Created
February 2, 2017 13:42
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| {"cells":[{"cell_type":"markdown","metadata":{},"source":["## 8.4.1 チェーンでのinference\n\n一般的なBelief Propagationを元にした sum productの話の準備として、まずチェーンの例を考える。"]},{"cell_type":"markdown","metadata":{},"source":["問題設定。\n以下のようなマルコフネットワークのチェーンに対し、"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nsHniZvTn7uooAKKKKACqUXhvw5Brb+JYPD9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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["まずはx_nのマージナル、つまりp(x_n)を求める事を考える。\n\n同時確率を書き下して、マージナライズすれば良いのだが、何も考えずにやると以下のようになり、"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nSVWCuWO0NuK8YFAH7g/scavoHw//AOCXHwtsZPiNpnhaa6+Fel22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eWl3pd2YLqyuEztl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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["これを一般的にマージナライズするのは大変。\n\nだが、今回はチェーンの表す独立性を満たしているので、これを端からやるともっと楽に出来る。"]},{"cell_type":"markdown","metadata":{},"source":["----\n\nまず、同時確率を求める。\nグラフから、ファクトライズ出来て、以下のように表せる。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\n/BWL4n+H20zxX8Y/2pNS8TWX2eB1uLmza80i4tJSp+YLLPHqLx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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["ここで間のどこか、n番目のx_nのマージナルを求めたいとする。\n\nこの時、端のノードのランダム変数は必ず一つのポテンシャルにしか含まれていない事に注目する。\nこの例ではx_Nとx_1。\n\nそれ以外のノードは全て2つのポテンシャルに含まれている。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\ndLtRELSB/lJ5c5hUjOVadrLSOtmtru1ndt6eh9v9HfMsoxWAw/DmXK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ftY/Fyx0K2aKQ6RoySpJqetSIBmGyttwed+VBIwibgXZBz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YV+Bus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\n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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["このように、x_1だけの和を実行すると、次はx_2が一つのポテンシャルだけに含まれる事になる。\nだからx_2の和はこのポテンシャルだけの和になって、計算すると今度はx_2が消える。\n\n\n順番に繰り返すと、x_(n-1)まで消せる。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA\nAAITAAMAAAABAAEAAAESAAMAAAABAAEAAIdpAAQAAAABAAAAZgAAAAAAAABIAAAAAQAAAEgAAAAB\nAAaQAAAHAAAABDAyMTCRAQAHAAAABAECAwCgAAAHAAAABDAxMDCgAQADAAAAAQABAACgAgADAAAA\nAQKAAACgAwADAAAAAQEKAAAAAAAA/9sAQwACAQEBAQECAQEBAgICAgIEAwICAgIFBAQDBAYFBgYG\nBQYGBgcJCAYHCQcGBggLCAkKCgoKCgYICwwLCgwJCgoK/9sAQwECAgICAgIFAwMFCgcGBwoKCgoK\nCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoKCgoK/8AAEQgBCgKAAwEi\nAAIRAQMRAf/EAB8AAAEFAQEBAQEBAAAAAAAAAAABAgMEBQYHCAkKC//EALUQAAIBAwMCBAMFBQQE\nAAABfQECAwAEEQUSITFBBhNRYQcicRQygZGhCCNCscEVUtHwJDNicoIJChYXGBkaJSYnKCkqNDU2\nNzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6g4SFhoeIiYqSk5SVlpeYmZqio6Sl\npqeoqaqys7S1tre4ubrCw8TFxsfIycrS09TV1tfY2drh4uPk5ebn6Onq8fLz9PX29/j5+v/EAB8B\nAAMBAQEBAQEBAQEAAAAAAAABAgMEBQYHCAkKC//EALURAAIBAgQEAwQHBQQEAAECdwABAgMRBAUh\nMQYSQVEHYXETIjKBCBRCkaGxwQkjM1LwFWJy0QoWJDThJfEXGBkaJicoKSo1Njc4OTpDREVGR0hJ\nSlNUVVZXWFlaY2RlZmdoaWpzdHV2d3h5eoKDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2\nt7i5usLDxMXGx8jJytLT1NXW19jZ2uLj5OXm5+jp6vLz9PX29/j5+v/aAAwDAQACEQMRAD8A/fyi\niigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKK\nKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoooo\nAKK5KD4//AO6+K8nwItfjf4Sk8bw2/nzeD4/EVqdVSLAPmG0EnnBcMp3FcYYetdbQAUUUUAFFFFA\nBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFZXjvxv4V+GXgXWfiV461iLT9E8P6Vcal\nq9/N9y2tYI2lllb2VEZj7CtWvn7/AIKzSyQf8Eov2k5YnKsPgH4w2svUf8SW8oA+P9e/as/4LWft\nzeDdJ/4Kb/8ABILxR4Hm+C974fX/AIRr4IfFLw9Hbax4luLe7vba/mnuEOLZ98Mf2cR3oikjwz7G\nBWT6g/4JYf8ABUr4Uf8ABUX4Q654l8O+BdW8E+OvA2sf2L8Svhz4iGL7w5qQLjy2JVS8bGOUK5RD\nmKRWRWRlHy5/wTB/b2/Z1/4Jt/8ABs78If2ov2g/Eot9K0vwrexaZpcDA3etag2p3vlWNsn8UruC\nM/dRQ0jkIjMPlH9nj4zfta/8E/v+CbX7Sn/BbD4teGIvD3xt/bG8eafZ/B/wbPEQ9p9oluhZSpE6\nglliubqeNJAd8VjCzZ81gQD94rLxb4T1LxFe+ENO8Uafcatpsccmo6ZDeI1xapIMxtJGDuQMOQWA\nyOma0K+MP+CXH/BGj4Df8E97XQvjpfXWr698b9S8F3Nj8TfHOq6u11Lr+oX9zbXt9LKzKGkCz26R\nwkn5YlJO6SSSR/sLxJ4l8N+DPDt94v8AGPiCy0rSdMtJLrUtT1K6SC3tII1LPLLI5CxoqgksxAAB\nJNAF2iqfh7xB4f8AF3h+x8WeE9ds9T0vU7OK703UtPuVmt7u3kUPHLFIhKyIykMrKSCCCCQauUAF\nFYuo/Ej4c6R47074Xat4/wBFtfEusWc93pPh+41OJL6+t4dvnSwwM3mSpHvXcyqQu4ZIyM7VABRR\nRQAUUUUAFFYPxQ+KXw1+CPw81X4s/GDx1pfhvw1oVm11q+t6zeJb21pCvVndyAOwA6kkAZJAPxB+\nw9/wcPfsm/8ABRr9vu7/AGKP2SfhJ458Q6XYaDd6nc/EuawS201Ug2DeYZGE6QOzpGskio5kdF8v\nad4APv2iiigAooooAKKKjN1ardLZNcxiZkLrEXG4qCAWA64BI59xQBJRRRQAV5lf/tqfsbaV8