/eDpT/l6xT5tlXrZvfep6FvAMfAdv/\nh/3/tr8ZBrXt7QDpY4MvY7xIL7scvYgcqJcc4p+nltLDljmXUOcMCsUx0KDZSuRGa30kmYM1ZGVl\nEWUR2dnZ8OET7w2RrKwszvMA2EzucLJx40ZO5h5gM+zffvstPvjgAzzxxBNQqVQ4ffq03cuUp6Sk\nEDfH6WvLh/r+jiTGAT/pPaf8vFjz/9iMr6cnm/H95/tk1wx9BAI22PXzs2/2krRI5+3Nzm3qVNYV\nxJj/twb47QpWJvH4E8Cvl7FFT+7wZYNYkl64ssp0GfA3Xud/DTa9Dly8COTtM2x3dweiogzbGIa8\niVAgMNy85+3Nlic3xhKP6n37zJ9DoVAciIZiFRERERoAup/Kykqb++ro6NC4uroa9AdAExERoVGr\n1Xac9U3q6uqIYwYGBjpsTBIdHR0aoVDImYdEItHI5XKHj5+dnc0ZG4AmJSVF093drXucn5/v8Lk4\niujoaIPnFh8fP9JTolB0yOUajYenRjNOePNn6a9vHu/u1mhu9zE8zvfj4cn2V1ZOPt7YaHouvb0a\nzd3h5GtffY08XuYmwz4qKsjX6z8nLbt2c88b76LRtLbyz7GuzrLXYpxQo5keYPHbQKFQrIBmmq3E\nWHs8lM1zOTk5RGnC5s2bHSLLUCqVSEhIII6ZmZnpkDH5yM3NNXDF0G+fOnWqQ8dWKBTYvHkzpz0h\nIQH/+Mc/4OnpiaysLCQlJREt+8YKxvKMkXRHoVCMmTqVtVJb9ms2g71oIfCPv9887ukJfPC/lvX1\n1t/Y/my1kXN3Z+dCko98+y23TakEXn+D1SJr2f0uuW+SPptUjIZhTEs0nv8L/zFjWlvZOTY3s9KS\nw59bfi2FQjHBSEftYw0vLy+D7F1FRYXNfQUGBnIynVFRUXacrSFJSUnE7GpkZKTDxuQjJiaGM4+Y\nmJhhGTs9PZ2Y4e7u7h6W8YeLuLi4YfvdolAcRf5+01nVR3+v0egvkpEyxisfsmys6QHca1fEmx5b\no9FoZDLy8fEubAacxIJF3PMX308+N2eP5Vlm7U/ePo1mgvvNx8//xeKXnEKh8EAzzVZinK0zzuZZ\nypkzZ4iOGST/ZHuwe/du5Ofnc9pdXV2HvRKgSqUi+i0nJSU5fOz29nZkZ2dz2tPS0gwqJ94KGK+C\njJSlIIUyFFb/nrXXe/pPhh7Nc+YA7+9ls9H6i2QkS7fiz8xX+jtzhuxgERLCb+3XdKPPVY+Qj8ev\nYDPgJEgbMI9+ybWsa2nhdw7x9ARuv5187PEnDMtvZ+80XY6bQqGYhwbNVsCY2k1iJaRS2SKRyCFy\ngOLiYt5gPCsrCyGWboW3E3V1dURpRnR0tMPH3rVrF2dsLy8vu1vZUSgU+xEUxFrgXZCxP1e7gW9q\n2Y2Nxqqy5cvJfWx63fQYO98mt//qV8CRw2zwboyXJxuQ8xUQXbuWf7zER8gbK7WOHVo2/BlQKMh9\npK4F5t3HP4Y+DMNfUpxCoVgGDZqtgKQFNi4gYSkkn+SwsDC7VBfUp76+njeDm5ycjKefftqu41mC\ncVVFAJBIJPAjleeyIwqFguh7nZ6eDndLvbDGEPZaFaFQRhM+Pqat65bcT7bE2/8vtjAJX7W/akLx\nlJAQNlsskQC1hMD49tuBJ/9I7i88nJ0LH97e5AIx+ftZSzuALV9e/Bn5eh8f1mGEpJkmERRkueUf\nhUIhQ4NmKyBlR0ltlkAqaWxvT+C2tjZER0cTl+UjIyNtKpxiD0hZ9sjISIePm5ubywkkhUKhQ6oM\njgZIdn4Uys8Bkl0dwG7Wu28+W6zEmFBCoP3XN9lMdtZ2Vr5hzPcN5L4AYMd28/N8gbC5j2GAV15l\n+zW1+e+9d9kgOH6FZVaAT//J/DkUCsU0NGi2AlJQa2ugSwpk7ZkJ7OzsRGxsLLGgha+vLwoLC0cs\nu0ryRg4LC3P4uKSqf/Hx8Xb3fx4NKJVKzg2drasiFMpY45Hf8Xsv19cDpPvJt/528xp3d1Yvvfw3\nrDTCWDIBsGWqv/mGPMaK35Ir/xkzZw45G523D3ghg1+W8cTj7NwANmOd/pzpcRYtBFKeMD8fCoVi\nGho0W4E9M82urq6cNntZgqlUKsTGxhIzja6urigpKXFY4RRLIAXNjq5G2N7eTqz8l56e7tBxRwrS\nJtPhrvhIoYwknx403DioD6lm0dSpwNfVADPIaqbX3CijXXCAHLxqJRTGeHsD7/Doo0m89iq3jWGA\nz/6PfL6PD5sB1+f1TWzFRRJr/wj859+0rDaFYg9o0GwFpKDW1opxvr6+nLbq6mrU1BCEdVaSkpKC\n2tpaTrtQKERhYSHmkMpmDRPt7e3E7LejM80ktw5fX19EREQ4dNyRgqSZp0Ez5eeEjw9wooYNGvU3\nC67+vfkqiPqQqs+PHw8MDpLP/8ff+YN1EvPnAw8/xG3nk3388302MDfm3d2sy8i/9rObJv++B/ip\nlW2nATOFYh/sK6L9GdLa2mrT8n5oaCinrb+/H1FRUcjNzcWaNWtsms+mTZuI1nIA6xyxnG9r+TBB\nyn4LhUIEBwc7dNyysjJOW3R0tMmCLgzD6EpP9/f3Q61WIzAwcFiLwNgK6aaJdKNGGVm2nH0X0qsN\niJu6GGvuJEROlCExdSobNL71N6CxERAKyaW2TWG83cLJiT9gfvklVpphLX99ky1sYmwJZxycv/yS\n6c2FQUHsD4VCcQw0aB4itsozYmNjERYWxtkUp1arkZycjLq6OqSkpFgVpB08eBCZmZnEY5mZmVhr\nyv9omCA5ZwQGBtrdNcQY0uZD/UCdYRhIpVLk5eWhsbERTU1N6Ojo4GjPRSIREhISsHnz5hGVuJhj\nJCQwFOvY9+MneOXMDgDAwYulNGh2IO7u1mWX9VlyPyt/KC8H2n4CCMonAGzGmCS1sISAAOCN14G/\nvGDYPjjIapHvuAMIDSVnpCkUyjAy0tVVxhLd3d2cSnJDqQhYV1enEYlExCp92h+xWKyJi4vTZGVl\nacrKyjS9vb3EvqRSqUYoFBL7SEpKsnmO9iYlJYUzv5SUFIeO2d/fT3xdysrKNBqNRpOfn68JDg42\n+T6Q3pfS0lKHznsokKpNdnR0jPS0KDdQX1drgv/7a43TZ4Eap88CNZLDw1+Vk2IdRcX81femTOWv\n/Gcp3d0azSRvbt+vvGqf+VMolKFDNc1WQNIvk/S5lhISEoKSkhLipkD9/ktKSpCeno6YmBhIJBIs\nXboUW7ZswcmTJ6FQKNDZ2Ym4uDhi1jsmJmbYK/6ZgiQbcHQGVCuxMEYsFmPp0qVISkoiZmZN0dHR\ngbi4OOzcudMeU7QrKpWKsxEwMDDwlnQJGas0KVtwpve87nHC7bEjOBuKOaqqgEcJxU0ANot95DB/\n5T9L8fQEklZz2638aKJQKA6EBs1WIBAIOLZwfAGZpSxatAi1tbUIDAy06Pze3l6UlZVh48aNiIiI\ngFgsRkxMDNH32d/fHwUFBQ6XPlgDX1GX4R5TKBQiLCyMqHW2FLVajfXr1+PQoUNDmJ39MSdFoYw8\nTUrDes0SlykjNBOKOVQq4Mm15BLUAgHw8UfW66T5WEEodjKEvAyFQrEzNGi2EuPg1h42cSEhIaiu\nrraphLZarSYGSa6ursjPzx9V2cWWlhbi6+XoTDPp9bFVi04iKyvLbn3ZA5JufDh8sCmWo9YwRo9p\nfePRyq7d5MImnp5shnnZr+03VvQibsbawnwKhUIZBmjQbCXGBSJIfri24O3tjU8//RQVFRWIj4+3\n2cpOi9aJ4+6778bu3buh4HPJH0b4qiA6OgtqzXsUFRWFjIwM5Ofno7KyEpWVlairq4NUKsX69euJ\n11RUVEBFSkONEKSbBIlEMgIzofAhdp5k8Liu59wIzYRijqNHuW1z5gDHjgKLFtl3LIEASHzEsI2U\nfaZQKCMDdc+wEuOsKEmjOxQWLVqERYsWgWEY1NXVobq6GhUVFZBKpVbrbgE2gEpLS0NGRgYyMjKQ\nmpo6YtlnPu9gR1u4WVJOOiEhAZmZmQgJIdTSvcGOHTsQFhaG5ORkzjG5XA4/P7+hTNNujFTFRYrl\nSFwMb75lfdwbSsro4Lk/A3X1QEsLPtmOnAAAIABJREFU65DxxOOs9thRH1vP/RkoPcxmt1/4y83K\nfxTKz50zvedRJD8CqaIBag2DGPE8JN/5EFwEwydBpUGzlRgXw2hsbIRCoYCnp6ddxxEIBJgzZw7m\nzJmjs4prbm5GRUWF7oeUueWjt7cXGzduxK5du1BYWIj5ltR4tTOk0uFDzahbAl/QLBKJkJSUhMzM\nTEy1cBcPXylq0nMbCRiGIQbNVNM8ujDWMDf2ngejYSBwGv0e4D83Fi0Czp0B+vvZTX+OxseHLVJC\noVBuckrRgIKfDqGiowY13exq6sGLpcj78RPk/yoLAe7Dk7Si8gwriTRyuler1cTyzI4gICAAycnJ\nkMlkxICZL6DTRy6XIyYmxi6VB62FpGc23lhpb5RKJdHhZNeuXZDJZHjvvfcsDpgBfqnHaJE/yGQy\nzussFotHlbadArgL3eA34abPt5Lpg7z/8gjOiGIKgWB4AmYKhUJmjuds/HV2OiqjCrAj5GVde023\nFLHVj0Op7huWedCg2UqCg4M5gd5QHBisJS0tjRiki0QiVFRUoLKyEqmpqSaD0f7+fqSmpg67Dre/\nv5/T5uigmS/IjYqKsimQJJXjHk1BKUnPbHyjRxkdhHrMMnhcq6DpRQqFQjGFwEmAtOmPwcf1ZqKq\nue8Css/nDcv4NGi2EoFAgLi4OIO2vLw8MAzDc4X92Lt3L3JycojH8vPzERISgvnz5+O9995Da2sr\ncnJyOHISLVKpFNnZ2Y6cLgeSPZ8pj2p7IBSSFUiWZOWNaWlpQUlJCac9KirK6r4cBXXOGDt4jZ9o\n8Lixt3mEZkKhUChjB4GTgONtX9E5PKvnNGi2gcTERIPH3d3dKC0tdeiYhw8fRkpKCvFYVlYWVhht\nsXZ3d8fatWtx4sQJ3gIqRUVFDpkrH6RMM6nNnvBppkmbEk2hUqmQlJTEW0BmtEDKhPPdOFFGlmDR\nDIPHjT3nec6kUCgUij6ya4YS1eGy7aRBsw1ER0dzZAWFhYUOG6+5uRkJCQnEY/Hx8bxWaFqWL1+O\nrVu3ctrtZZdnKSRNs6lMM8MwOHz4MJ566iksWLAA06dPx8yZM3HPPfdg6dKlePLJJ7F9+3a0t7fz\n9iGRSIjZZmtdTzIzM4myGC8vLyQlJVnVl6NQKBREeYavr+8IzIZijtCJhvKM4cqUUCgUylim7Zoc\nJe1fGLSJBMOz6YAGzTbg7u7OyTYXFBSYDN5sRalUIjExkejOEBYWhvz8fIss20hL9EMp8KFUKrFt\n2zasXLkS27dvt1kfTQqaGYbBwYMHERERgdjYWOTk5KCyshIymQxNTU2ora1FWVkZcnNzkZ6ejsDA\nQBQXFxP7d3FxIT53UkaWj4MHDxJvOgB2Q6G9nVNspaysjPOeikQiKs8YpURNDjd43HKtDc1GlQIp\nFAqFchMVo0JC7TNgjApEJfkOj6E5DZptxDi72N/fj127dtl9nI0bNxKzomKxGAUFBXC3cEs3SY5g\n6ya88vJyREREICMjA0VFRUhPT0dSUpJZXTdpPOPs85kzZxAdHY2EhARi1pREb28v4uPjsXfvXuLx\n6OhoTltRURG2bdtmtu89e/ZwbpC0JCcnY/Xq1RbNcTggyW3i4uIc7oNNsQ1v50kI8Zhp0EazzRQK\nhUKG0TBIOfWyznJOi98EH8RLhkcmSYNmG5k/fz7HlSA7O9uu2eby8nLiZj2hUIiSkhIEBQVZ3BdJ\nPmJcEtwcg4ODePLJJxETE8PxAi4sLOTVXGshyST0M+jFxcUICwuz2cIvJSUFBw4c4LTHxsYSzgYy\nMjLw4IMP6qolMgwDhUKB+vp6HDhwAKtWrUJqaioxIx8aGsq7KXMkUCgUxKCZ77lTRgcxYkO/9LLL\nx0doJhQKhTJ6Uar7kPztC9jfxl1VzvnlG8NW4IQGzUMgPT3d4HFvby+ysrLs0rdKpUJaWhrxWHZ2\nNubOnWtxX/v27SO6PpAysKY4ePAgcnNzeY/n5eVh//79vMdJ2lqth/KePXsQHx8/5I2BmZmZnIz3\nkiVLOJUctZSUlMDLywtOTk5wdXWFl5cXQkNDkZiYyKtTF4lEKCoqgovL8FUhMkdFRQVHwiMUCjlO\nL5TRRextCw0eV3dZtrpCoVAoPxealS2IOLaSGDC/9YsMLLttwbDNhQbNQyA+Pp5TaS07OxstLUPX\nJebl5REru8XFxeHpp5+2uJ/6+nqkpqZy2oVCodnMsDF9fYbm4aTM8caNG3llGiSbN5lMhvr6et4b\nBO04cXFxyMrKQmZmJtavX4/k5GSiM0ZjYyPxdcvLy+O1n9Niicbb1dUVhYWFCAgIMHvucJKXl8dp\ni4+PHzX+0RQyxg4aLdfacKaXumhQKBQKwFYCjKxcRfxcXCGJwXMBTwzvhDSUIVFaWqoBYPCTmJg4\n5H5DQ0M5/YrFYo1cLrdqbiKRiNMPAE1KSorVc1IqlZqEhASNv7+/Jjk5WdPU1KQRCoWcvpuamojX\nl5SUEOcSGRlJbAegG4dEdXU18RqpVEo8v6KiQuPv7887lrkfiUSiqaystPp1czRyuZw43/z8/JGe\nGsUM6utqjbj0Ho3TZ4G6n9yWAyM9LQqFQhkx+tX9msrOWk16/V81wv8LMvh81P5EVT6i6R64Ouxz\no5nmIbJs2TJOcYuCggJeNwdLOHz4MOrquNXBMjMzLS75vH37dsTGxhJdNwIDA20qbOLm5oaPP/4Y\nP/zwA/75z38iICCAWNiDr0Iin0SCVJDD1dUVOTk5unFIkMpjA/yFSxYtWgSpVIr4+HjicVPExMSg\ntrYW8+fPN3/yMEPagOrl5WXT86QMLwInAaK9DaVWpZeOjdBsKBQKZWRQqvtwqP0LPHnqJfiWLcCC\nqkRsb97LcckAgCemrUJZ5D54jvcY9nnSoNkOkHTMycnJaG62rcIXSTcsEomQnJxs9tqTJ09i8eLF\nHL21FldXVxQVFVnsumEL+fn5xPbg4GCipMLYdi4yMhK1tbVYu3atyXFIGwbFYjF8fHx4r/H09ERh\nYSGysrLMViP09fVFQkICSktLceTIEZP9jhQMwxClGYmJiQ59jyn2w9h6ruxyFVTM8Ja4p1AolJGg\nvuccnv9+KySf34cHv/4j9l74GJ0DXcRzBU4C7Ah5Gf+Y8+awbfwzxrTIk2IRc+fOxfr16w2yt93d\n3UhISEBFRYXVPr4ke7jU1FTeIIhhGJSVlSEnJ8dklT9XV1cUFBQgJCTEqvmYIjQ0lON5XFlZiYMH\nD+Lhhx82aBcIBIiIiOCcHxYWBplMht7eXqSmpmLr1q0W2aSRMtqWVL8TCAR47rnnkJqaisrKSt3m\nQ6FQCJFIBC8vL/j6+o4JPXB+fj5aW1s57aY04pTRRbxkKTbUb9E9Vqh7UHr5GFYMk4UShUKhDCed\nA10ou3wcuRc+QnmHZY5BQaIZKPhVNuZ4znbw7ExDg2Y7sXnzZpSWlhpsQpNKpUhISEBJSYlVTgsk\n2YG+5EClUqG1tRXV1dUoLS1FaWkpr1RBi0QiQVFRkVWuG5aQmppKlAfk5eVxgmaAlTkYB83V1dVo\nbW21KpNbVVVF9K+2pqS1u7s7li1bZvH5oxHSax8ZGWnXGyOKY/Fz88GcibNx6mqDri1H9i8aNFMo\nlDFN2zU5Om5kjQsvlkLW1wbp1e9R33PO4j78JvggbfpjSPNPGrHssj5OGo1GM9KTuFU4c+YMIiIi\nODri2NhY5OfnW5y5XLBgAUd6EB8fD7lcjtbWVmJm0RRRUVEoLCy0WA9tLaT5CoVCyOVyznM+c+YM\nx3EEALZu3YoXXnjB4jGXLl1KzDTX1tYiPDyccMWtx6FDh4iWcoWFhcQbFsroZfcP+XimbpNB27H5\nBZg/2T6/yypGhdZ+OVqvydHaz36R9V9XQX2dgVqjhlrDoFfdB+E4AVzHuUDoJIC/my98XSWQuE6B\n2HkSxM6TIHCihXIoFMpNlOo+1HafRlNfC2R9begevIq6nrOo6znHK7MwR4jHTMTethDJdz6MYNGM\nUfW5Q4NmO1NcXIyEhASOfVlwcDDKysosyqY+88wzdqku6OrqivT0dGRmZjq0Kty+ffuIeuuNGzfi\njTfe4LTPnj2bYwsXGRmJr776yqLxDhw4QKzSFxMTgyNHjlg26VsA0o1DYGAgGhsbaRXAMUbnQBd8\nj0RBdX1A1xYkmgHpws9syq60XZOjorMGFZ01qO6SQtbXBiXTZ/5CMwS4TYO/my8iJ4UhclIYgkUz\n4O/mO6q+1CgUiuM4pWiA9GoDyi4fR2NvM6RXG4ib9azF23kSEu9YjpRpvxtxCYYpaNDsAPbv388p\nsw2wG8vy8vKwZMkSk9eXl5dbJTMgERsbi127dg2Ln3BnZyckEgnnRkEikaC1tZUTwG3atAmZmZmc\nfqRSKebMmWNyrLa2NoSGhnLKbwOszMPe8pPRSlVVFdG5JC8vD2vWrBmBGVGGyramPXixwXBT8Rrf\nh5Ab9qZFQWl9zzkU/vQflF46xikz60gETgL4T/CB2HkywjxnQ+IihsRlCiSuUxDo7gex8yR4CT1G\nxdIqZfSgGOwxeNyrVur+r7YhCBMJ3SB0Eo6Io8KtimKwh7357qiB9Or3qO2us8vNtz4hHjOxfkYy\nknxWjInPCBo0O4ht27YhIyOD0y4UCnXZX1M657vuuotoO2cKoVCI+Ph4pKWlYdGiRVbPeSisXLmS\nuAmxrKyMc5NQX1+P0NBQzrmJiYn48MMPecdQKBSIjIwkFi9JSkrCBx98YMPMxyYPPvggp8qjRCKB\nTCYbVZUKKZajVPch4thKjom/9ksldspC+EyQ6NpVjAqVV06iorMGeT9+grZ++XBP2Sq8b0g8JC5i\neI2fCP8JvvAa7wGv8RPZwHr8RPi7sVVDJS5iiARuY+JL9OcOo2HQPXgVrdfkkF1rg6yvFR0DXWi9\noWdt7Zeje/Aqugevolcv4LJHdpIPvwk+EAnd4D/BF4Hufgh094PXeA/4ukrgNX4ivMZPBADdvyKh\n289+taTzxntW13MWtd11qFWcRnWX1O7vk6fQA6ETZyFGPA8xU+bbTYI2XNCg2YGUl5cjISGBmBWN\njY1Fbm4ur1zj1KlTiI2NhVxu+ovQ19cXcXFxiI6ORmxsrNVOHfaCT1+blpaGd955h9POp4Ouq6tD\nUFAQ5/zOzk7ExsYSN/+JRCI0NjaOSks4R3D06FFiCfTs7GysW7du+CdEsRsnu+twz7GVvMcD3KZB\nOE6IfkaFlmttNo0hcBLAa/xEiARuEDtP0mX1vMZ7QOgkRMdAF3rVSnQMdEGh7jHTm2Pxdp6km6dI\n6Aax82Rd4C12noxg0QyInSfB382XZhgdBKNhIO+/jI6BLnQMdEF2rRWNvechVTRA1teK1n65gaxo\nLKINmLVBNAkvoYcu4BYJ3eAlnAjfCRIIb/w96c67cY6vq+TG7+mkUXfzp2JUaOq7gLqrZ1F5pRYV\nnTVWbc6zhAC3aQidOAthE2fDd4IEEpcpiJwUBm/nSXYdZ7ihQbODaWtrQ3x8PDHYE4vFyMnJ4d20\n1dnZiZycHMjlcvT29kIsFkMkEiE0NBS+vr4IDAwcNbZoDMNALBZzbhBEIhE6Ojo42c+DBw8iISGB\n009wcDDy8/MRFhYGgUCA9vZ2lJSUYPPmzUQrPoC1XVu9erXdnsto57777uMUhPHy8oJMJhuxmyaK\n/dh05m1sOsu90bSFALdpiJx0N6LF9yLUYxYC3f2syuAqBnvYjYOqK5CrOtCkbEF1lxS1itNoV5l2\n7BluXMY5I1gUcCOI9mElIi5TbmQap8HXVTLqgpfRyMnuOkivfs++z911qOs569Cs8M8B7xsSJQAQ\nCd3hNd4DYufJ8Hfz0a24+Lv5wn+CDySuU+yS9Vaq+yC9yt7YyPraILvWiiZlC5qUF+y2KiVwEiDU\nYxaiJocj2nvujYz+REhcxLfs3xoNmocBhmGwdetWbNy4kXg8NTUVGzduHPOZUj6tcmVlJaeSHsMw\nCA0NJUotADbr7O/vj6amJpNj8mWyb1X49PK7du3C008/PQIzojiC7c17kXnmbav1g9oKg/GSpYi9\nbQEC3P0cNEN2Obex97xuGV569Xs0KVvQek0OuarD7tpHexDuGYpAdz9ETgpD1OQIhHnO/tkvy7er\nOlB2uQqll46horNm1Mt8bnW0K0H+E3wMZCReRisp6uvcGxnhOAEbIPe1Qnatze43O+4CN0R4hSLC\n6y5EeoUhWjx3zGeOrYUGzcPIqVOnkJKSQsw6e3l5ITs7e0xv4lIqlQgODuZY4vFt8OOTdFiKOQ30\nrYZKpUJgYCDn9fX19UVTUxPVMt9itKs6kNvyEQp+KjG5dOop9EDU5AjE3x6DhNsfGDUyBaW6D3LV\nZQObu151HzoGuiBXXYZcdfnG/ztstqYaKgInASI877oRRIf/LIIArUVYkbwM0qvf42jn1yM9Jcoo\nxV3ghtjbFiLaey5ib1tAnXJAg+ZhR6VSIScnBxkZGbpKdPpER0dj/fr1iIuLG5O2YYcPH0ZsbKzu\nsZeXF+RyOW9A98orr2Dz5s1Wj5OYmIj8/Pwx+RrZCt/m0oKCAjzyyCMjMCPKcNHS14bKK7VoUrYA\ngG7zXLAoAKEeM8f8Uihzwydaq6XuHryKbnUPetVKyFUd6GdUbNDNKNGkbEH3YA9kfa0O0VzPmTgb\noR6zEDNlHqImhzs0W+9oGA2j0x5rN3hVdNY4bBXA23kS/Cf46DSsEhcxfCdIEOoxC2LnSXAd56LL\nnroKXHQBGKNh0K9XOt4W94zuwavov67Saa/l/ZfR1NeCJuVN/+DuwasjrtMfrQicBLoVmFCPmQjz\n/MWo80geDdCgeYTo7OxEdnY2du3aRdwo6OXlhdTUVMTFxSEsLIy3hPZoZOfOndi4cSNEIhFyc3Ox\nfPlyk+c/9thjyM/Pt6hvoVCIzMxMvPzyy/aY6pihvr4eYWFhHFu/iIgInDhxYoRmRaGMLIrBHshV\nl9GkbIFcdRmNvefRPXj1xuMOdAx0DTmL7eMqQdjE2Tpv6jDP2aM2G93S14ba7tOo7paisee83QNk\nT6EHfCdIdK4UYZ6zdUHyWNGMqxgV+q8PQK1Ro1fNvjbiG+9n9+BV3uu61T3oHryqu6nTOoQYX9et\nvnnM1s26jsZd4AZ/Nx8EiwIQLJqBaO+5iJwUBneh20hPbdRDg+YRpr29HXl5edi6dSsxeNYSERGB\niIgIhIWFwd/fH8HBwZBIJLfMknxNTQ0yMzNRWlpKPC4Wi5GUlITU1FSiu8atDMMwiIqK4mz+EwqF\nkEqltGQ2hWKCzoEuyG4Ek0197EbGoVppzZk4G1GTw5FweywiJ4WNWLBY33MOpZe+ROmlL9HYe95u\nemR3gRsiJ4Uh2nsuwjzZzLvvBAnNOtpA5w0JkpYO1RV0q3t0ziOyvjZ0DFyBrK/NrkG2wEmAYNEM\nRHjehUB3P3bT4Y3NhvrWlRTroEHzKEGhUKC6uhoVFRVobGxEXV0dZDIZJ7MIsJX+goODERMTg4iI\niFtqab6lpQUymQytra3o7u6GSCRCRETEzzow3L59O9LT0zntfBUXKRSKabTOAlJFg65qoq0Bp7vA\nDcl3PoQk3xWYOynMzjPlYqnW3Rq0S/PxkqWImhyOCK+7aIA8Aujb+7X2G2axje3wSBIWod4mQnu5\ncFAMoUHzKEepVKK7uxvd3d0QCoXw8vKCl5fXLZNhppjGlCyjsrKS/h5QKHaiWdmCis4aFF0ss1nW\n4OMqQfKdDyHV71G7Z/PaVR3IPPM2ci98NGRXBH2XlTDP2QibOJsuzVMoFkCDZgpllKJSqRAVFcVx\nWxGLxZBKpWPeopBCGa0wGgaNvedRdrkKtd11qO76Fs19Fyy+XuAkQMLtsdg462mEeMwc8nz2/fgJ\n0k5vsimQFzgJEDZxtk6/GjkpDKETZ2Gqi3jI86JQfm7QoJlCGaWQ3DKEQiEqKysxd+7cEZoVhfLz\npHOgSyfnKL30JU4q6iy6btmUBcgKedGm4Lm+5xwyvn8Lhy59YfE1IR4zETbxF4jwCkWoxyy6wYtC\nsSM0aKZQRiEHDx5EYmIiR5ZB7eUolNFB2zU5Si9/ibwfP0HVlZMmzxU4CbBx5p/wWtCzFvXNaBhs\nPbcHmWffNivF0HrpxktiEDNlPs0gUygOhAbNFMoooqWlBbm5uUTv6pycHKxdu3YEZkWhUExx+NIx\n5LcWo/Dif6C6PsB73hPTVmFX6Gsm3TYUgz2IP5FqtujIEvE8pE1/DDHieTSTTKEMEzRoplBGCKVS\niYqKCohEIshkMhQVFaGkpISTXQ4ODkZubi6nFDmFQhlddA50IffCR9j1Qz6vG8dqnxX44FdZxGP1\nPecQV/OkSeuxALdpyLv7b5g/Odwuc6ZQKJZDg2YKZQRpb29HUVERSktLIZfLoVar4eXlhYiICISG\nhiI4OBjh4fTLkUIZS6gYFfJ+/AQZDW8RK9B9FfUxx56uWF6GpG+e493sJ3ASIM3/MWydnT4miohQ\nKLciNGimUCgUCsUBtF2TI/Gb9RzNs362mdEwSDu9CXtaPuTtJ9wzFHl3/80uThwUCsV2aNBMoVAo\nFIqDaOlrw/TyaIM2b+dJuLzsayjVfYj7+kmT+uUXAtdic/AGWqiCQhkFjBvpCVAoFAqFcqvi5+aD\nALdpBm2dA103Nvw9xRswu4xzxgd3Z+Gvs9NpwEyhjBKEIz0BCoVCoVBuZboJuubY6sdR0y0lnu/j\nKkFhxDvDUpabQqFYDs00UygUCoXiINquydE50GXQ5u08iTdgXiGJgXTRZzRgplBGITTTTKFQKBSK\ngyhp51bzMw6itaz1exTv/fJ1R0+JQqHYCA2aKRQKZRTCaBjktnwEueoy4iVLMcdz9khPiWIDpKCZ\nxMsz/4Q3gjc4eDYUCmUoUPcMCoVCGYW82JCFbU17ALDL+bIlFbTy2xjkziMLeAudaHlt1jMWl9im\nUCgjB800UygUyiij7ZocWc25usedA13oHrxKg+ZbDHeBG/J/tR0rJDEjPRUKhWIBdCMghUKhjDJy\nWj4Eo2F0j13GOUPsPGkEZ0SxlfSAJzhtAicBnpi2Ck1LymnATKGMIWimmUKhUEYZFZ01Bo8PhL9N\nSyePUdbNSEagux9yZGzFvzDP2Uib/himuogdNqZisAep372C0ktfIva2hcgL20Z/fygUO0A1zRQK\nhTKKYDQMXA+FGGSaLy/7Gt7DmGnuUF3BgGYQd7hOHbYxKfbjgerHcfjyMd3jN4I24OVZfxrBGVEo\ntwZUnkGhUCijiNZrcoOAOcBt2rAFzGd6z2Px8dW47fO58D0ShfcvfDws41LsS1nHcaPHVSM0Ewrl\n1oLKMygUCmUU0T141eCx6zAtqzMaBjFfrTFweii8WIrHp60alvHbVR2o7pKiSdmCxt5mNClbAAD+\nE3wR5R2OxDvi6EZIC9G/6QKA9ICUEZoJhXJrQYNmCoVCsSMtfW3YJfsATcoWhE1k9avWZIqF4ww/\nliUuU+w9RSKll77kWKMtm7LAoWMyGgYFbSXY2rQH9T3niOccxdfY1/oJMs+8g7ywbVgyZZ5D53Qr\nUt0lxfKpi0d6GhTKmIfKMygUCsVOtF2TI+zog9jevBfF8jJsOvsOgr9YhvLLx81ffAOJ0QaxywNX\nsL15L28VOXtReulLg8eeQg+sm5Hs0DGTv30Bj32bzhsw69PWL0dCbRraVR0OndOtgN8EH4PHUkWD\n7v+MhkFLXxsnG02hUMxDg2YKhUKxE+nfb4VC3WPQ1jnQhfgTT1kc9Ho7T8I9Xr/UPf7uaiOe/34r\nUr971a5zNabVKMts/DyGwuFLx7Cq9hk8//1W3etQfvk49rcVW9WPQt2DXT98YLd53ar4TpAYPK68\nUgtGw+DwpWPwL4vG9PJo+JdFo6WvbYRmSKGMTWjQTKFQKHZCq8M1Rsn0IaPhLYv66BzowlV1L6fd\n11XCaWtWttgt8yojBFD2yEYeav8CD9Q8joMXS7G9eS/STm+CilFBZKM+uUh+ZMhz0rJH9iFW1T6D\nJ0+9hJouqd36HWmMPb0V6h6s/ubPeKDmcZ0Ep61fjvxWy25ampUteP77rZhZvgST/vMr3HlkAR77\nJp0G3ZSfHVTTTKFQKHYiyXcFTirqiMcqOmqI7fqc6T2PhNo0nOk9b9Du4ypBxsy1useKwR6knHoJ\nBy+WQuAkQP7d2/GIz/Ihzd14AyIA+Hw+H+PHjUd6wBM2SzWMbxYO/HQI3YNX8Z/I9zFn4mycuspK\nB16e+ScEuvtB7DwJoR6zIHQSoEnZgsVfJRlc39h7Hkp135A3Ba488RSK5WW6x/mtxWhc/Dn83HxM\nXDU28BJO5LR99NO/OW3mNpm29LVhff1mg9cJYIPw/W3FKJIfQeX8AszxnD20CVNGBTVdUmQ0vAWh\nkxCbgzdg7qSwkZ7SqIMGzRQKhWIn1s1IRrT3XNQqTmNj4w6DLLDsWhtUjIq3yIRisAfRx1dzMscL\nve/FwYhdBpsJf1PzBL7q+hYAmw1O/e4VxN62EJ7jPez6fC4NdAIANtRvgb+br03V67Tz9pvgg5Zr\nbGby8OVjOKVowPc9TQCAR+5YjjeCN3CuJQV1jIZBY+95hHuFWj0XLQfaDnECQdX1AWSfz8OO0Jdt\n7neoMBoG/YxqyDcE/hYE/gFu05Ay7Xe8x/e3FiPl1EtQXR/gPUfJ9GHzuXfxccQ7Ns2TMrpI+uY5\nNPddAABUHq9F0/3l8JnAXeG6FWA0DGq7T6NJ2YLuwR54jfdA3NT7zX6G0qCZQqFQ7Mgcz9mY4zkb\n/cwAnqnbpGtnNAxqFXWYPzmceF2R/AhRavFTfzvHfUMbMGtRqHsgVXyPReK5Ns+blGnWJ+30JsRO\nWWB1Zbnie3LwVde3uMfrLiSeXI/yGx7ClVdO4sh9efhW8T1v8CYSkIPH1n45wmF70Jx59m1iu/Tq\n9zb3aS2KwR7I+loRLJoB4Ti+rQxcAAAgAElEQVQhsppzsfXcHijUPVh+22IUhGdbHTwzGgaZZ97G\nX8/lmDxvrlcYiu59jzdAaFa24LFv0y0a03gD6a2MilGh8GIpiuRleOC2hcNmxzgcKAZ7dAEzwN5E\ntvbL4TNBgmJ5GXJk/0J1lxQioTuiJodj46ynEeIxcwRnbBuKwR7ktPwLObIPdTfxWjyFHsi7+28m\nkwNU00yhUCgOINX/USwRG9qj8WmeAcB1HDkY1f9i2nk+D+NLgonnya45Vl/a1i9HSfsXVl/nOd4D\nsbcthLfzJMTetlDXHujuh4Xe92LdjGTe4NARpZ+PdtRw5C9a4iVL7T4eiRcbsiD5PBJ3f/lbBP43\nBnE1T+LFhizd5stDl77A+vrNVvWpYlSIq3kSW869i+u4znvea7OeQcW8fJNlvFuvyXmP/VxpVrYg\nsnIVHvs2HQcvliLl1Eu3lKbbc7yHgcXkCkkM5k4Kw7amPVh54ikcvnwMCnUP2vrlOPDTIUR8GY9m\nE59n9kKp7kPVlZN2Gav88nEEf/FrvNiQhZZrbfB2noR3Ql/DsfkFmOsVBoW6Bwm1aTjZTZbYATRo\nplAoFIcgcBKg6J73sG56MlzGOQMAgkUzeM9/xGc53gx+Dh5CkUG7tjBFsbwMG+q38G7O+4P0BRyy\nIai1hl0y250rzvSe1+mbQzxmItr7XntNyyqymvdy2gROApxY8KnDLfYAVie8rWmPTvbQ1i83KHmt\nJb+1GEp1n8X9Jn2bTuxHn0/veQ+vBT1r9mZE4kr2Bl/kfa/ud1lL4hC19GOBmi4pIr5cqdPfA6zs\nyGs8Vzs+limZ+w98cV8+GhYfRmHELgCAUn2NeK7q+oDDHX1OKRrgXx6NBVWJmPnfGGxr2mNzXwfa\nDiG25nHdat6cibMhXfgZnp6ehPmTwxF/O5tdZjQMCi+W8vZDg2YKhUJxEO5CN+wIfRkdy07gP3Pf\nN7uxZorLZPToOWeskMRg/uRw7P4hHytPPGV2vNru0zbP1RKLuaOdX5vMwvChVPch9btXwGgYhHjM\nRNl9/2txFlngJOC02TIHgA1YD13i3ljETllolUa6WdmCLWffxcoTT2Fm+RJML2O/2A9fMh20AoDX\n+InwFBrKIkjPUXV9wKxkRsuWs+/ioIkvet3YQss070GiGXgjaINuXstvW4xvF36G0rnvG2icJ433\nRHbIRov6HKs0K1sQ89Uag7+PORNno2LefniO90C7qgNVV06iWF5mkd+4vTmlaMCWs+9i74WPhpyN\nFTgJsEg8F0GiGbr3PiNwLd4I2oB105PhbiSXKu84btWNnTXU95xDZGWCgVXniw1ZNr3GJ7vrkPTt\nc7qEg98EHxTd855Or61iVNj1Q77u/LqrZ3n7oppmCoVCcTDuQjcsu810db2Wvjak1281aMsIXIvd\nP+QbaKP1meE2Dedv6BBdxjkjanKE2bkoBnuQ+t0rOPDTIayQxCDnl2+YXKo3Ju/Hg1YFmIrBHiSe\nXIejnV9jzsTZKLtvn1UVEkkcu3JC938Vo0JT3wWL9JVZzbnE9oQ7Yi0ee9OZt7H53LucjH/LtTY8\nUPM43gl9DU9PT+K5ml0GPx71EUIqHtC1rZu+Bjt/2GeTxV9BWwleObPDonOlVxss1r2/POtPyJi5\n1mBjIqNhcOeE2/HjtYsAACVzDR0DXUPauHig7RDyfjwIkdAd62ck82r+R4q005ugZG4GhvMnh2Pr\n7Oex64cPUNL+BaeK5mqfFcj55evDUvJ9e/NePP/9zc8MgZMAqX6PIjPo2SH/jWlxE07Ay7P+BKW6\nDzt/yOMc7x68avfnqlT3Iemb54ibUJuULVZrqdNObzL428r55Rs6l5zOgS6knHrJ4H005SpDM80U\nCoUyCkj97hWDbFa4ZyiK5GW8AXO4Zyjqo/+NI5H78MHdWZDFHLWoxHRGw1s48NMhAKzkI+ar/wfF\nYA+c4GTRPHMvfATFoGWFTw7+VIrEk+tw+PIxeDtPQq9aiY2NO3BKr0KdKToHuoiB5OTxXgDYLGDE\nsZW4q+I32CP70GRfjIZBkZFjBsBu/km43XzQrBjswcoTT2HT2XdMBreZZ982G/xO1JPguIxzxhLx\nPM41nkIPs5ZwAHdTKGkMLfqVAU9212FBVSLnvdR/bwROAoOAKKs5VxcwA8DA9QGLvZ5JHGg7hEe/\nWY/Dl4/h4MVSRB9fjZ3n82zuz96UXz5uIHkZh3EYuD6IBVWJ2NPyISdgBoD9bcVIO03+m7Un7aoO\njp0jo2GwW5aPmK/WoM3OuvQOnuJMIqG7XccBgKRvnzOQwugjJKzKmKL88nHUdN/0YPeb4KNLYNT3\nnENUVSLHSSfam//GkgbNFAqF4kAUgz2ounLSZEXAU4oGjh5V7DyJV8O3yPtelMz9B1wELlgyZR5W\n+66wOFvc2Nts8Li+5xzSTm+CBhrOuYu9