{"id":6762,"date":"2023-11-08T18:52:47","date_gmt":"2023-11-08T09:52:47","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=6762"},"modified":"2023-11-08T18:52:47","modified_gmt":"2023-11-08T09:52:47","slug":"sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/","title":{"rendered":"SAT \u3092\u30b5\u30fc\u30d9\u30a4\u4f1d\u642c\u6cd5\u3067\u89e3\u304f"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><a href=\"https:\/\/colab.research.google.com\/github\/T-QARD\/t-wave\/blob\/main\/notebooks\/random_K_SAT\/random_K_SAT_article.ipynb\" target=\"_blank\" rel=\"noopener noreferrer\"><img decoding=\"async\" src=\"https:\/\/colab.research.google.com\/assets\/colab-badge.svg\" alt=\"Open in Colab\" \/><\/a><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\" >\u6587\u732e\u60c5\u5831<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E6%A6%82%E8%A6%81\" >\u6982\u8981<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E7%92%B0%E5%A2%83%E8%A8%AD%E5%AE%9A\" >\u74b0\u5883\u8a2d\u5b9a<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%9D%E3%83%BC%E3%83%88\" >\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30dd\u30fc\u30c8<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E5%95%8F%E9%A1%8C\" >\u554f\u984c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E3%82%BD%E3%83%AB%E3%83%90%E3%81%AE%E5%AE%9F%E8%A3%85\" >\u30bd\u30eb\u30d0\u306e\u5b9f\u88c5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#Hill_Climbing\" >Hill Climbing<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#Simulated_Annealing\" >Simulated Annealing<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#Warning_Inspired_Decimation\" >Warning Inspired Decimation<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#Survey_Inspired_Decimation\" >Survey Inspired Decimation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E7%B5%90%E8%AB%96\" >\u7d50\u8ad6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\" >\u53c2\u8003\u6587\u732e<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2023\/11\/08\/sat-%e3%82%92%e3%82%b5%e3%83%bc%e3%83%99%e3%82%a4%e4%bc%9d%e6%90%ac%e6%b3%95%e3%81%a7%e8%a7%a3%e3%81%8f\/#%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\" >\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb: Survey Propagation: An Algorithm for Satisfiability<\/li>\n<li>\u8457\u8005: A. Braunstein, M. M\u00e9zard, R. Zecchina<\/li>\n<li>\u66f8\u8a8c\u60c5\u5831: <a href=\"https:\/\/doi.org\/10.1002\/rsa.20057\">https:\/\/doi.org\/10.1002\/rsa.20057<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span>\u6982\u8981<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>$K$-SAT \u306f\uff0c\u3044\u304f\u3064\u304b\u306e\u5909\u6570\u304b\u3089\u306a\u308b\u8ad6\u7406\u5f0f\u3092\u5145\u8db3\u3059\u308b\u3088\u3046\u306a\u771f\u507d\u5024\u306e\u5272\u5f53\u3092\u6c42\u3081\u308b\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3067\u3059\uff0e\u30e9\u30f3\u30c0\u30e0\u306a $K$-SAT \u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u5145\u8db3\u53ef\u80fd\u6027\u306f\uff0c\u7bc0\u306e\u500b\u6570\u3068\u5909\u6570\u306e\u500b\u6570\u306e\u6bd4 $\\alpha=M\/N$ \u3092\u5909\u3048\u308b\u3068\uff0c\u3042\u308b\u70b9\u3067\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u5177\u4f53\u7684\u306b\u306f\uff0c\u3042\u308b\u81e8\u754c\u5024 $\\alpha_{\\mathrm{clust}}, \\alpha_c$ \u304c\u5b58\u5728\u3057\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6319\u52d5\u3092\u793a\u3057\u307e\u3059\uff0e<\/p>\n<ul>\n<li>$\\alpha &lt; \\alpha_{\\mathrm{clust}}$ (easy-SAT \u9818\u57df): \u307b\u3068\u3093\u3069\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u53ef\u80fd\u3067\u3042\u308a\uff0c\u30b7\u30df\u30e5\u30ec\u30fc\u30c6\u30c3\u30c9\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0 (SA) \u306a\u3069\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u5bb9\u6613\u306b\u89e3\u304c\u5f97\u3089\u308c\u308b\uff0e<\/li>\n<li>$\\alpha_{\\mathrm{clust}} &lt; \\alpha &lt; \\alpha_{c}$ (hard-SAT \u9818\u57df): \u307b\u3068\u3093\u3069\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u53ef\u80fd\u3067\u3042\u308b\u304c\uff0c\u5c40\u6240\u89e3\u304c\u975e\u5e38\u306b\u591a\u304f\uff0cSA\u306a\u3069\u3067\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u56f0\u96e3\u3067\u3042\u308b\uff0e<\/li>\n<li>$\\alpha &gt; \\alpha_c$ (UNSAT \u9818\u57df): \u307b\u3068\u3093\u3069\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u5145\u8db3\u4e0d\u53ef\u80fd\u3067\u3042\u308b\uff0e<\/li>\n<\/ul>\n<p>\u6587\u732e [2] \u3067\u306f\uff0c $K=3$ \u306b\u5bfe\u3057\u3066 $\\alpha_{\\mathrm{clust}} \\approx 3.9$, $\\alpha_c \\approx 4.3$ \u304c\u5831\u544a\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u672c\u8a18\u4e8b\u3067\u306f\uff0c\u30e9\u30f3\u30c0\u30e0\u306a 3-SAT \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u3044\u304f\u3064\u304b\u5b9f\u88c5\u3057\u3066\u6027\u80fd\u3092\u6bd4\u8f03\u3057\u307e\u3059\uff0e\u305d\u3057\u3066\uff0c\u6587\u732e [1] \u3067\u63d0\u6848\u3055\u308c\u305f\uff0c\u30b5\u30fc\u30d9\u30a4\u4f1d\u642c\u6cd5\u306b\u57fa\u3065\u3044\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\uff0chard-SAT \u9818\u57df\u3067\u3082\u52b9\u7387\u7684\u306b\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E7%92%B0%E5%A2%83%E8%A8%AD%E5%AE%9A\"><\/span>\u74b0\u5883\u8a2d\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%83%9D%E3%83%BC%E3%83%88\"><\/span>\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30dd\u30fc\u30c8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"kn\">import<\/span> <span class=\"nn\">random<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\n<span class=\"kn\">from<\/span> <span class=\"nn\">tqdm<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">tqdm<\/span>\n\n<span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">seed<\/span><span class=\"p\">(<\/span><span class=\"mi\">42<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E5%95%8F%E9%A1%8C\"><\/span>\u554f\u984c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>$K$-SAT\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u751f\u6210\u3059\u308b\u95a2\u6570 <code>create_random_instance<\/code> \u3092\u5b9f\u88c5\u3057\u307e\u3059\uff0e\u3053\u306e\u95a2\u6570\u3067\u306f\uff0c$K$-SAT\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092 CNF\u5f62\u5f0f (\u30ea\u30c6\u30e9\u30eb\u306e\u8ad6\u7406\u548c\u306e\u8ad6\u7406\u7a4d\u306e\u5f62) \u3067\u8fd4\u3057\u307e\u3059\uff0e\u4f8b\u3048\u3070\uff0c\u8ad6\u7406\u5f0f<\/p>\n<p>$$<br \/>\n(x_0 \\lor x_1 \\lor x_2) \\land (x_1 \\lor \\lnot x_2 \\lor \\lnot x_3) \\land (\\lnot x_0 \\lor x_2 \\lor x_3)<br \/>\n$$<\/p>\n<p>\u3068\u3044\u3046\u8ad6\u7406\u5f0f\u306f\uff0c 2\u6b21\u5143\u914d\u5217\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff0e<\/p>\n<pre><code>[[0, 1, 2], [1, ~2, ~3], [~0, 2, 3]]<\/code><\/pre>\n<p>\u5404\u7bc0\u306b\u3064\u3044\u3066\uff0c $K$ \u500b\u306e\u5909\u6570\u3092\u91cd\u8907\u306a\u3057\u3067\u4e00\u69d8\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3057\uff0c\u9078\u3070\u308c\u305f\u5404\u5909\u6570\u306b\u5bfe\u3057\u3066\u80af\u5b9a\u30ea\u30c6\u30e9\u30eb\u304b\u5426\u5b9a\u30ea\u30c6\u30e9\u30eb\u304b\u3092\u78ba\u7387 $1\/2$ \u3067\u6c7a\u5b9a\u3057\u307e\u3059\uff0e<\/p>\n<p><strong>\u5b9f\u88c5\u306e\u898f\u5247<\/strong><\/p>\n<ul>\n<li>\u5909\u6570\uff0c\u7bc0\u306eindex\u306f0\u59cb\u307e\u308a\u3068\u3059\u308b\uff0e<\/li>\n<li>true \u306f $1$, false \u306f $0$ \u306b\u5bfe\u5fdc\u3055\u305b\u308b\uff0e<\/li>\n<li>\u8ad6\u7406\u5909\u6570\u306f$i,j,\\dots$\u3067\u8868\u3059\uff0e\u7bc0\u306f$a,b,\\dots,$\u3067\u8868\u3059\uff0e<\/li>\n<li>\u80af\u5b9a\u30ea\u30c6\u30e9\u30eb\u306f <code>i<\/code>, \u5426\u5b9a\u30ea\u30c6\u30e9\u30eb\u306f <code>~i<\/code> \u3067\u8868\u3059\uff0e\u7b26\u53f7\u3092\u898b\u308c\u3070\u80af\u5b9a\u304b\u5426\u5b9a\u304b\u308f\u304b\u308b\uff0e<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">N \u5909\u6570 M \u7bc0\u306e K-SAT \u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u4f5c\u6210\u3059\u308b<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">):<\/span>\n    <span class=\"nb\">vars<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">clause<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n        <span class=\"c1\"># K\u500b\u306e\u5909\u6570\u3092\u9078\u3076<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">sample<\/span><span class=\"p\">(<\/span><span class=\"nb\">vars<\/span><span