cof\n2ZdS/as+HsHxEuLhbeDwRL4vs11Z5mXcsQtTL5u8ryF25IIOOa+DP2+/2vv2vf8Agoj+3rff8EYP\n+CY/xSn8CWHhfT1u/wBof436bC0svh62lXA0qxkUgJdsJACVZZfMBVXiEFww9f8ABP8AwTm/4Iq/\n8Ek/gb4Z8R/FLwJ4G0gab4z0meH4o/E0w3Gsal4l8wfZruS+mXcJjKrTBI9kMREkgRFVmAB9w0UU\nUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUVk+EPH3gL4hWt3e+APG+k63DYX8lj\nfS6RqMVyttdR48yCQxswSRcjchwwyMigDWooooAKKKKACiiigAooooAKKKKACiiigD84Pjp/wazf\n8Eofit4f1nWvCvhTxz4V8fahrd3rkXxG0jx7fT6st9M8knzG7eaJ0EjKeUEny58wMzM2n/wbG/ti\nfHH9sP8A4JiB/wBpDxre+IfGXw58e6p4O1XWtXuHmvr1bdLe4ie5eQlnkWO6WLe3zMIgWJbcT+hl\nfkJ/wb4XU/wL/wCCt/7fv7Fz3rW+mW3xOTxP4a0R24t4Jr2+8yRB1IMNxp6k+iJ9SAfr3RRRQAUU\nV86f8FKv+Cov7LP/AASm+D+i/GD9p251qeDxF4jh0bRdG8M2SXV/eSsC0kiRPJGDFFGpd23cZVQG\nd0VgD6LopkEyXMCXEYYK6Bl3qVOCO4PIPsa/Nn/g6f8Ai/8AEzwB/wAE4fDnwh+G3iu40YfF34wa\nH4L1+9tJPLlOm3CXU80SuOUDtbRK2OqF1OQxBAP0oVldQ6MCCMgg8EUtfL3wK8D/ALHn/BFH9lz/\nAIVf8S/2pdI8J/DmTx3qMngn/hP/ABAlpBotvfXDzwaLbTXUxeWOAF9rMxfaHdsAEjjtH/4KkeL/\nAIuf8FrLb/gmf+zr4R8Oa94L8KfDB/FXxW8aG4lkmspp0iawtbRkYQnIubORifM3pctt2GFtwB9p\nVwH7VXxY8d/Ab9mfxv8AGz4afDaDxdrfhXw1d6rY+HLrWF0+O/MEbSMjXDI4iG1WbO0524HJzXf1\nw37T+iHxN+zH8Q/DSpuOoeBtWtguM58yzmX+tAHnn/BL39ufR/8AgpT+wd4D/bO0nwgNAfxZZXI1\nHQxdeeLG8trqa0njWQqpdPMgZlJAJRlJFe+V+Wv/AAZ6+KrrxD/wRntdIuJSyaF8S9csYAf4Vb7P\nc4/76uGP41+pVABRRRQAUUUUAFFFFABRRRQAV5F/wUC8NQ+NP2AvjZ4NuIy8erfCLxJZugXO4S6X\ndIRg9fvV67XnP7YdzBZ/sf8AxSvLqUJFF8OdbeR26KosJyT+QoA/EP8A4N7v+CLvjD9vX4FfBz9t\nj/goX8WLbxl8HfAun3sHwS+D8U0jWkMkOsXguZ9RiMaxsDdxyP5YMhuF8pZW8qIQH63/AODixf7e\n/ae/YE+EEwT+y9Z/aq0ea8tNo2OsF1ZR9OnCXEgx/tV6j/wa8o6f8EGfgYrqQfJ8RnB9D4k1Qj9K\n8i/4Oa2X4c/Ev9iT9qHU38vS/Av7UujjUJmOFRZJoLrk9vk0+T8jQB+q9fhN/wAF5P27/wDgof8A\ntA/tI6J/wRw8WfsvP8NPht8a/i7pfhnwn44Gsk6h4o02DUora6lZVJVLaWSe2lCkKwRAGMgchf3Z\nr+eL/gud/wAFJfh34r/4Lo/BP4mabp+oah8KP2R/iVo2n/EnxXpumySpYa1c6k1xeW3A+Zkh0tgq\njlntpwucDIB/Qd4V8L+HfA3hbTvBPhDR4NP0rSLCGy0ywtYwkVtbxII44kUcKqqoAA4AAq/X5lft\nqf8AB1D/AME3vgB8L9L8Y/sveObH4xapeeLNP0rU7HTnvNPttItZ1lke8nnltGztjhfbHGjuzcEA\nA12v/BFz/gvf8Ov+CyXxI+KHw98MfAHUPBD+A2trvRpb7WlvG1jTZ5ZolmkVYkFtKpjjLRBpB+9A\nDttJIB5H/wAHSnw61n4CfBXwF/wV2/Z88SXnh34tfBjxnpVlBrFrfSrHf6NPcyM1hPCD5c0ZuWhY\nq4IZGkVshsV+nHwZ+JmjfGv4N+FfjN4eheOw8WeG7DWbFJCCyw3Vuk6A44ztcdK/Mf8A4PEPizbe\nEf8AglJpnwXsni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j1aO1gs2DdHt8Ac/N+5f7Q3xt8F/s0fADxn+0T8Rbh49C8D+F77XdW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fmzVeG+R4X3sw4kwMI/9O3iK8vup0GvnzH3lTLi4t7SIz3VwkaL955GAA/E18By/8EX/ANpTxZ/o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\nP/b4+CGhaNPqIfTpdJsbsSDU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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["これをx_N側からもやると、最後に残る変数はx_nだけで、これこそまさに求めるマージナルとなる。\n\nここでポイントなのは、和をとる時にはいつも一つのポテンシャルだけで済んでいる所。そこはペアワイズなのでパラメータの数もK^2で済んでいる。\n他の変数との相互作用を表すパラメータが不要なので計算量が減らせられる。"]},{"cell_type":"markdown","metadata":{},"source":["## メッセージパッシングと解釈\n\n上図のチェーンの緑の和と赤の和を関数で置くと下の式が得られる。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nsKDecgCM4HSv6ifEnjDwh4Msf7T8Y+K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BNfOB/wB81+qNFaxyHK4/8u7/ADf+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\n7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UBkIeNhyPQ9DX82X/BSj/g4Q/bi/4KlzeMoP2b/ihqPwI+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\n7FuBYRRW0jRQZUEbpZNykg+UwzX9Mfwf+Fvg74F/CLwv8Efh7Zvb6B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+wz8J18D/EDSddNh8NNBt759L1SK6MMyafAjpIUY7XDAgg85BzXtlfgL8OP+DNq28efBfwF8VPgz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\nFdMupnltJ1B/5Zyv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object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["つまり任意のノードに対して、次のノードへのメッセージは、\n\n前のノードからのメッセージ ✕ 自身と次のノードとのポテンシャル\n\nの和を取った物と解釈出来る。"]},{"cell_type":"markdown","metadata":{},"source":["### こんな風に考えるメリット\n\nx_n以外の、例えば、x_(n-3)のマージナルを求める場合を考える。\n\nそこより左側のメッセージは全部x_nの時と同じ事に気づく。\n\nつまり全ノードのmu_aとmu_bをひとたび求めてしまえば、どこのマージナルを出すのも近隣の2つのメッセージだけをかけ合わせれば求められる。\nメッセージは各ノードについて右向きと左向きがあるから2つ覚える必要があるが、たかだか2Nで済む。"]},{"cell_type":"markdown","metadata":{},"source":["## 2つのノードの同時確率\n\n次にp(x_{n-1}, x_n)を求める事を考える。\n定義から、これも全同時確率からこの2つの変数以外の変数の和をとれば良い。\n\nそれも良く考えるとx_{n-2}より先は先程のケースと同じである事に気づく。"]},{"cell_type":"code","execution_count":1,"metadata":{"collapsed":false},"outputs":[{"data":{"image/jpeg":"/9j/4QC8RXhpZgAATU0AKgAAAAgABgEaAAUAAAABAAAAVgEbAAUAAAABAAAAXgEoAAMAAAABAAIA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\nhiXLyv3woOBknABNfK9l+3b+35+0xFJ4o/ZA/YU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QyZ5wyp14GBXjY7G4/Du6VOEP5pza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\n+y+3ir+3D8PfAek+HG1n7J9n+3GytIrcz+Vubyw/l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BVlMplkujG8QK7C0jJI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PPv3pT+eMN8t2jxer3F25cgXXX3899uzZg/e97324dOlS\nUfNkc/nyZTzxxBO49tprcdVVV+GZZ/KrLN3d3S1wL+d60CCImoYRJSOTyRiA9BKPx6UWaVcyO8vY\ne44ytlfGX5relmQej/g2Pp+P99kBYHv37q2u4ISARCLB9u7dK/hsHnzwwby2j0QiTKlUprfT6XTp\n1+LxOLPZbIK5AbDh4eES5WbsDw/xr79gsKQpq4LP52NarVb0nLS3t7NwOMx7v16vF7ynUMLhMFOp\nVLx51Go1i0QiRR9HOBxm7e3tgmNQKBR5z6FWq3nb9vT0FC0PQUgFWe5KJBaLpWt6pcheJyrPue8C\nf3qNsDvA4cPApdf3IldFjuPHj4u60Et10RGlsbq6ijfeEMZE/vrXv85re4fDwXPh+v1+rK2t4eWX\nX4ZWq8X4+Ljodi6XqziB36ShAbjvXv7YM18racqKs7Kygs7OTtEMWABwu93Q6/W4kuqzBuFvXDG/\neQMDAwL3bjgcxtTUVMFzAVzxbL1eD7fbLXjNarXmNQcVZybqBVLuSkQs2JaUu+ry9FeAD58CNjb4\n4w9+HHj9IqfgbUVzVqf3N954o6iszNtvvx179uzB7bffXvC2BJ9AICA6/vrrr+e1fWaoRIru7u43\nS+Pk/mxnZ2cRi8XyEzIH1ru57NkU48/UdlmU0dFR0aLEmSwvL8NsNmMj+0v2JoUmuszNzeVU4opV\nsC0Wi+D3WKlUYmxsDE899VRec4hdd5Q5T+xESLnbhrW1NVy+fBkLCwuiP2xixTyJ6pBMAh+7H3jo\nNH983z7gR27gy08C+VRneMtb3iIYKzRw/8qVK3jxxRcBAC+++CIu1kiLgoWFBVx//fU4cuQIvvWt\nb0ktTt44nU7R8X/5l3/Jq+6YWJyUmEUnm3g8nlOxzJd9+4DejBZkySTwxBdLmrKieDye9P8KhQKd\nnZ3o7e0VvG9+fj7daznbmrWdcpjJxsbGlpa07J61+bC4uAiv18sb0+v1CAQCePDBB/Oex+fzCcao\n5iWxEyHlLotYLIZz587hL//yL3H11VdDpVJBp9NBq9VCo9Hg1Vf56W9iroxsSxBRftbXgRv/XFhL\n7Phx4CeXkNMNK4aYpabQAPFsa4PUrpxkMolnn3027ab613/9V3z0ox+VVKZ8SSaTmJ6ezvl6d3f3\ntm5zuVye177EWsyV44Ht9EN8693k87VrvcvsLDEyMoKXXnoJX//610UtaCnlLvv7kctyt7Kygltv\nvRU33nhjOhPVZrOJKlEpwuEw1tfXCzqG7PIlqbEDBw7g3LlzuP766/N6KBD77KX+LhNEUUgd9FdL\njI2N8YKwxRaZTMZmZ2fT22QHZiuVSgmPYHewvCyeOHHzhxiLRguf7+1vf7vgc/7lL39Z0BxDQ0O8\n7f1+f+GClIlIJMKMRqPgmHbKtenxeLb8DgJg09PTW87h8/kEiU6ZS0tLC7Pb7WxqakrwWn9/f1mO\n4+HP8a/PT3+mLNOWnVAoxE6fPs2+8pWvCF7r6uoSnJ9IJML6+/sF46urq4LtOzo60q+bTCY2MTEh\n2G5kZEQwVuj3x2w287bXarUsHo8zq9WaHhsaGtp2HrFkDEqQI3YiZLkDZym4+eab0dfXt607LpFI\noLu7O23tqeWiqvXIygpw403CxInTDwHf+XZ+bthsfvtbYZeKQssfZL9fyk4Kw8PDAheVTCbDxMSE\nRBIVRq5kh0xsNlvO+C+AS5Sx2+0CC55SqcTg4CDm5+dx5513ivawLcTFuBX3f4xf1Hj8Ga72Xa1x\n8OBBjI6O4oEHhG34xIp5r66uipYQErN6ZV6H4XBY4O7t6emBwWAQbCf2u7qxsYHXXntN1KqX6iiR\n4l3vehdMJhOvU1B7e7tgu2yyP3uNRpOzFR5B1DKk3AGYnJzEzMyM6GttbW0C100wGERfXx8A4Y9Q\nvRTzXF1dxS9/+UupxeCRTAJ/+d+B7DqjX3sG+OIT/BtpvqysrIgq9D//+c8Lmie76PFWQeEXLlzA\n9ddfj2uvvRZPPvlkQfvJh+zYMrlcDo/Hg1OnTuXYona4cuWKqIvt2LFjvPXV1dVtA+/vuOMOLC8v\nY2pqCmNjY3A4HAiFQvj85z+fDp0QK1ZdrkLJ+/dzyRUpYrHaz5zNRuz3zOfziSp32bFysViM9/uY\nHcLS1taGiYkJ0X1kJ6WdP38+/Vus0+nw6KOP4pOf/CQ++clPwmKxCB6mvv/97/NcvzqdDidOnNji\nSLmHfLG2agSxI5HadFgLdHZ28uoh9ff3M4/Hk663FI1GBXWdADCfzycw46tUKomPpnSmpqaYXC5n\nb33rW5nb7ZZanDQPfFzoip0+W9qcYm4iAMzhcBQ0j9vtFtTrEiMUCjGFQlHSvrbDZDIJjmd+fr6s\n+6gUPT09op+Hy+Vik5OTPFdrd3d3yfsLhUKCfZnN5jIcSWp+xt7SuHm9vq2ZCyvYKdjtdsH5GRsb\nY9FoVDButVp528bjcSaXy0U/T4PBkP599fv9gtc9GYUp+/r6tnXTb7dYLJZtjzUSiQi2M5lM5T2h\nBFEldr3lLplM8lwHPp8PX/rSl3DNNdekn+6bmppgt9sFrrepqam6qnG3sbGBW2+9FT09PYjH4/jt\nb3+L2dnZmqj59so/CK0e33xhs+NEMayvr2NoaEj0tWw3z3Zku/fC4bAgUSOZTMJqtQqsvdku1FIR\ny+7LVcOslrh8+bJoeQy9Xo/29nbcfffdcDgc6e9hORIfxNzv5exIcPCg0Ho3daZs01ccMataJBJB\nU1OTwHqXfR03NjbyWjOm6O3thdvtTv++iiUspL4jsVgMY2NjRcufIp+MV7FQCkqmIHYqu165c7vd\naTeMTqfDkSNHRN935MgRmM1m3pjL5RK4cCrR+7JaOJ1OgUtsYGAA/f39EknEsbEBPPBx/tjph4A7\nSiwnNz4+nrMp+FbZfGKIFULOVqicTqdoOY5yx+eJuZJq6aFDrMVXMplET0+P6Pv7+vrS7eBOnjwJ\nr9eLzs7OspSoqMb39bOf4a+/8M2K77KipJTf7PM/Pz8v+GwffPBB/OxnP8PU1BTsdjuCwSC+/vWv\n81p8iV2bqTG5XF5SqItMJoPVahUt7ZKNWKxlvYTZELuPXa/cZT4VDgwMbPne7ODiRCIhuDns5BiN\nXD9kY2NjOHv2bJWl2WTkCSCzNeiRI8DnHyttzvX19XRZBzGKKWabff4yr41kMpnz+ir1mllbW+PJ\nKlanrZYsEGKWypmZGVG5DQYD7rjjDt7Y8ePH8dJLL+G5554rWRYx5a7cN/QDB4Br/mxzfW6Ofz3X\nMmI151LnR6yMjFgcpFarxR133IE777wThw4dKmj/DQ0NcDqdOXtA5+Id73gHbDYbgsEgnnvuubx6\nRYtdC2IJJQSxE9jVyt1rr72W/jHS6/Xo6ura8v3ZX36xm8BObjJ93XXXYXJyEh0dHYLjsFgseOWV\nV6ou09IS8PgX+GNff4ZfQ6wYhoeHt7TaRKNRXnHXfMh2t2auT0xM5HQjFlMBf2NjAy+88AKuvfba\ndC3GFNVQWIrl8uXLsNvtvLG1tbWcRW2Hh4crKo+YtaYSN/STJ/nr3u1LrtUEYt+B1LVmNpsF2cgD\nAwMFh3Fs5xo/ceIEfvrTnyIcDiMQCMDv98Pv98Pr9cLr9eL555/nbdvU1IRf/OIX+OpXv4qDBw/m\nLUcoFBKM1dJDEUEUwq5W7jItCCMjI9s+3Ym1NMqmltxfxXD33XfjBz/4gSD2KR6Po7OzE+fOnauq\nPI9/gcuSTXHfvcA2SW/bsrS0lFdZkELbIGXf6FIu342