IzltqusDyPvxoNlxarqkWHXyGd3z6hzoQnPfBexp+RB3\nf/lbbDpDdrDQwmgYJNSmEY/NnxwOpboPCbXP6JZrN5rJtpZe+pIY5MRMmW82U9bS14aoqkc4X64k\nOge60Miz0VCLxHUKgm7o29OmP4ZZIn/OOQp1j8llYi1PTFsFsfNkTBC4Gsg8lk6J4pwru9YKgL3Z\nSJb+BVVXTqLySq1u3hvqthA139rjm8++y2kPcJ9mdo58VBsVlGFvbAyL17T0teGVxh1Y+tUarDzx\nlNmbI3uS02I41nVcx4nu78xeV/BTicPLlFd3SXnHOHW1we56416GK8MIcJtmd5vLp7571eTfGanI\nkylyL3xk8Djhjli0qzrw/PdbEXb0QaInfpLvCt7+aNBMoVAoDuCn/nZsqNsCyeeRWFCViOAvlvEG\nzhsbDQO+EI+ZvJu6lt+2GKVz37dKUqFPjHg+p42vnPUfpj1M1Ntmn88zqWVs6WvDvh8/NTmPTWff\nMZlx3nx2N452fk089uO1i0g7vckgG2VO/5vDE2wl3mF6IxsbnKdZpaU0py0XOAlQOb8AX9yXj7d+\nkYEAdz/4WBkMaPnlxGBcWlaDhyTLdEHUWr9HETaRW3CkWXkBLzZkIembdN3z8Ro/EUc7ahB5LAE7\nf8hDwU8lRG1s9vk8A5kCALwetB6JPnE2zRsA4qYu5rQd7fwaVVdOAmClMIH/XYIt595FecdxFMvL\n8NTpV/GZvNzmMS2lpa8Nn1783KZrVdcHIOtrtfOMDPFxnWry+KFLX+heR3vgP8GHswk0xY/f59sW\n9sg+xJ4W/psil3HOCHT3s7g/FaPiOP7I+zvgeyQK25v3cm46vJ0noey+fSZvBGjQTKFQKHampkuK\nOUcfxM4f8nS6vM6BLmLmsKWvDaWXDb1u+QK0h2+PRWHEO0OyYls/I9liveNdHkFIvIMbFLVca0Pa\n6U1o6WtDS18b9l74CI99k467j/4WEw6FYHp5NHJa/gUAWCKeh9dmPYM3gjYYWFoBQNkNz2Zjarqk\n2HSWv2BGSft/sa/1E4M2iQvZ8QFgM6ukDYBTXcSIv30p2q7JeW9oMs++Tazy6DLOGa/NeoZ4jSVL\nyN7Okwz0xbvues0gKFnkfS+ivM1r1AE2OCj4qUT3OOH2WPgSilK09svx+eVjuuVql3HOkCoaEFO9\nRufRy2gYlBptaKy6chJbzhlmmQVOAmyY8QeL5sfHkinz8E7oa5z2p09n4sGaP/JKYfQlIo6gWF6G\nxceTTFr3mcPRtn0RXnchd86bWOR9L5bftpj4N7357G67jecudENe2N90N9Fr/R7FC4FrzVxlOVVX\nTiKNR4qmJfnOh63ST5e0f8G50dvfVkz8nQrxmImKeft1K0B80I2AFAqFYmfiTzzFCcJ8XCWI8LqL\nc25+K/lD3JgXAtdic/AGqJgB/NTfjjtcp0LFqJB74WMInQRI8fsdMStsjLvQDeunJ1u8eWz9jGRi\nJnpf6yecwNWYZVMW4D+R7wNg/ZGzjTYSyVWXOdco1X1IPLneZL/6RRi0hJrYHGS8zK4lyXcF/Mui\ndbKN1T4rkB36skEAUnTxCOe6FZIYZP0igxNcauHTf5pihSQGTfeXo0nZApHQ3eqKh0Inge73aGn1\nGozjyYn9oJcBjZcsJWrmXQWGGUWSbjn5zofssgEsyXcF0r//q8Gmr++uNuK7q43E80M8ZuKRO34z\n5HH52Na0By82ZFl07iLvexE28RfEDXJil8l2nhmXx6et0hVYaVd1IOzogwYFksxZEFrLIz7L8YgD\nLAbbrskRf+Ip4ufgnImz4TfhDngIRdg6+3mL+yv46ZBFMjKBkwDrZyRjc9AGi5IRNGimUCgUByFw\nEmBX6Gvov65CsCiAGGSUdVSZ7MNd4IbcOW/iEZ/lONB2CMnSv+C6RoOz9x/B1qY9uuVM2bU2/HW2\nZVXc4m9fanHQHO4VijW+D5kNkI1xGeeMrJAXAbDLruvrN3N2w0d4cm8iMhre4lTqsoSYKVzZCcBm\nTvk2q2030u/ubytGXc9Z1C78VHcD0k2w4vv0nvcAAHIV+TWxVnepxWeCxKayxS4CF6yf8QcDDTxf\nllRfxqLdEKqPwEnAKfJCkpvktxYj1GPWkL2tPcd7IGXa77Bblm/yPB9XCXbd9Rripi626ObQFiwJ\nmD2FHkjyXYGUab+DSOiG0ApuAO/tPMmkJ7sjmOoiRuX8AqR+96qu6qaxnMLeaG/aCy/+B7K+NnQP\nXoXvBAlib1uI5DsfttjlIvW7V4krPRMErqjrYVfnSiPfN6ufbulrw9amPcj78aDJ8u9aVkhikDnr\nWczx5EqZ+KDyDAqFQrEzFfP247VZz6B2wadY6/8o1s1I5rWcEzvzZ6SCRDOwPeRF7Gv9BJvOvI3U\n716B6voABjWDqOs5i4rOGt25eT8etHjzUbBohlUa2s3BG6y2sNo6+3mEeMxEfc85PHX6Vc6X2BPT\nVnGyVocvHeMETy7jnBFpxt/ax1WCVL9HiccqOmqI5cn5OHW1Abt+uFnEZePMPxkcf9r/pp3caKqc\ntzl4A56YtmrIgVKq36Oc91pMeO9V1wewoX4LVtU+Y3KTqyWsn5FsMhAOEs1A7cJPsUIS47CAub7n\nHGdvgT4TBK54767XIf/1V3jnrtcwx3M2MhqyiMFZqt+jDpunKQLc/XDkvn062VDC7Q+YucJ2arqk\nCPxvDJ6p24SjnV+j5VobFOoe1Pecw/bmvbir4jcWZez3XviIKJ1yghOuMf1gNAxOXW1AjuxfvH2o\nGBW2Ne1B4H+XYE/LhyYDZoGTAKt9VuDEgk/x6T3vWRUwAzRoplAoFLsTJJqB14Isy2DwBXtr/R7F\nn2c8jtTvXkHppS+x6ew7Oks6d4Ebor3nop9R6c5vV3VY5LYAaLOJMRadC7AZUEs3H7qMc8an97yn\ny0DybYiq6KgxCPI7B7qQdjqTc17a9Mfwwd1ZnIIg+uPlhW3jlQrk/WhdhhwAtjbtgerGa7tuRjKO\nzS/AjpCX8VXUx3jnrpsaXK3zhDGkIFNLS1+brm97InAS4B9z3kTr0kocidyH/7v375zqkuYIEs3A\n5uA/c9rTpj/Ge83Bi6UI/mIZyi+T9emWEODux+vP7OMqQVnkPps3vlpKjuxfJm86k+98GGv9H9Ut\n4R/8qZRYUMZd4Gby9RoOXgt6Fg2LD2PXXVy9OIm2a3Krbiz3XvgIUVWJRDcafbY17cGTp17iPa4Y\n7EEGT2DtPG68wWO+5IJisAfRx5PwYkOWyfeP/fvYgo5lJ/DBr7Kslj9poUEzhUKhjCBLpszDV1Ef\n42n/JCwRz8NqnxU4Hf1vRHvPxdrvyNXWYqbMg7vQjaMJllvxxZd858NWZSXDvULRdH85sTIYwAav\na/0ehSzmKFboBeRRkyOIAU9z3wUDR4uMhrc4WuUAt2nInPUsAtz90Hj/53ghcK1BhjzEYyYq5x/g\n9adWDPag8OJ/LH6OWtpVHcjX03HPnxyOdTOSDSo6KtV9aOUJGkib8LT9Jkv/QpR82Atv50lYMmUe\nlk9djGkTbrf4ugC3aSi59+/EJfDlUxdjLc/NHcDe8CytXoPdP5iWWPChVPfhYv8l4rGXZz5lk2TF\n3vQZlZPmKym/OXiD1QF+50AX6nvO4VD7F9j9Qz42nXkbm868jZ3n8yzO4neormD2F8swviQYO8/n\nIdDdz6ScQcWosO/HT/BA9ePwL49GSft/LRqHDYRftnhVa++Fj3GonZtJBoDs8/8kPr+Hbl/GyRb3\nXyffaCbUphn4MGsxzvRHTgrDE9N+N2SLPKppplAolGGC0TCo7T6N0ktfIsl3BQJu2CfNnRRmEJDV\n95xDsvQvBteOdxqPQc0gAPYLQDHYw/li6Ri4whmzpkuKwoulqO6SorpLCl9XCQrCszF3UhgKwnci\n+du/WFRCG7hZFnzr7HRUXjmpCxoD3f0QNnE2MdvrOd4DJff+A5vP7eb4r5Z1VOHp6UnYeT4Pey98\nzLl2112Zuj6nuojx19np+OvsdLRdk8NV4GJWMlJ48T8WaRtJ5Mg+xBPT+C21pFcbiH17Cj3g7+bL\naT/ZXYeE2jS0XGuzukCDrVhahGaJeB4KI3aZDCje++XrSJv+GJK+4S888UzdJjT2Nhtk4y1h87l3\ncU4pIx471F6BVP/fW9WfLcRMmW9SV218gxQsCuBYIi4Rz+NdOdJSdeUkcls+gvRqA4ROAjQpW0z+\n/W1s3IH8X203uBElsa/1U53n8Ib6LWjtl+OtX2QQzz2laEDKqZcMXGGalNzNtcZsb95r8SZJfVJO\nvYTGxZ9zfr9Iew2WiOfhlx5B+OTiYbP9nuyu0+m3tbiMc0aS7wrO50nslIVWz5sEzTRTKBSKAzjU\n/gU21G1B+eXjONldh1cadyDyWALuq1yF7PN5uoCZxMbG/zEIyG5z9tYFzAAQ6RVGlD003fDXVQz2\nYOf5PNx99Le4r3IVtjfvRdWVk2A0DFqutemKVKyQxKDrgW9w/UHLPYgB6IqqrLnzIay58yHMnxxu\n0kkh3CuUWOK7V92Hgz+VYkP9Fs6xddP5deA+EyQWaayNPVr5IG1YOqmoM+lza1wkRotI6G6Q5VIM\n9uCZ05twz7GVaLnWBoGTAF7jJ1o0L1vpHOjCK407eDPhWgROAvx1djqOmPGm1cJm9guwbnoy7zm7\nZfk40MbdYMhHfc85ZJ//J+9xe/sNt6s6sO/HT1AsLzOQyayQxOC1Wc/wrr5UXqk1uAnZOvt5LJuy\nAJ5CD7gL3LBuejKK7nnPpAPDlrPvYkFVIva1foJTVxtwUlFn9oZVybA+4ebkLxGehnKD7c17iV7q\nxfIyRFUlcmwUXc2sOpVfPs6pQKjPVBcxwj3Jkod2VQc2nzO0v9MWO9InwG0aCsKz8amc61hDkjx5\nGf3OrvZZgcbFn3M2sgLAK2d2YPYXy4ge5NZAg2YKhUKxM8+c3oQHv/4jdv6Qh6XVa3DPsZXYcu5d\n3ReVucyZrM/QPWLrLwytlviCrs3n2C9l8eF7sKF+C29GUOLKXT4mBaGmtLnWwGgYTmUuAPB380Hq\naW7lsrleYdhqoRMIHypGhdJLX5o9L9wzFMl3Pkw8ZmxZpb+UbPweadEvKnJK0YDgL35tkMH0dZU4\nbJOYilFh74WPEFrxG46vsjFi58momLffaq9d7WrDP+Zs4Q0w07/favHy/eazu82uBuhvzBwKh9q/\nQGD5EvxB+gJWnngKEcdWGszztaBn0bHsBE5H/5tzrer6gIGEwXO8B/4T+T66HvgGPb85hR2hL5u8\ncWzoabLYscYYRsMg20x58UXiuXgjaIPBeyIzcqHZdOZtrDzxFMe7GIDJoiEqRoXU714x+Z4KnYRI\nvvNhg42y+hS0HTK43lhK5jLOGfm/2g71jY1/xmjtOpX/v727j4uqzvcA/oEDDMyAw5MyOMggDwI5\nBjoo+IwbvaS0xfWhLG2lldYyKy28chf3aitrerNdVDZtw7LSlU3asKzYK61YWpGQuKEoCIKBjQkC\n8qQ449w/aGZn5vzOnBnAlPq+/+PMIzDo9/zO9/f56rpMOfZhMhX2jcvGdL8JWBI0Fzlj1kElVfKm\nShqd7agV7KG2FxXNhBAygE62Vdq8zMs5cVgh8B+LkfXl+6brln1/CvehzIJWb9CbVpSFyDgp0sPS\neMc9GX3K7v0YomJuT8MB3rhaoHdCHSvPOk+T3a8BLgBQ2lYhWoxJnN2QG7MR8wOTmbfvurAfY4rv\nx6+OP4lHv05Hkdlq3zmBFasQqRIAsLfhABKOzudtsGJldQ+Ek22VSDi6AI+fzLRrU1fPzR6ovUb1\n+fWWBj+IoolvMft3G69p7TphOXaljBl7Z+3vFz8UXCE821GLMcX3Y2RRIjp1XWi70Y4Zny+C8wcR\nFj3Wr9btwwNf/daiYDzVXs3L4Za5SDHaK4J59YF14meviwI92/aQOLshI0L85CZz1HIcnfx3U9+/\n8d+RTl2XaVgMy3S/CTYnO+bU7WFmo5trvKbF0xUvINEvnpnM03hNa/PvJzdmI+J9Ypm91eYRfhXt\nVUgr/52p1esh5SwcnrQXb4zdDLmrF45dKWO2ehk19VxBvcAJrz2oaCaEkAEkdkl8U/Rq0Y1N1itE\nfm7eFl97clIoPRSCiQNCOCcOeZps5tQr6yKcc+Icjpljua6/jvVntzHfy3Gr/N8AiT8KE16H6ofC\nsz+Km0pE75PzQ3SYSqrEdL8JzPucaq/GAW0R9jYegMKsQBQqml2cXPDYiTV49EQ6s2if4uDvzB5b\na3dj7Ke/FLyywHJV14HyttP9fm2hFcozjJMka2vP/Il3TMZJESgZxjtubCkyV9JSjtgjD+BUezXq\nuxuxpSYXGZUvmXqNt9Tk4mxHLR47sQaFlz/FPMbJkfU0TiPW1YcjzV/hiB2fK5ZpfuNxjz97w6o1\nuYsXlO4KTPebgOfDlqJ0WoHdf+sabzW+vfcznJj2PiI9Q1HTWY/YIw8wY90AQOWhRJ5mq+DVj8Zu\nLfP3BPQOHrGWfX43Vgpkd5sXxCEeStPrfxz/OhYFpQAA8i/yE0nmKJLQ0K3Ff1duwZRjC1HSWi44\n2l5sRf5I81eIPfIAGvsYF0kbAQkhZAAZ0yJYq31Lgubi+bClNh+vN+gtBlAAQKh0BFIUSTigLert\nofzhMvCWuzIw5dhCuy6F3+M/CVlRqyw2HJoLl6ks+hzFspHtlf9dIXNYyWJlCtRDRiGj8iXoDXrM\nC0zGpuh0hMlUqO9qRPnVShQ3lZh+FuEyFRJ8YhEuU9lVVItN5Xto+CyLjX7pYWm8jV3WorzCRJ8/\n98I7zMvfQO+Jgq0Vvb5o7mlB+ulNfXpsf6bW/b3xQyw+8bzgZ08sw3pvwwHmzzsrahXcnSV40qpt\nJ+/iQWy6a7XFynbh959anJi8ULUdKo//fDbquxuhLr4fyUOnIT9uO/K/48fE6W6y3//C4bNMn01z\naSd/h/LpHzg8DdHV2RWHJr6JS9