class=\"p\">,<\/span> <span class=\"n\">K<\/span><span class=\"p\">):<\/span>\n            <span class=\"c1\"># \u80af\u5b9a\u30fb\u5426\u5b9a\u3092\u9078\u3076<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"o\">~<\/span><span class=\"n\">i<\/span>\n            <span class=\"n\">clause<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">clauses<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">clause<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">clauses<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u307e\u305f\uff0c\u591a\u304f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306fSAT\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u56e0\u5b50\u30b0\u30e9\u30d5\u3067\u8868\u73fe\u3057\u3066\u6271\u3046\u305f\u3081\uff0c\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u56e0\u5b50\u30b0\u30e9\u30d5\u306b\u3088\u308b\u8868\u73fe\u306b\u5909\u63db\u3059\u308b\u95a2\u6570 <code>build_factor_graph<\/code> \u3092\u7528\u610f\u3057\u307e\u3059\uff0e\u56e0\u5b50\u30b0\u30e9\u30d5\u3068\u306f\uff0c\u5909\u6570\u30ce\u30fc\u30c9\u3068\u56e0\u5b50\u30ce\u30fc\u30c9\u304b\u3089\u306a\u308b\u4e8c\u90e8\u30b0\u30e9\u30d5\u3067\u3042\u308a\uff0c\u56e0\u5b50 $a$ (\u3053\u306e\u5834\u5408\u306f\u7bc0 $a$) \u304c\u5909\u6570 $i$ \u306e\u95a2\u6570\u3067\u3042\u308b\u3068\u304d\u306b\u56e0\u5b50\u30ce\u30fc\u30c9 $a$ \u3068\u5909\u6570\u30ce\u30fc\u30c9 $i$ \u306e\u9593\u306b\u8fba\u304c\u306f\u3089\u308c\u3066\u3044\u308b\u30b0\u30e9\u30d5\u3067\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">\u4e0e\u3048\u3089\u308c\u305f\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304b\u3089\uff0c\u56e0\u5b50\u30b0\u30e9\u30d5\u3092\u69cb\u7bc9\u3059\u308b<\/span>\n<span class=\"sd\">- factor_to_var: \u56e0\u5b50\u30ce\u30fc\u30c9\u304b\u3089\u5909\u6570\u30ce\u30fc\u30c9\u3078\u306e\u96a3\u63a5\u30ea\u30b9\u30c8<\/span>\n<span class=\"sd\">- var_to_factor: \u5909\u6570\u30ce\u30fc\u30c9\u304b\u3089\u56e0\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u96a3\u63a5\u30ea\u30b9\u30c8<\/span>\n<span class=\"sd\">- J: J[a][i] \u306f\uff0c\u7bc0 a \u3067\u5909\u6570 i \u304c\u80af\u5b9a\u306a\u3089 -1, \u5426\u5b9a\u306a\u3089 1<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">build_factor_graph<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">factor_to_var<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[[]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)]<\/span>\n    <span class=\"n\">var_to_factor<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[[]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)]<\/span>\n    <span class=\"n\">J<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[{}<\/span> <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)]<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">clause<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">enumerate<\/span><span class=\"p\">(<\/span><span class=\"n\">clauses<\/span><span class=\"p\">):<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clause<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"n\">l<\/span>\n                <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>\n            <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"o\">~<\/span><span class=\"n\">l<\/span>\n                <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n            <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/span>\n            <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">return<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span> <span class=\"n\">J<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E3%82%BD%E3%83%AB%E3%83%90%E3%81%AE%E5%AE%9F%E8%A3%85\"><\/span>\u30bd\u30eb\u30d0\u306e\u5b9f\u88c5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3053\u3053\u3067\u306f\uff0c4\u3064\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3057\u307e\u3059\uff0e<\/p>\n<ol>\n<li>Hill climbing (HC, \u5c71\u767b\u308a\u6cd5)<\/li>\n<li>Simulated annealing (SA, \u713c\u304d\u306a\u307e\u3057\u6cd5)<\/li>\n<li>Warning inspired decimation (WID)<\/li>\n<li>Survey inspired decimation (SID)<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"Hill_Climbing\"><\/span>Hill