NjS2VlEKUiczixBaLJX3zzbwZiikstWJR\nnp6eFnyPent7RRVSi8WC6667rqLyiCkWYuVRSsV0DX+9RhqYbMmlS5cEyp1MJkufn3379glCNsLh\ncMEPRWLXptg1fODAARw5cgRHjx7F0aNHceLECZw4cQLHjx/nve8d73hHXpa6bMTCI1paWgqehyBq\ngV2t3PX09ODkyZPo6+vL6yaST0PpaDRacHX1WuTUqVMCa0oikUBvb69ozFQlWFjgKvunaGwUxi8V\nw9DQkMDKJnZDL/QmlX09pCx1DocjZ2xfrn1ns7i4iCeffBIajQa9vb08F6ZMJuMp47VqudvY2MD4\n+DhPvrvuuku09IlCoai41S4XbW1tFZiTX4MxMJf7vbWCWL3Bzs5OXrzc0NCQIFaymPZhpZCtgBVr\neRX73pDljtixSJ2uu5NQqVS8NPmuri7W1tYmSJ8PhUJSi1oWEokEr8J8ahkYGKjK/j/6sfJX+A8G\ng6KdCzweD1Or1YJxr9eb99xarVa0/IJYGZ3UolarWSKREMwVCoWYy+ViNptNMG/molAoBOVqsq9T\nmUwmuo9q4/P50t0DEolEzrInANj4+HhVZHI6nYJzFS2mzUkeXH1481q++nBFdlE2xMqT5Po+JBIJ\nXrmSQq83sbIqU1NTeW+fXcKk2BI5YtejlJ1mCKIUdrXlrhCWlpYErgK1Wi36ZCdld4Jy0tDQgOnp\naUFMWK6Cz+VkZYVvtWtqAh78eO7358vIyIjAdd7V1YVrrrlGNOZSzKqUi+zzFA6Hcfny5S3LqhgM\nBp4L6Te/+Q1OnDgBjUaDjo4OjI+P5yxjolKp4PF4BFZnMQtEMW6qcpPqF7u6ugqLxSJa9gTgOgnc\nf//9VZEp20rX1tbGs0yVk0zvY603thkcHBSMGY1G0ULADQ0NeOqpp+D3+zE7O1twpnlTU5PA+lZI\nl5Dm5mbe51hMDCtQuxZvgigGUu7yRKyEhV6v5zXdTlGu9kW1QHNzM4xGI2+sGnGFE8/yY+2sd3MV\n/0thYWFBEMwvk8nSte4sFotgm8nJSaysrOQ1f/YNyufz5VRgUmRnHP7jP/4j/umf/mnbfbW3t8Pv\n9ws6NwDCG5LYNVptNjY20opyJBLJeV7UavW256ycHDx4kKcYGI3GgrOk80XZvPl/HuG7knHhwgU4\nnU7B+HblRI4ePYpjx47h2LFjBT9MZIcmFJqYltlaLPv3Kl/EWp6RckfsVEi5yxMxC47JZBL9ESpE\nuYvFYnjhhRfw9NNP48KFrVPoNjY2cPny5YrdfHLtMzuxoNCyBIWSTPILFjc0lMdqNzo6KlBMzWZz\nurbh0aNHBZacaDSadxHV7BtBNBrdVlHJ7qt51VVXbfl+o9EIt9uNH/7whzhw4IDoe2rx4SIQCGxr\n0VYoFHA6ndhfqhZfIGNjY1CpVNBqtejr66uY5W6nIFZ4uLW1Fd3d3RXbZ3bcXqEPkH19fZDL5ZDL\n5RVJiCGIHYfUfuGdwOrqqiBOq62tjTHG2OjoqCBOY2hoKK95E4kEa21t5W3b29sr+t6JiQmmVCoZ\nAKZUKtnk5GTRxxOJRFg4HM4rLmZqakpwfCMjI0XvOx9mzvNj7W7+UOlzLi8vC1ohyWQyQXyk2PEi\nz9i7sbGxgloiKRQK0c9gdHSU6fV61trayvR6PbNYLMzhcLBgMJjXsWbvR6fT5XeSKojH49nyXKjV\najY7Oyu1mBXl+g9sXtNX7ZdaGnGyYxBTy/T0dMX3bbVa0/uz2+0Fbx8KhfL+joiR3UqyVmJVCaIY\nSLnLg+Hh4ZwKzuTkpOC1vr6+vObNdcMLBAK89w0MDIi+TyzYNxaLsZ/97Ge8sXg8ztxuNxscHGQd\nHR1pRXW7HprxeFw0yaDSQca33c5X7lyvlD7n0NCQ4DjEAq8TiQTTaDSiClI8Ht9yH7n61OZaKqV0\n1aJyt7y8LOipm1pMJhNbXV2VWsSKU+vKndjDJgCm1+urJkPq97QaymQ29dgnnNi9kHK3DcvLy2mL\nmZjFR+xJt729Pa+5I5GIYO7s7W02W07loKurizdfKBRiV111Vdq6p9VqmU6nE80OzUdOMaU232Mr\nlnicsd/ft3kTfOdBxkp9eI5Go6LnOZelyOVyiZ6v4eHhLfcj1mQ9c8mWIZ9m5sWQvd/tlPhq4fF4\nmMlkYkajkZlMJma1WpnL5ZJarKpx7fs3r+vfaZJaGiG5rNbV/oz6+vqKstyVik6n4x23RqOpugwE\nUS5IuduGwcFBwY+d1WpNv+71ekVv4vma84PBoOCJEeDKqWzn5pPL5Txr0le+8pWCLEdb/WjnKhmS\nXXaj3Lhe4VvtPvqx0ucUs9qZTKYtt+nt7RVsI5PJtnTP5ro5ZlrQMtfzdd8XQiKREHxu/f39Zd8P\nUTiZyt3v75NaGj65rPSdnZ1VlyUSiQi8F9Ug+/u53W8EQdQylFCxBYuLi4L+ozKZDH19fel1seDd\nSCSSs9VUNocOHRItO+B0OgXV37OJx+O8IPXf+73fy2ufAJcZesMNN+SRZXQRAAAgAElEQVR83Wq1\nCoKae3p6Kt4x4Px5/vott5Q2XywWE02I2O7cDg8Pi/YSNpvN2ya+iNHe3s7L6AMq07Q+Ho8LPjcK\nMK8Nohl5ULXUpTCZTGJiYkI04UWKQtLNzc3pJKdqkv19LLakCkHUBFJrl7VMZoBvasm02qUQK2Q8\nODiY934SiYSg8KxY7EtLS4tgzOl0pueJx+PMbDbntBwpFArW2dnJpqent7Qsjo+Pi1ojl5eXCzuB\nRfCHh/jWjW3C3LZlenq6aNdyIBAQtV7K5XJms9nYzMwM7zw6HA7R865SqVgoFBLMVwnLHWNMcJ2E\nw+GK7IcojMxr+z1HpZaGIx6Ps1AoJBq20NPTI7V4VSX7HJSStEYQUkPKXQ4CgYCociSm4Ii5bnN1\nHsiFmGs2c5HJZKJuv0zlLkUikWA+n49NTU2xkZERNjY2xmZnZ7dNCGCMywwWc8+MjY3lfSzFEg6X\nP0vWaDTmdc5ysZ2rtaOjI/3eeDwuUKxUKhUvAcXj8TCNRsMUCkXFskMzXcpSuNUIcTJjSa99v9TS\ncAQCgZwhCFK4RqUk+0GOulMQOxlS7nLQ1dUl+MHLFVCfq1WPz+fLe3+5MmJTy+joaN7KXSlkthFK\nLVqtVrQl0+rqKltdXc1LacyH6bN85W70ydLmm52dFRyLwWAoeJ7JycmcSSkA/ysUCASY2WxmJpOJ\n9ff3S2I1y7weq9XGi9iaRIKxtzRuXtu3flhqiThGRkYEJYKA3RmnmXn8Go2GyqAQOxpS7kRI9cDM\ndktGIpGc2xgMBsE2Yi7cXGyVPGEymVgikRB9j8fjKcchM8Y4pWCrJIpgMMiGh4eZTqfjlbWQy+XM\nYrFseX7y4eHP8ZW7AnRjUcQSKYpNCAkGg6yrq4t3fpRKZc0qT6mHk0J64xKVY3WVf23f9RGpJeKy\nyLOTCFLX9W4oTZNNptXdZrNJLQ5BlAQlVIggFkQ8PDyM5uZmkXdziFVvn5qawpUrV/LaZ652O62t\nrXA4HGhoaEAoFBK8Ltbbthg2NjZgsVhEOzjMzs7iPe95D7RaLQYHB+H3+3mteuLxOOx2+7ZJCtvh\n9W7+39AAlNoII/t8mUymohNCDh06hO985ztYXV1FKBRCKBTC6upq1XqgFkqqe4per5daFALA8jJ/\nvUxf25KYnJyE3+8XjA8ODmLfvn0SSCQtnZ2d6f+tVquEkhBEGZBau6w1xGqcqdXqbV2Py8vLolYv\njUaTl2suFAoJirzqdDretnq9XhAXI+YuLQaxmnZyuXxLd2T2IpPJSpLh6sOblo3/dqz0Y8q0dKpU\nqpKq1+80gsFgVYvPElvj8ZQ35KBUlpeXBUlcAJfIVa4wi51GKBRiarWaihcTdUENJeRLTzKZhM1m\nE4wPDAygsbFxy233798Pq9WKiYkJ3ngoFEJ7ezsCgcCWzbQPHjwIn88Hh8OBSCSCtrY2WCyW9Dax\nWEzwlN3W1laWPpgLCwsYGhoSjMcL7G5eSumAWAxYWNhcV4u3TS2IBx98EHK5HMvLy7BYLDh48GDp\nk+4QDh06VLIllSgfq2v8daktd6Ojo6I9iO12+7a/dfXKwYMHMTY2lncvaYKoZUi5y2B6ehrBYJA3\nptVq0dvbm9f2o6OjcDqdgnpR8/Pz8Hq9uOaaa7bc/siRIznrO83OzgpcpkajMS+5tmNsbKzgRt0A\noFarodFooNfrReu4FUK226pcJabuu+++8ky0Azl16pTUIhBvkv2cJKVyt7i4iPHxccF4T08Pjh8/\nLoFEtUNHR4do+AtB7DRIuctA7IltaGhoS4tbJk1NTfB4PBgaGoLX603/SGg0mpILYno8HsGYwWAo\nac4Udrs97/e2trbCbDaju7sbR48eLcv+ASC0yF8/dKhsUxOE5FSgXnXRjI+PC6zyCoVCULB9N9LU\n1ASLxSK1GARRMqTcvcnc3BxmZ2d5Y2q1Gl1dXQXNc+jQIXzrW98CwLk7I5EIdDpd3gpiLrJlA7ig\n+Wogk8lgtVphtVrLcixiZFvulMqy74IgagZl7tysiiPmjh0YGMD+/fslkKb22I3JJET9Qcrdm4hZ\nr3p7e0uKPzlURvNTIBDgravVahw4UIbANHDWSbH4LLVajd7eXlit1or/8GdbNki5I7ZiZWUFXq8X\nLpcLoVAIwWAQ0WgUiUQCMpkMra2t0Ol0MBqNaG9vl/yGnR31UEQURNnQ6/W83zu1Ws1rqUgQxM6H\nlDtwiRSTk5O8MZVKVVM/eNmlUsrlkgWA06dPQ6FQYHp6GkqlEmq1GmazGSaTqSJWOjGyb3aK0vNE\niDpjYWEBk5OTcDqdgoedbLxeL7xeL8bHxyGTyWAwGGA2m9HT0yOJhSq70pGUvWV7e3sRDAYxOTmJ\ntrY2TExMlCUxiyCI2oGUO3CJFNlNo7u7u2vqB6+npyed0SqXy8ueCXnfffft6uQDonY5e/YsJiYm\nRONO8yGRSKSVveHhYQwMDKCvr2/XZoU2NDTgqaeewlNPPVXR/cRiMYRCobQ1VaPR1NRvKkHUM6Tc\nAXC73bx1mUxWc2UkHnnkEeh0Ovj9fnR3d+Pw4cNSi0QQFeXChQvo6+sTjTcVQyaTbZv1HYlEMDAw\nALvdDofDkTM7vdzUklu2Eqyvr8PtdiMQCGB2dhZ+v19QNUAmk6GtrQ3t7e0wm804ceKERNISRP1D\nyh04S1gmVqu1JmuinTx5EidPnpRajIqQHWMXWZdGDkJ6kskkBgcHMTo6mlNZUygUMBgM6Zi61tZW\nKJVKNDQ0pGtC+nw+OJ1OUYvf/Pw8DAYDnE7ntiWKiNycOXMGExMT8Pl82yrWiUQCfr8ffr8fo6Oj\n0Gq16Ovrg9Vq3bVWVIKoGFJXUa4FAoFAulp7d3f3rq3QLiXOl/kV/CeelVoiQgrC4TAzGo05O6B0\ndHQwh8NRUGcWv9/PbDYbk8vlot1n8ukgUyrDj/Ov70Cg4rusKPPz84KOOcUuarWazczMSH1IBFFX\n7GGMsSrpkQSRkytXgD9q21x/8OPAl5+UTh6i+szNzaGjo0PgzgO4JACbzVaSG3VxcREdHR2Yn5/n\njbe2tsLn823ZO7pU7r0PeP5vNtf/VxCoQedAXpw7dw49PT0Fd7DZjp6eHkruIIgyQcodUROsrwP/\nV0bV/mv+DPjRq9LJQ1SXS5cuoaOjQ1CDTavVwm63ly0+KxaLob29HT6fjzduNpvxve99ryz7EOND\ntwDn/35z/TdRYCd6Ip988slt45EVCgV0Oh10Oh1aW1uhUCgQjUbh8/ngdruxnF3UMoOUq1zq0jUE\nsdMh5Y6oGf5YD1y+zP3f0AD8en1n3gCJwrh06RLa29tFM9YnJyfLbsmZm5uDwWBANBrljTscDtxy\nyy1l3VeKD9wAvPoj7v99+4B/z63f1CwPP/wwhoeHRV/T6/WwWCzo6OiARqPJWUIpmUzC5XKlE1rE\n0Gg08Pv9FbWkEkS9s1dqAQgiRft1m/8nk0CWcYWoQ5aWlmA2mwWK3dDQEF588cWKuOiOHDkiqGsJ\ncF0aNjY2yr4/APBf3vy/paUiu6goTz75pKhiJ5fLYbfb8frrr+P+++/HoUOHtqyN2dDQgJtuugnf\n+c534PP50NraKnhPKBSCxWJBMpks6zEQxG6ClDuiZsj2vL38fWnkIKpDMplEV1eXIMZubGwMjzzy\nSEX3ferUKRiNRt5YMBjMaU0qhZUVYG1tc127w/omv/DCC6Ku2JaWFvh8Ptx5551FzXv8+HH4/X5Y\nrVbBazMzMxgZGSlqXoIgSLkjaoiOGzh3bArny9LJQlSeoaEhQezb6OgoHnzwwarsX0x5EGtDWCqB\nOf768eNl30XFuHjxInp7ewXjGo0GXq8XR48eLWn+xsZGPPfcc6L7GBwcxMWLF0uanyB2K6TcETVD\nYyOn4KW4cgWYm8v9fmLnMjc3J3Dz9fT04PTp01WT4cSJE9BoNLwxj8eD9fXyFlnMDi9oaxN/X62R\nTCbR29sryIpVq9Xwer1l7Z09NjaG9vZ2wfjg4GDZ9kEQuwlS7oiaIrtG89lvSyMHUTmSyaTAFafV\najE2NlZ1WTo7O3nriUSi6DZnubhwgb9u2CGWu+npafj9ft6YQqGAy+XCgQMHyrqvxsZGTE1NoSUr\nINHtduNC9gkkCGJbSLkjagrzSb5r1v4Cl1xB1A/T09MCd+zU1JQk5S90Op1gLFuhyWRtbQ2PP/44\nrr32Wrz3ve/FBz/4Qdx11114+OGHcfbsWVy+fJmXCJBMAt4M3eTwYS5bttZJJpOiCRR2u71iLdv2\n79+P0dFRwbgUSj9B7HSo/RhRU+zbB3TetFkTbGkJcL8K3PABaeUiykMsFsPAwABvzGaz4bhEgWjZ\nblkAgszdFMlkEgaDAcFgcMs5lUpluoeqUvl+xGJ/mn7NVKFOZ2tra+nElLa2ti0zVvPB5XIJij0b\njcaKlYpJ0d3djYGBAV6SjdPpRCwWo+LGBFEAZLkjao7s5LtnnpFGDqL8TExM8G7ccrlc0rgqmUz4\nfBsKhUTf6/P5tlXsAE459Hq9GBoaQt8nnLzXfvazb+HMmTOYm5tDLBYrSuZMYrEYXnnlFVgslnTh\n4JaWFpw9e7akeScmJgRj1ficGhoaBMkV8Xi87K5ygqh3qIgxUXMkk8AfHuKsdil+HgLKHOazxf6T\nCIVCCAaDCAaDWF5eRjgc5ll0FAoF5HI5WlpaoFKpoNFo0gsVXxVnfX0darWaVzx4eHgYn/3sZyWT\naW5uDm1ZGQ7t7e344Q9/KHjvxYsXYTAYCpp/z94fYc/ea9PrbyT2A/j39LpWq+VdO2q1GiqVCmq1\nGgBnBQQAlUqF1dVVRKNRRCIRBINBhEIh+P1++Hw+QdcHuVyO1dXVoqxdKysrUKvVSCQS6TG9Xo/X\nX3+94LmKQewzsdls+OpXv1qV/RNEPUBuWYlZW1uDx+OBx+PhWQZkMhmUSiU0Gg20Wi3a29vR3t6+\nKxSHhgbg/o8Bn8m450+dAT71V5XZ38bGBrxeb9oV5fV6c7rm8kGr1cJgMMBgMKCjo6OsWYU7Gbvd\nzlPsVCoV+vr6JJRInOwWaCn0ej30ej1mZ2fznOntPMWOsZ8gU7EDkH6AKDfxeByBQKAod7fD4eAp\ndgBgsVjKJNn2tLa2Qq1W8yy82TGaBEFsAyMkwefzMavVyuRyOQOQ16JSqdjAwABbXl6WWvyKs7zM\n2F7Z5vKOA4zF4+WbP5FIMKfTybq7u5lCocj7Myhm0Wq1bHh4eFd8brlIJBJMrVbzzsvIyIjUYrFA\nICD6eeVidXWV2Ww2ZjKZmNVqZRMTE6y3t5cZjUamUqn4c+35EO8a3rP3sYpeZ5lLa2tr0efEaDTy\n5pLJZFW/dru7u3kyKBSKqu6fIHY6pNxVmXA4zLq6ukr64VapVGxyclLqQ6k4t93OV/Bcr5Q+ZyKR\nYJOTk0yr1VbtRpta5HI56+vrY5FIpPQD2WE4HA7BzboWzkOhyt12BINB5nA4mNVqZb/b9CLv+gX+\nuCrXmVKpZIFAoCj5o9Eok8lkvPmMRmPR56NYBgcHBccVDoerLgdB7FTILVslkskkJiYmMDAwIGhY\nXiirq6uwWq3wer2YmJhAY2NjmaSsLe6+m1/n7vz50rJmX331VdhsNkEW4FaoVCq0tLRAq9Wm45+A\nzYzKUCiEcDic05WXSTwex9jYGKanp2G323HDDTdsu029MDU1xVvv7e2tiRCDUtzvYhw6dAiHDh3C\nLbfcgpd/AMRXuPG3vvX/w1986I/wz//8HzkTNkpFLpejp6cHg4ODOHjwYFFzeL1egUvWbDaXQ7yC\nEOs5G4lEyl5fjyDqFVLuqsDS0hJ6enq2zPiSyWQwGAwwGo2Qy+WQyWQIh8MIBoPweDyCH1yAi2FS\nKpV46qmnKii9dBhPAM3NQKphgPNl4GtFZM6mym+Mj49