ebcPDSv1DeVokOXRe8XYcgXKZCiFSJEGkQgtwV/U54AIAYeTRK\nWsox5/iTglcelO4KHIx/zWbax/qqbcyTP86JQ37cdqz45gWLyYNftpSjYPwOrGZ8Jr9s+U/KRYw8\nGtW/KMKWml1Yf3YbFpY9CxdnF1zpaeU97sNLxbzVY71Bj7quBt4VAfPseiFtunbs/vYfyBy1XPS+\n1qhoJoSQASR39ULp1PeQe+EdFDV9jg5dF9Reo7Bi5GLBgtVcQ7eW9x+1t+sQ7Bn7Mgq0hyymzcX7\nxJqmgLFWGY3T3TLCl4nmks4OmGFxqTzDwV5XIQVWiRlGK0Y+Co23GitCFqPHcAMXur/Dzvp9KPz+\nU+YKktE9/pNwaOKboq/raaOomeyrQW7MRotjxli1VwVGbs8LTLYrSkyoYAaA9aOeGfC84XOd9Xb3\nDxs9GbIIk3zG2j2xzdq7Fwvx8Ne2R52z+uaN9AY9s9APkPib0idyL7xjcRJn7Ck2P9FhRftZn3Dq\nDXqsHbUcEk7CzOwWigdUeigwO2AGL/GlpusC1p75M/6szhT8/mwJkPjbTGUZKJ9c/hyzv3pcsEUp\n0jMUBeN3MK86GZ1sqxTMOV8Zmgp/N1+LQhjo/Xl7clLTYCNz5Vcr0anrgsxFimcrNuCVur12fXat\nozWNFJKhvPfryUnRDPGYPqHfuxgqmgkhZIApPRRYF/kM1kU+4/BjWe0d4TIVZC5S0yVMc/E+sTgx\n/X0caSrB0StlaOppQZCHAv5uPkgeNs3uIm1RUArOdNTi6JVSrAx9DLMCZjj83q3pDXpmb2uYNBjF\nzSUo0B5CcXMJytsqbRab5qz/oxSyUDkbW2pyeUXDkqC52Hn3H5g90zlj1kEh8UdO3R6LXmuNXI3s\n0ZZFUpCHwqFx36O9IgQvW/dHvE8sIj1DeT3jUZ5hggkfvq5y5mfJHmWtFVgoUjADQKJfvOBtufXv\nMFc/V4ammn4vuTEbkXB0vsXvr8MqDSJ1xDxkVb1i8XvosPocTfebgHifWDR2a5mrkLGMFgOjtRFP\n4eClw7zCbuv53VAPifhRit++ELsKMHPoVOwZ97Jo+1VW9SvM5wiQ+GP9qGewvmobL/0jQOIPCSdB\n8rBpvKJZb9CjrrsRo70isP38Ww5+V5ZSFEm8hYD1VdtE/yY5Jw6LlSlYMmJun16XimZCCLmDWK+U\nBUj87boUPN0/HtP9hQsVe2yIWtWvx1s701HLLIZrui4wL9+K4Zw4pIu0txiN9opA0cS3kFX1F5S2\nVcDdWYKVoak222M4Jw7rIp/BytDHkP/dx2jo1iLIQ4HFyhRekZ3oF293FFqAxB8HJ7zm8CV9ex2c\n8Fes+OYFnOmoRZz3GKQo7sFj5eyMXgB449t3MUzih0eUDzjUt952ox3zS1eIrg5GeoYKbnjUG/TY\nUpPLO650V2ClWZRdjDwauTEbkVq+xvR61qkxnBOHcJnKolDSG/TgnDjoD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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["次にランダム変数からファクターへのメッセージは以下。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nKKKKACiiigAooooAKKKKACiiigAoo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wkaFmPoAMn+VfOn7OX/AAVM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X7LX/AAUP+D/7S3wK8S/HOewuPDdl4QnkXXIdSkVvJjEfmLIGU4YMueOuQR6E/Ljf8F2v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\nn6gm1pIcjg7Gxg98c1+vH7FPxuvf2i/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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["和を取る時にはいつもこの二段回の範囲だけ考えれば良い。\n前の前のノードの和はその前の段階で全て取られているのでいつも消えている。\n\n(ここで具体例Fig 8.51を考えるのが良いかも)"]},{"cell_type":"markdown","metadata":{},"source":["メッセージを次に届ける為には、その手前までの計算が終わってる必要があるが、それが何らかのデッドロックにならいのか?というと、ツリーならならない。\n帰納法で考えれば任意のツリーで大丈夫(p407)"]},{"cell_type":"markdown","metadata":{},"source":["## 別のノードのマージナルが欲しくなった場合\n\nもう一回同じ計算をしても求まるが、共通のサブツリーからのメッセージは全部同じ事が容易に分かる。 \nもう少し考えると、全部のノードで葉からのメッセージと葉に向かうメッセージの2つだけ覚えていけば、任意のノードのマージナルを周辺のメッセージだけから簡単に計算出来事が分かる。\n\nそこで、一つルートを選んでマージナルを計算し、今度はルートから葉までのメッセージを送り返せば、全てのノードで行きと帰りの二通りのメッセージを受け取るので、これを用いれば任意のノードのマージナルが計算出来る。(8.63を用いて)"]},{"cell_type":"markdown","metadata":{},"source":["行きと帰りで2倍の計算量で、全ノードのマージナルが計算出来る。お得!"]},{"cell_type":"markdown","metadata":{},"source":["## あるファクターに繋がってるノード群の同時確率が欲しくなった場合\n\nあるファクターを共有しているランダム変数達の同時確率を求める場合を考える。\nこの場合も全同時確率から和を取っていく事を考えると、そのランダム変数のノードの手前まではまったく同じ式となるので、同じメッセージが使える。\n\n最後の所は8.72式となる。"]},{"cell_type":"markdown","metadata":{},"source":["なお、ファクターにパラメータがあってEMアルゴリズムでパラメータを求める場合はこの8.72を使うから大切だそうで。"]},{"cell_type":"markdown","metadata":{},"source":["## 特定のランダム変数が観測された場合\n\n観測された変数は、その観測値のデルタ関数やidentity関数などを同時確率に掛けるだけで、それ以外のアルゴリズムは同じで良い。"]}],"metadata":{"kernelspec":{"display_name":"Python 2","language":"python","name":"python2"},"lanbuage_info":{"codemirror_mode":{"name":"ipython","version":2},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython2","version":"2.7.11"}},"nbformat":4,"nbformat_minor":0}
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