Climbing<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>HC\u306f\u6700\u3082\u30b7\u30f3\u30d7\u30eb\u306a\u5c40\u6240\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\uff0e\u5909\u6570\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u5909\u66f4\u3057\u3066\uff0c\u76ee\u7684\u95a2\u6570\u304c\u6539\u5584\u3057\u305f\u3089\u305d\u306e\u5909\u66f4\u3092\u63a1\u7528\u3059\u308b\u3068\u3044\u3046\u3053\u3068\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\uff0e<\/p>\n<p>\u5177\u4f53\u7684\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\uff0e\u3053\u3053\u3067\uff0c\u30a8\u30cd\u30eb\u30ae\u30fc $E$ \u3092\uff0c\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u7bc0\u306e\u500b\u6570\u3068\u3057\u307e\u3059\uff0e<\/p>\n<ol>\n<li>\u3059\u3079\u3066\u306e\u5909\u6570\u306e\u5024\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316\u3059\u308b<\/li>\n<li>\u5909\u6570\u3092\u30e9\u30f3\u30c0\u30e0\u306b1\u3064\u9078\u629e\u3059\u308b<\/li>\n<li>\u9078\u629e\u3057\u305f\u5909\u6570\u306e\u771f\u507d\u5024\u3092flip\u3059\u308b\u3053\u3068\u306b\u3088\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u5909\u5316 $\\Delta E$ \u3092\u8a08\u7b97\u3059\u308b<\/li>\n<li>$\\Delta E &lt; 0$ \u306a\u3089flip\u3092\u63a1\u629e\uff0c\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u68c4\u5374\u3059\u308b<\/li>\n<li>$E=0$ \u3068\u306a\u308b\u304b\uff0c\u65e2\u5b9a\u306e\u30a4\u30c6\u30ec\u30fc\u30b7\u30e7\u30f3\u4e0a\u9650\u306b\u9054\u3057\u305f\u3089\u7d42\u4e86\u3059\u308b\uff0e\u305d\u3046\u3067\u306a\u3051\u308c\u3070\uff0c1\u306b\u623b\u308b<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">Hill Climbing \u3092\u7528\u3044\u305f\u30bd\u30eb\u30d0<\/span>\n<span class=\"sd\">\u8fd4\u308a\u5024\u306f (\u6700\u7d42\u7684\u306a\u30a8\u30cd\u30eb\u30ae\u30fc\uff0c\u6700\u7d42\u7684\u306a\u5909\u6570\u306e\u5272\u308a\u5f53\u3066\uff0c\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u63a8\u79fb)<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">hill_climbing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">4<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span> <span class=\"n\">J<\/span> <span class=\"o\">=<\/span> <span class=\"n\">build_factor_graph<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"c1\"># \u5909\u6570\u306e\u5024\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316<\/span>\n    <span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)]<\/span>\n\n    <span class=\"c1\"># \u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u8a08\u7b97<\/span>\n    <span class=\"n\">energy<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"o\">~<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">])<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">val<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">energy<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n    <span class=\"c1\"># \u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5c65\u6b74<\/span>\n    <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">energy<\/span><span class=\"p\">]<\/span>\n\n    <span class=\"c1\"># \u3059\u3067\u306b\u5145\u8db3\u3055\u308c\u3066\u3044\u305f\u3089\u7d42\u4e86<\/span>\n    <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n        <span class=\"k\">return<\/span> <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span>\n\n    <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_iter<\/span><span class=\"p\">):<\/span>\n        <span class=\"c1\"># \u5909\u6570\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3059\u308b<\/span>\n        <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># \u30a8\u30cd\u30eb\u30ae\u30fc\u5909\u5316<\/span>\n        <span class=\"n\">delta<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n\n        <span class=\"c1\"># flip\u524d\u306e\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u7bc0\u3092\u6570\u3048\u308b<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n            <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n            <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"o\">~<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">])<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">val<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">delta<\/span> <span