v+T6lUgmj0Qi9Xg+j0QidTpd37bWNjQ1e\ngLvX680Zm7W8vIyOjg7YbDaMjo7WrXKeYn19HU4nP2u0mjFcWyGmaGUq8cVy8SLXUzbFrV2/g2++\n8C0A3PWYulZSiTuhUAihUAiRSCRvhTMVj6vT6WAwGMoSk+v1egVjYp0jKo1CoRCM5fMARRAEByl3\nFeaVV15Bd3d3zh9svV6P3t5edHd358xsi8VicDqdGBoaElidxsbGoFarq9q2qVo0NgLt1wHnvsut\nLy0Bi4tAIUaJhYUFdHR05AxaVyqV6OrqQk9PD4xGY9H1wRobG3H48GEcPnwYp06dAsAly0xPT2N4\neFiQzQgA4+PjSCQS+PrXv17UPncKTqeT93DS1tZWsUK4hSKmMIgpFoWS3Vnlpps2/29qasKRI0dy\nnoNYLIbV1VXE43HE43EkEgnE4/G0XEqlEi0tLRV5KMhW7lI1+6qN2GdQbisrQdQ1UvuF65mxsbGc\ncTEajYY5nc6C5ovH42xoaEh0vpmZmQodhbSMPc2Pu7O/kP+2MzMzOZMllEolGx0dZdFotHLCv0k8\nHmfj4+NMqVSKyuJwOCoug5SYzWbe8Y6OjkotUhqLxSL4PLq6ukqaM5Fg7J0HN6/Z32libHW1PPJW\nmuykkI6ODknk8Hq9gs+l0N9LgtjNUBHjCpBMJvGJT3wiZ5mHvr4+BAIB3JT5OJ8HjY2NeOSRR9Dd\n3S14zWq1YimzMFydkF3R/9Kl/LY7f/48urq6ROMbbTYbgsEgTp8+XZWq942Njbj//vsxOzsrWiet\np6cHi4uLFZdDCsRcsl1dXRJJI0QsVEKsJVkhuF/l12g0n9wZLcfW19cFlkwprHYARMNQxMYIghCH\nlLsyk0wm0dPTI9oPUaVSweVy4amnnipJqZicnITJZOKNra6u1kwcUzlpa+Pcsyn8l7ff5sKFC+jq\n6hLcDBQKBWZmZvDVr35Vkj6mhw4dgsvlglar5Y3H43FYrdaqy1MNsl2yBoOh6GD/crOysiIac5f9\n3SqUM2f469kdV2oVsdCF7Gu1WojFPZJbliDyh5S7MpJMJmGxWDA9PS14rbW1FX6/vywZkk1NTZia\nmhLEpbjdbjxTZ726GhoAvX5z3efjOljkYmlpCWazWaDY6XQ6+P1+nDx5skKS5kdzczNmZmZEP7tL\n+ZoldxBut5u33tHRIZEkQux2u2BMJpOVZLlbXwcc5zbXDxyoXD/ZclNLyh1BEKVByl0ZGRwcFJR8\nAIDOzk7Mzs6WNY3/wIEDovsaGBjAwsJC2fZTC7RlxJ0nk0CuShIp5TrbtaTX6+HxeGqmU8SRI0cE\n/TMBCNyX9UB2gL4UZTVyIfYQZjAYSrKqO84BGxub61238C3PtYxY0o9Uyp1YOIVYH2CCIMShb0uZ\nePrppzEyMiIYt1gsmJycLDoLcytOnjyJ3t5eXpPvaDQKm82GH/zgB2Xfn1RkJxWGFgExPW1sbExg\nKdJoNHC5XDVRUy2TVBmUTBwOBx555JGyzL+xsYH5+XkEg0GEw2EkEgneDTPl4pLJZFCr1VCr1dDr\n9WV1mS4tLfGsQS0tLZLFcGXz2muvwe/3C8ZLsSwmk8CTX+aP3fnfi56u6oi5qFUqVfUFAReqkE05\nspgJYrdAyl0ZeOWVV0STJ6rR7Hp4eBhOp5PXh9HlcuHixYtF9ZWsRTQa/vr8PHDd+/lja2trGBoa\n4o3J5XI4nU5J4uu24+DBg9BoNLwbaiAQQCwWK9hylOqNOzU1hXA4jHg8Dr/fX1SxbLVaDZPJBJPJ\nhNbWVrS2thZ9/rLdfG1tbRV5yCmGXDUPS0n2cJwDrlzZXL/pz4GjR4ueruqIJSxUI+FIDLH4unLU\nHySI3QK5ZUtkYWFBNHu1o6NDNKmi3Ozbtw+Dg4OCcTGX7U6l9TB/XczrPDw8LFBmRkZGaqaemhhi\nsV2Fdi9YWVlBW1sb2tvbYbfb4Xa74fV6i+6CEg6HMTU1BavVCqPRCJVKhQceeKDouTKpFavdlStX\n4HA4BOOdnZ04fPiwyBbbk0wCj3+BP3b//UVNJRnZ14yUypRYFxlN9lMeQRA5IeWuBDY2NtDV1SV4\nytTpdHA4HFWzUlitVqjVat5YPcVvtbTw17P1n7m5OYEi3draCpvNVlnBSkTM5VVoRuDw8HDOAs3l\nYnx8HE888UTB22XHPtaK5aW/v190PFfponyYOgPMzW2uHz9eWqs8KciOaZMyxi27u0sqfIAgiPwg\n5a4ERkZGBHE7KpUKMzMzVXVnNDQ0oLOzkzcWCoXqpnZaUxO/Tlgwy3I3PDws2GZ8fLxmXIC5EIsh\nKlRRy7aOVYrBwUGsZPbTyoNaUhZSvPbaa6IPPgaDAdddd11Rc25sAE98kT/2+ceKmkpSsq9Hqdp9\nJZNJ+Hw+3pjBYKj57/NWxGIxrKf6KBLbsrKygtdeew1PP/007rnnHnziE5/A008/jSuZcQ/Elkj/\na7tDuXDhgiDGSyaTYWZmRpI6XmJZbX6/v2ZqipWK7ijw6o+4/zOT+i5evCjIeuzs7Cz6Rl1NytFi\nyWKxYGZmJufrKpUKWq0WcrmcZzlL/R+NRhEOhzE7O7tlkdhEIoGZmRncd999BcmXidR1yjY2NnLW\nExQLbcgX+wv8WLujR4UxoTuVYmJAS8Xn8wkyd/WZ9ZBqmLW1NQQCAczOzsLr9cLr9SKRSKSvfbVa\njaGhIdx9991l3/dPf/pTuN1utLe3493vfjcWFxcRj8eLDjXIxOVyIRQK4bbbbqtYctr6+jrsdjsc\nDodoj2OAi6N2u904ceJERWSoJ0i5K4JcN4mhoSHJLjox5W6nN9re2NhIKxwq1VsBvAUAsLbGdQA4\ncACicY2l3KirSTksWSdPnoTD4UgruBqNBhqNBgaDAS0tLXmX31lfX0cwGITL5YLP50M8HkckEkm7\nx4qp/5atvErdYaC/v1/UMtrR0VFwt5gUS0vAJ/+KP/alL4q/t9YRi2lbXV2tunIn9rCS7ZkolZR1\nMBgMIhQKIRKJYHV1FdFoFJFIBDKZLP37mZlZniJ1LctksvT/qW23us7D4TCsVitMJlNZSzMtLi7i\nT/7kTxCJRHDVVVfh6NGj8Hg88Hg8JSt3s7OzuPHGGwEAzz77LOx2O46WMVNoZWUFDocDQ0ND296z\n4vE4RkZG8NJLL5Vt//UKKXdFMDo6Kgj41ev1OWN5qoFYPJNY3SopicViCIVC6R/TUCiE5eXl9Ho4\nHEY0GhX/gu/5HPY2PJpeXV4G4vEFgdXObDbXTZZwvtxyyy245ZZbSpqjubkZx44dw7Fjx3jjly9f\nRigUgl6vL7hOY3ZMYbFJHuXg3LlzOTNkxUoY5ctHPwbEYpvrx47tnKLF2YhZkldXV6tq/d/Y2BAk\ngymVypK7hmSSKlsl1e+jUqksa4mZVH3PlBL6q1/9Cl6vFzMzM2UxNmS2tfT7/eju7sbs7GxJSn8y\nmcT8/DwCgQACgQBaWlowMTGBRCIBuVyOUCiUVqaj0ShcLle6VaDb7UYymdzRbvqqIHVz253G8vKy\noBm9TCZjwWBQUrn8fr+g0XZ/f78kskSjUTY7O8tGR0dZT08PMxqNgnNW8LLnw+lG7HtljFnu+hEb\nGxsTvM/v90tyzMVgtVoF8g8PD0stVtlwu928Y2tvb5dEDp/Px+Ryueh1NTAwUPS8488w3jW5V8aY\n11tGwauMx+MRnJ+pqamqyjA1NSWQwWazlW3+kZGR0n6HSlw6OztZIBAo2/EwxpjdbuftQy6XM4/H\nU7b5l5eXmVqtLvl7k0gk0kskEmHLy8t5b+v1enn7D4fDBe9/t0GWuwIZHBwUWCCGh4cl734g9tQt\nVgi0EqTqrPl8PrjdbszOzpbfSsP4iQN2uwfXmv4Hb0yv15fVXVBpAoGAYKyeyj20trby1v1+f9Wf\nuC9evIiOjg7R74JOpxPEzebLqz8CPvEQf+zBjwM7ORRILLRDrCRJJRELsyhn3+XsRI1K09LSAoPB\ngPb2dnR2dlbECiqXy9P/q1Qq2O12XHNN+czH+/fvh9/vh06nSydw2e12tLe3i8Y2b2xsIBKJIBKJ\nQK1W8+RLffebm5sLit07ceIEOjo64HK5AHAJg+Xs+FSPkHJXAAsLC4J+lGq1umZLblQyk3JhYQEz\nMzNpc3nl46n4x7Jnjwr/9m//xhurpb6l2xGLxQTlHgChQrSTOXDgANRqdfo6XF1dhc/nq1pc6sWL\nF9He3