class=\"o\">-=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"c1\"># i\u3092flip\u3059\u308b<\/span>\n        <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n\n        <span class=\"c1\"># flip\u5f8c\u306e\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u7bc0\u3092\u6570\u3048\u308b<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n            <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n            <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"o\">~<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">])<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">val<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">delta<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"k\">if<\/span> <span class=\"n\">delta<\/span> <span class=\"o\">&lt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"c1\"># flip\u3092\u63a1\u629e<\/span>\n            <span class=\"n\">energy<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">delta<\/span>\n        <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n            <span class=\"c1\"># flip\u3092\u68c4\u5374<\/span>\n            <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n\n        <span class=\"n\">history<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">energy<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># \u3059\u3079\u3066\u306e\u7bc0\u304c\u5145\u8db3\u3055\u308c\u305f\u3089\u7d42\u4e86\u3059\u308b<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">break<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>3-SAT \u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u52d5\u4f5c\u78ba\u8a8d\u3092\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">alpha<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.2<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"n\">hill_climbing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy = \"<\/span><span class=\"p\">,<\/span> <span class=\"n\">energy<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">history<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"iteration\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>SAT\nenergy =  0\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[12]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Text(0, 0.5, 'energy')<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u5358\u8abf\u306b\u6e1b\u5c11\u3057\u3066\u89e3\u306b\u5230\u9054\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"Simulated_Annealing\"><\/span>Simulated Annealing<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>HC\u306f\uff0c\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u6975\u5c0f\u5024\u304c\u4e00\u3064\u3057\u304b\u306a\u3044\u5834\u5408\u306b\u306f\u6700\u9069\u89e3\u306b\u52b9\u7387\u3088\u304f\u5230\u9054\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u3057\u304b\u3057\uff0c\u6700\u9069\u3067\u306a\u3044\u6975\u5c0f\u5024\u306b\u4e00\u5ea6\u5230\u9054\u3057\u3066\u3057\u307e\u3046\u3068\uff0c\u305d\u3053\u304b\u3089\u629c\u3051\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\uff0e\u305d\u3057\u3066\uff0c$K$-SAT \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u306f\u3057\u3070\u3057\u3070\u591a\u304f\u306e\u5c40\u6240\u89e3\u304c\u5b58\u5728\u3059\u308b\u305f\u3081\uff0cHC\u306f\u52b9\u7387\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff0e<\/p>\n<p>SA\u306f\uff0cHC\u306b\u30e9\u30f3\u30c0\u30e0\u6027\u3092\u52a0\u3048\u308b\u3053\u3068\u3067\uff0c\u5c40\u6240\u89e3\u304b\u3089\u8131\u51fa\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u3068\u3057\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\uff0e\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u975e\u5e38\u306b\u6c4e\u7528\u7684\u3067\u3042\u308b\u4e0a\u306b\u591a\u304f\u306e\u554f\u984c\u306b\u5bfe\u3057\u3066\u9ad8\u3044\u6027\u80fd\u3092\u793a\u3059\u305f\u3081\uff0c\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>SA\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\uff0e\u300c\u6e29\u5ea6 $T$\u300d\u3068\u3044\u3046\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u901a\u3057\u3066\uff0c\u30e9\u30f3\u30c0\u30e0\u6027\u306e\u5f37\u3055\u3092\u5236\u5fa1\u3057\u307e\u3059\uff0e<\/p>\n<ol>\n<li>\u3059\u3079\u3066\u306e\u5909\u6570\u306e\u5024\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316\u3059\u308b<\/li>\n<li>\u6e29\u5ea6 $T$ \u3092\u66f4\u65b0\u3059\u308b (\u672c\u5b9f\u88c5\u3067\u306f\uff0c\u7dda\u5f62\u306b\u5909\u5316\u3055\u305b\u308b)<\/li>\n<li>\u5909\u6570\u3092\u30e9\u30f3\u30c0\u30e0\u306b1\u3064\u9078\u629e\u3059\u308b<\/li>\n<li>\u9078\u629e\u3057\u305f\u5909\u6570\u306e\u771f\u507d\u5024\u3092flip\u3059\u308b\u3053\u3068\u306b\u3088\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u5909\u5316 $\\Delta E$ \u3092\u8a08\u7b97\u3059\u308b<\/li>\n<li>\u78ba\u7387 $\\min(1, \\exp(-\\Delta E\/(NT)))$ \u3067 flip\u3092\u63a1\u629e\uff0c\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u68c4\u5374\u3059\u308b<\/li>\n<li>$E=0$ \u3068\u306a\u308b\u304b\uff0c\u65e2\u5b9a\u306e\u30a4\u30c6\u30ec\u30fc\u30b7\u30e7\u30f3\u4e0a\u9650\u306b\u9054\u3057\u305f\u3089\u7d42\u4e86\u3059\u308b\uff0e\u305d\u3046\u3067\u306a\u3051\u308c\u3070\uff0c1\u306b\u623b\u308b<\/li>\n<\/ol>\n<p>$T\\to 0$ \u306e\u6975\u9650\u3067 HC \u3068\u4e00\u81f4\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">Simulated Annealing \u3092\u7528\u3044\u305f\u30bd\u30eb\u30d0<\/span>\n<span class=\"sd\">\u8fd4\u308a\u5024\u306f (\u6700\u826f\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\uff0c\u6700\u826f\u306e\u5909\u6570\u306e\u5272\u308a\u5f53\u3066\uff0c\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u63a8\u79fb)<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">simulated_annealing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">4<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span> <span class=\"n\">J<\/span> <span class=\"o\">=<\/span> <span class=\"n\">build_factor_graph<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"c1\"># \u5909\u6570\u306e\u5024\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316<\/span>\n    <span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)]<\/span>\n\n    <span class=\"c1\"># \u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u8a08\u7b97<\/span>\n    <span class=\"n\">energy<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"o\">~<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">])<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">val<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">energy<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n    <span class=\"c1\"># \u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5c65\u6b74<\/span>\n    <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">energy<\/span><span class=\"p\">]<\/span>\n\n    <span class=\"c1\"># \u3059\u3067\u306b\u5145\u8db3\u3055\u308c\u3066\u3044\u305f\u3089\u7d42\u4e86<\/span>\n    <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n        <span class=\"k\">return<\/span> <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span>\n\n    <span class=\"c1\"># \u6700\u826f\u306e\u72b6\u614b\u3092\u4fdd\u5b58<\/span>\n    <span class=\"n\">best_energy<\/span> <span class=\"o\">=<\/span> <span class=\"n\">energy<\/span>\n    <span class=\"n\">best_value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">value<\/span><span class=\"p\">[:]<\/span>\n\n    <span class=\"k\">for<\/span> <span class=\"n\">k<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_iter<\/span><span class=\"p\">):<\/span>\n        <span class=\"c1\"># \u6e29\u5ea6\u3092\u66f4\u65b0<\/span>\n        <span class=\"n\">temp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">temp_end<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"n\">temp_begin<\/span> <span class=\"o\">-<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">k<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_iter<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># \u5909\u6570\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3059\u308b<\/span>\n        <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># \u30a8\u30cd\u30eb\u30ae\u30fc\u5909\u5316<\/span>\n        <span class=\"n\">delta<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n\n        <span class=\"c1\"># flip\u524d\u306e\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u7bc0\u3092\u6570\u3048\u308b<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n            <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"o\">~<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">])<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">val<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">delta<\/span> <span class=\"o\">-=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"c1\"># i\u3092flip\u3059\u308b<\/span>\n        <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n\n        <span class=\"c1\"># flip\u5f8c\u306e\u5145\u8db3\u3055\u308c\u3066\u3044\u306a\u3044\u7bc0\u3092\u6570\u3048\u308b<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n            <span class=\"n\">val<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"o\">~<\/span><span class=\"n\">l<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">])<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">val<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">delta<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"k\">if<\/span> <span class=\"n\">delta<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"mi\">0<\/span> <span class=\"ow\">or<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">delta<\/span> <span class=\"o\">\/<\/span> <span class=\"p\">(<\/span><span class=\"n\">N<\/span> <span class=\"o\">*<\/span> <span class=\"n\">temp<\/span><span class=\"p\">))<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"p\">():<\/span>\n            <span class=\"c1\"># flip\u3092\u63a1\u629e<\/span>\n            <span class=\"n\">energy<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">delta<\/span>\n        <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n            <span class=\"c1\"># flip\u3092\u68c4\u5374<\/span>\n            <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n\n        <span class=\"n\">history<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">energy<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># \u6700\u826f\u306e\u72b6\u614b\u3092\u66f4\u65b0<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">&lt;<\/span> <span class=\"n\">best_energy<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">best_energy<\/span> <span class=\"o\">=<\/span> <span class=\"n\">energy<\/span>\n            <span class=\"n\">best_value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">value<\/span><span class=\"p\">[:]<\/span>\n\n        <span class=\"c1\"># \u3059\u3079\u3066\u306e\u7bc0\u304c\u5145\u8db3\u3055\u308c\u305f\u3089\u7d42\u4e86\u3059\u308b<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">break<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">best_energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">best_value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>3-SAT\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u52d5\u4f5c\u78ba\u8a8d\u3092\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">alpha<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">2.5<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simulated_annealing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"mf\">5e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy = \"<\/span><span class=\"p\">,<\/span> <span class=\"n\">energy<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">history<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"iteration\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>SAT\nenergy =  0\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Text(0, 0.5, 'energy')<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u9014\u4e2d\u3067\u5897\u52a0\u3059\u308b\u3053\u3068\u304c\u898b\u3066\u53d6\u308c\u307e\u3059\uff0e\u30a8\u30cd\u30eb\u30ae\u30fc\u304c\u5897\u52a0\u3059\u308b\u3088\u3046\u306a\u9077\u79fb\u3092\u78ba\u7387\u7684\u306b\u8a31\u3059\u3053\u3068\u3067\uff0c\u5c40\u6240\u89e3\u3092\u8131\u51fa\u3057\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>HC\u3092\u540c\u3058\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u5b9f\u884c\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"n\">hill_climbing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy = \"<\/span><span class=\"p\">,<\/span> <span