i76oKFUKjEzM4PGInqDLSwAN3+I3+P46NGdmSGbyYEDB6BUKnmJL4XWXSyFM2fOCL4TJpOp\nrA9snZ2dgpg+hUIBhUKBeDyePv6US1ChUOQdc6dQKCCXy9HW1gaj0QidTgej0VjUNVYIp06dQjQa\nxfLyMmw2W0USHvbt24fh4WFYLBYAXMhPe3s7VCpV+nyljr+7uxvt7e0wGo1ljdfs6upKK3dEHkht\nOtxJ9Pb2Su62yEU4HBbI1tXVVdZ9RKNRZrfbWWdnJ5PJZFVxY8hksjeXt7I9Df+Zdn/t2fsPNftZ\n5IOY+0mpVLJEIiG1aGWlp6eHd4wdHR1VOUaXy5UzFEAmkzG3213UvOEwY+84wHfF/v4+xiSOyigb\nOp2Od660Wm1V9huNRllLS4vgs3I6nWXfl91uZ21tbUyv17PV1dWyz1+viIUkZS4Gg6Gs7uBs4vE4\na21tJbdsnkhquYvFYhgdHYXRaNy2dMX6+nr6CSGVkZR6asrumyn2hJVJ6vXM1zKfwHQ6neDpJxaL\nCQJ9tVqtaHeKemNlZQXDw8OYnJwsydWberrTaDRQqVTQaDTpvqYqlQpqtRpKpRJKpTL9GWV+Du9q\n3exO8c7/8sf4eYg//04qcprZDzhFe3t73QUJ9/X18b43LpcL/f39GB0drdixnjlzBhaLJac1eXx8\nvKhSOWtrwI03AZnl/hoagO98W7zX8U5Er9fzancGg0EsLCxUPOxkdHRUkOBgNBqLzmLeijvvvBN3\n3nln2eetd/bv349AIICxsTFMTEyk7wVdXV3o7u6G2Wyu6O9XY/DIvs0AACAASURBVGMj7HY7PB4P\nuWTzQSqtMh6PM4vFkg4AjUQibHV1lbndbjY+Ps4sFgvr7OxkKpWq6kGvcrmc9fb2skgkkpY3O2gV\nAJuYmJDq9AkIhUIC+cxmc0lzxuNx1t/fnzMYfatFJpMxo9HIBgcHmcPhYLOzsywajZYkz7Xv37SW\nyN76BgP28vY5MzNT0vzVwufziZ6zSlgpaoGBgQHBsWo0GtbV1cWGhobY0NAQGx4eZmNjY2xqaop5\nvd6irHuJRIINDg5ueV0W+50Nhxl7z1FhAsXUmaKmq1mmp6cF56zSST6zs7OinoB6/T7UA/F4nHk8\nHrJ81jCSKXcejyf9hZbJZGlzay0tmdl97e3tvNcUCgVP+ZOaQCBQVuUuGAwKXDRbLQqFgnV2drLh\n4WHm9XpLVuTEuOsj/BurTPb2HXkz6OjoEJw/tVpddy7ZFPF4nOn1+oK+eyqVig0MDOSdUef3+5nB\nYNhyzmLd9sGg0BW7V8bY5PNFTVfTJBIJplQqeedNLpczn89Xkf1lutpy/fYSBFE4kih38XhckFpd\nqwtjjK2urgqeLLu7u6U4dTnJThUHwKxWa1Fzzc7OCn7gxRatVsv6+/uZ2+2uimIy/Dj/5trcfDNP\nnvHx8YrLUCpisXYA2MjIiNSiVZTl5WXW2dlZ8PdPLpdvaW2LRCKsv79/yxhQuVzOHA5HUXL7fIy9\nrVmo2E2fLfZM1D7Dw8OCc6jRaCrywGaz2UQ/r/n5+bLviyB2E5Iod2KKSC0uarWaMcaYw+EQvFZr\nViIxpaFYd4qYZSm1tLS0MJvNxmZnZ8t8BNvjfJl/g1WpvsCTbXBwsOoyFcLq6qpo0LhSqawpK3Cl\nSCQSzG63M7PZXHC4RabLPeUSstls29ZPVCqVRQd5O84x9pZG/jX3O03cdVjPRKNRptFoBOfSbDaz\neDxetv04nU7Rz2xsbKxs+yCI3YokCRUtLS3bvkcmk0GtVkOj0aSD7FOp1kqlkpdQAfA7NBSaUOFy\nuQQp1nK5PF32JDPAOLV9OSumlwOxtkrF1kwTO2darRYjIyMVD5rdCl1WRYSGt/CD4qtdw6pQent7\nRaviDw0NVaxfYy3R0NDAC2a/8cYb4XK50NfXB4vFAq1Wi3g8jmAwiMnJSUxNTaWDtm02G/x+P/x+\nPzweT159arVaLVwuV8HJAMkk8OnPAE9+mT/e1MQlT9zwgYKm23E0NTVhZmYGBoOBl0A1MzOD9vZ2\nTE9PlxzQvri4iJ6eHsG40Wis2dJSBLGjkEqrnJycZCaTiSmVStbS0sJMJhOzWq3MbreXJfg+X4aG\nhkQtdpkxJtnxdm1tbVWRrRC6u7sFx+Etslz+1VdfzbPUTUxM1Ew82NWHM9yyv7/OO16ZTFZQ1fNq\nItZNI3WtldMaspOoZLcAq9Va1G9IMMjYe48L3bDvPMjYDmp+UhYmJydFz61CoSjJcxGNRkXj7BQK\nBQuFQmU8AoLYvezqOndiil12lixjTOCiKDaWrZKIxcgVm8k0MDDAtFotGxgYqBmlLsVtt/NvusAf\n8I5ZqpZrWyHm1k8txdZbqwfEMrxLXTQaTdHndOY8V7MuW7F73wkuW3Y3slX2sclk2vIB0ufzsa6u\nLqbRaNjk5CRjjHOpm0ymbV3vBEGUxq5V7kZHRwXxJLkywrIVp1qL7QoGg6KxRrWmmJWD0Sf5N96D\nBx8QWO9qqZhxZlZ49tLX1ye1eJKTy6JZ6KJSqdjo6GhRVtBIRJiJnVo+8RBjVXIi1Cx2u33Lckhq\ntZrZbDZmt9vZyMgI6+/vF2Qu6/V6Fo/HBV6QzIdqgiDKx65U7lKWFJVKxYaGhrZ15WVb7mrtpizm\nPuns7JRarIoQCvFvvjff8r9FbxZjY2OSK7c+ny9nwH/qZkdw7tliaikCXIiE3W4vOozD/ap4mZO3\nNDI28WyZD3QHEwgEti01s5Xi7fF4clrsjEaj5N9Vgqg3dp1y53a7mclkYk6nM+8flLa2Nt6PUbnb\nepWKWLzd6Oio1GJVjHcf4cdCnT79SdGbhk6nK+nGXwpbtb9qaWmh9jlZRKNR5nQ6mc1mY21tbTlL\n8ajVatbZ2clGR0dZsISeX/E4Y5/+jLi17g8PMVbBLko7lkQiwcbHx/Mqk5Ra+vv7WSgUylnnUK/X\n74pMcYKoNrtKuQsEAmx8fLzgH5Ouri6BtaAclEPpEKvBB0CSUiXVIvum/PrrG1taFVQqFbPZbMzp\ndFZF0bPb7TldsSqVigUCgYrLUA/E43EWiURYKBRioVCobJ9dMMh/QMhc7rmX3LDbEY/H2dTUFDOb\nzYJ6pTKZjGm1Wtbd3c18Ph/z+/05a5rqdLqaTYAiiJ3OHsYYwy4gmUwiHA7j4MGDBW/7+OOPY3Bw\nkDc2OzuLY8eOFSXL2toaenp64HK5YDAY8OMf/7ioeXLJplar8Ytf/KLoOWudixeBPzFurp9+CPji\nE9y5GBoaytlTFODK2Oj1erS1tUGhUPBK6CgUCkSjUahUKsjlcrS2tkKv16OxsTEvuZLJJIaGhjA8\nPCz6ulwuh8fjwfHjx/M7UKLsnP02cM+9QCzGH9+/H/j614CTfyGNXDuZpaWldLkog8EAh8OBeDyO\nUCiE8fFx0e+jXq+H0+nE/v37qy0uQewOpNYudwJirb1Kibs7ffo0b65iiUajosVgay3hoxJklkT5\n/X2cm40xLrlkqyLMhS5yuZx1dHSwiYmJLbOPw+FwzmDx1DzFFtMlSmd5WZhpnVpu/HPudaJ0PB7P\ntt8pk8kkSagEQewmSLnLk+y4O6D4MhaZMXImk6lomfr7+wUy1XKtt3KS3Yosu4F7KBRiw8PDzGg0\nlk3RU6lUopm4Dodjy44LSqWyYr05ie2ZOc/FZpY1aSK4yJj/p4yF6/+7VgjhcHjLVnB9fX2UPEEQ\nVWDXuGVL5ezZs+ju7uaNKRQKuN3ugtxsr732Gq+7hcvlwg033FCwPOfPn4fZbBaMW61WPPfccwXP\nt9NYWQHeeZDrJgAAx44B/5yjQcXS0hI8Hg/m5+cRDAYxPz+PeDyOeDyedstqNJq0m7alpQWJRALR\naBR+vx+hUCjdAUSlUuFXv/oVAGB9fR39/f2YnJzMKWdrayscDgeOHDlSvoMn8mJtDXjg45wrNpuD\nB4EXzwAFe8gv/L/Aw18BXnt9c+zQfwHuvx2w3gI0/W5JMtcD58+fh9VqxerqanpMoVBgamoKJ0+e\nlFAygthFSK1d7iTEGp+rVKq8rTKRSIRn4SnWauf3+0Uz1pRK5a6w2qW49cN8S0whOSSp7gip4qrb\nMT8/z6xWK7NYLCyRSLCpqaltswY7OzuLLiRNlEaugsR7ZYx99GNFJk2Mn2Hsd3SM7f2j3Mt7b+Xe\nt8uJRqPM4/GwsbExNjMzQ98DgqgypNwVwOrqqqh7ViaTsenp6W23z8669RfRzygUCuV0Ae62htte\nL/+mfeuH8982M47SbrfntU0ikWBOp1O0dVL2MjQ0RO4nCQgGuRg6MaXunQcZc75cxKSR/8PYjfdu\nrdRlLzfey1hoqdyHRxAEkRek3OVJKgA4HA4zrVYrekMfGBgQtZzF43FBfFwxbbK22nd3d3fJx7gT\ned8JfgxVvq0pI5EI7/zZ7XbRosKJRIIFAgE2PDyc89xnLmq1ele3FJOKQCB3wkRJ1jr/Txl7902F\nKXapxXx/2Y+TIAgiHyjmLk/m5uaQSCRw9OhRXLlyBUajkRdTkkImk8FqtaKtrQ0tLS2IRCKw2+3w\ner3p97S0tGB+fh7Nzc157//KlSvo6OhAKBQSvNba2gqfz1fQfPXC2W8Dt9+xuX7fvcDXnslv23e/\n+92Yn59Pr6vVapjNZsjlcgBcuZtAICD6OYthsVgwOjqKffv25S0/UTzJJOB5DXjmGeD834u/58AB\n4FsvANdcU8QOFn4OvPfDwPqvxV9vaAB0rYB6PyCTAYrfBaK/AWZe5YQb7AUefaCIHRMEQZQGKXd5\nkkwmMTAwgP7+fuzfvx9LS0uwWCxwu90FzSOTyeB2u3FNAXebixcvoqOjA5FIRPCaQqGA3+/HoUOH\nCpKjXtjYAK4+DCwtcesNDcBPLgH55C989KMfxcTERMkyqNVqTExM4Kabbip5LmJrNjYA1ytcrcOp\nM5ufezbNzcAjnwN67wPyLFPIJ5kE3ncbcGlO/PX9KuBvHwduMApfW/81EN/g3kMQBCEBe6UWYKfQ\n0NAAhUKBgYEBJJNJHDhwAE6nExaLJe855HI5HA5H3ordxsYGnnjiCRiNRlHFTi6Xw+1271rFDuBu\n3F/64uZ6Mgl8+jP5bWuz2dJWumKQy+UYGRlBMBgkxa6CJJPAqz8CPnI38I4DwIduAZ74orhi19wM\nfO5h4GdXgAc/XqRiBwDT38+t2B3RAq9/W1yxA4Dmt5FiRxCEtEjrFd5ZOBwO0cSF6elp0f6umYtK\npWIulyvvfTmdzi1jvBQKRUHz1TOJBGPvPb513btceDyegpvWt7S0sKGhIcoArCDxOGOuVxj7xEO5\ns16z+8GOPc1Y2dqU3vOweBzdzTYuwYIgCKKGIbdsASwuLkKj0QDg2uxYLBYYDAa0traisbERCwsL\n8Hg88Pm4gmuJRAJarRY6nQ4mkwlNTU1bzh+LxeB0OjE2NpaeQwyVSgW3242jR4+W7dh2OpcvA+87\nwbntAM6C85NLXD2z7cjHxa5SqdDe3g6z2Qyz2Zx3SzIif5JJwOvl4iinzghbhGXT0AB0nwJuuQXo\nvIlbLxt/8THg5df4Ywf/APiZCwgtAc+fA5ZXgWNHAPN1wAFqo0UQRO1Ayl2BXHvttfB4PLwxmUyG\njo4O9PT0oLOzc1slDuBi+JaXl+H3++H3++Hz+eByubbsiwoAWq0WTqcThw8fLuUw6pJHHwMe+/zm\n+jV/Bvzg+/m75hYXF+H1etNJKynlvLW1FTqdDg1l1R6IFJcuAee+u3UMXYrmZsB4Ajh5Eui4gUuY\nqAjvt/ALFQOc9vilTwKf/jKw8Vv+a02/C3QYAc0fAEeuBkz/N6cMEgRBSAApdwVy4cIFGI05Ym3e\npK2tDRqNBjKZLD0WiUQQjUaRSCQQiUSwvLyMeDxe0L6tVivGxsbyUh53I8kkcOOfc/FZKT71V8AX\nHpdOJkKcxUUuMeLZb3BW161obOQsdKdOAaZrSoijK4SPPw4883ciwrxVqNjlYp+Sy6ZtUQGH/yvQ\n+oec0qd8W5nNjARBEHxIuSuCZ555Bn19fdta2cqFTqfDyMhIUW3KdhsLC8B7jwPr65tjd38E+Maz\n0slEcCSTgPNl4PnnOcUu1TpOjObmTZer8USVFLpMLv5P4E9uq8zcDQ1c+RTl73F/tf+Fc+tqD3Ll\nVFRKQN3CKYcEQRBFQMpdkczNzcFsNqd7jlYCtVqNgYEB9Pb2kkuwAF75B+D/b+/+42us+z+Av7jG\nYT9sMm3ZQkYjymrKzxpNUdQUN0pF6U6hpCTdJJSiRIri/qYIRTfdFOXXyoSs22rKYmUxbdqyZcs2\nDjvt+8fHsXOd63OdH9vZOWfXXs/Hw2M7n+s61/mY7tvL58f7c7vd5tWRDwDvvO2DkEDIzxdTrovf\nFiN2emzX0PVNBHw+QP3UHGDhSt99flAg0KihCHwBAYDtPyaDA0U4bNQQ6NROTAWHhYiRQYZCojqP\n4a4aLBYLlixZghkzZrhc6NaZ4OBg9O7dG8OHD8eQIUO4cL+Klr0HPDJG3ZZ4M/DfT/wgNNQRGRki\n0C1fUbnRRSbhJjHlOnyYGLHzG/kFwBW3uD4N6w9MDYH/mwWMuMPXPSEiH2K484DCwkIsWbIES5Ys\nQU5Ojtvvj4uLQ5cuXdC/f38MHDiQgc5DNn8O/GOoOlgw4NUsiwVYtx5YvVr8/PW0agXcN0KMqPp1\nmcbpbwKzJXP6TUOBv//WP73Cl0wNge8/AWKv8HVPiMhHGO48LCsrC8eOHUN6ejpKSkoutgcEBCAs\nLAzBwcEICwtDWFgYoqOjER0dzTBXg9LSgNsGAIWFlW1duwJfbHY8SlRaKtaFJScDO5LFGr6fD/vZ\nyJIfycoSU6/L3nO84zXpTmDkyBooXVJTik+L0TtZiNuwCGhzObDvAHDgMHD4V+DwUSA33/v9tBff\nERh3LzBykK97QkQ+wHBHhnfgANAnUb3JomtXYPtW7QheVhaw8E3g3WXqET9FEaceuFI3r64oLBQB\neNkyIGWX/n1BQcDDo4FxY/18lE7P4g/F7ll7id2Abcu07aVlIuSlHxa18DJ/BXLygSPHvRv8FAU4\n94P3Po+I/AbDHdUJGRnAjQnagPfRahHYcnOB1+cDixard3GaTGKUKTERGDWSGzIKC8VI5urVzne8\nxsaKI8DuG1HLp8HN54B2/eXB7POl+seQ6T2r4JQIfQWnRODLzgWOnRCvS8pEkeRyS/WnfBOuB75c\nXr1nEFGtxHBHdUZGhhjBs52iNZmA1q2BzEz1vVFRwIuzxCbFB0aKtqQ7RVhx8Whgw8jPF0Fu40ZR\nysRRoFMUUVx43Dig363e62ONm7kYmPW2tj0qAvhxozhPtiaUlomgF6CIr1aNTMBZsxgRPGsWgfCe\nSZV/OF2vAb74d831i4j8GsMd1SkZGWINnt66MJMJeO1VMY1oMon7r4lT3xMfD7zysiioWyvWjbnJ\nbAZ27wFSUsQoXWqq8/d07iw2RwwZXIOnRvhSYZFYe1dapr02YiDwwVzv98lebj6wIVkUTR6UaMz/\nOInIJQx3VOcUFgLPTAZWfFDZFhoqpl0nPKFeV2exAJe3EqNX9jp3FlO28fFAl3ggMtLx36dmM1BQ\nIMqV2RxecrF8WXi4+rW1tJnt14AAz04Nl5YCx44B6QdEkN29B9i3z/HonFVsLDAoCRh8t/gZGJ7e\n2jsA+HAeMOw27/aHiEgHwx153b1pE7HmxCY823YMXukwyWf9sIaZgAAx4qS3EzY1FbgjST2dqyc0\nFAi7UEM2IAAoKhLvs4Y+V0KTI9bnNGokPicyEggOEt/bhkAr26BoLcVYUir6VVCgXoPoilatRD26\npDvFmsU6xXwOuDoJyDquvRYUCHy/Hohp6f1+ERHZYbgjr+vwVT9klvwKAIgNboNOIVeivKI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HJoHnLO5OGl9hM1U8Kl5WWaMiuhASEIlUxDAkC4qTL0KfUUPNxyaK0Id7ln8rDo2Cp0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\n","text/plain":["<IPython.core.display.Image object>"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["MeatPieImage()"]},{"cell_type":"markdown","metadata":{},"source":["こうして隣り合った2つのノードの同時確率も、ひとたびメッセージを計算して保存しておけば、3つの項の積で局所的に計算出来る。\n\nこれはEMアルゴリズムで使うから重要、との事。9章でやるらしい。"]}],"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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