class=\"n\">energy<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">history<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"iteration\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>UNSAT\nenergy =  5\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Text(0, 0.5, 'energy')<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5c40\u6240\u89e3\u306b\u6349\u308f\u308c\u3066\u3057\u307e\u3044\uff0c\u6700\u9069\u89e3\u3092\u767a\u898b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3067\u3057\u305f\uff0e<\/p>\n<p>\u3064\u304e\u306b\uff0c$K=3,N=100$ \u3067\uff0c\u3055\u307e\u3056\u307e\u306a $\\alpha$ \u306e\u5024\u306b\u5bfe\u3057\u3066 $100$ \u500b\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u4f5c\u6210\u3057\uff0c HC, SA \u3067\u6700\u9069\u89e3\u304c\u5f97\u3089\u308c\u308b\u5272\u5408\u3092\u305d\u308c\u305e\u308c\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\uff0cHC \u3068 SA \u306e\u6027\u80fd\u3092\u6bd4\u8f03\u3057\u3066\u307f\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">n_shots<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">5e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span>\n<span class=\"n\">alphas<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">20<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ratio_hc<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"n\">ratio_sa<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"k\">for<\/span> <span class=\"n\">alpha<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">tqdm<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">cnt_success_hc<\/span> <span class=\"o\">=<\/span> <span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_shots<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">hill_climbing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">cnt_success_hc<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simulated_annealing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n    <span class=\"n\">ratio_hc<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">cnt_success_hc<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">ratio_sa<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">ratio_hc<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"HC\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">ratio_sa<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"SA\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"alpha\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"success ratio\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 20\/20 [03:39&lt;00:00, 10.98s\/it]\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Text(0, 0.5, 'success ratio')<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SA \u304c HC \u3088\u308a\u3082\u9ad8\u3044\u78ba\u7387\u3067\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e HC\u306f $\\alpha \\approx 1.5$ \u7a0b\u5ea6\u3067\u6210\u529f\u78ba\u7387\u304c\u534a\u5206\u7a0b\u5ea6\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u306b\u5bfe\u3057\uff0cSA\u3067\u306f $\\alpha\\approx 4$ \u7a0b\u5ea6\u307e\u3067\u534a\u5206\u4ee5\u4e0a\u306e\u6210\u529f\u78ba\u7387\u3092\u7dad\u6301\u3057\u3066\u3044\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"Warning_Inspired_Decimation\"><\/span>Warning Inspired Decimation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>HC, SA \u306e\u3088\u3046\u306a\u5c40\u6240\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u306f\u7570\u306a\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u7d39\u4ecb\u3057\u307e\u3059\uff0e<\/p>\n<p>\u7d71\u8a08\u7269\u7406\u5b66\u3067\u767a\u9054\u3057\u305f\u624b\u6cd5\u306b\uff0c message passing \u3068\u3044\u3046\u67a0\u7d44\u307f\u304c\u3042\u308a\u307e\u3059\uff0e\u3053\u308c\u306f\uff0c\u56e0\u5b50\u30b0\u30e9\u30d5\u4e0a\u3067\u30ce\u30fc\u30c9\u9593\u304c\u300c\u30e1\u30c3\u30bb\u30fc\u30b8\u300d\u3068\u547c\u3070\u308c\u308b\u60c5\u5831\u3092\u3084\u308a\u53d6\u308a\u3059\u308b\u3053\u3068\u3067\uff0c\u5404\u5909\u6570\u304c\u3068\u308b\u5024\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u624b\u6cd5\u3067\u3059\uff0e<\/p>\n<p>\u307e\u305a\uff0c\u3053\u3053\u3067\u306f $K$-SAT\u306b\u5bfe\u3059\u308b\u30b7\u30f3\u30d7\u30eb\u306a message passing \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3042\u308b\uff0c warning propagation (WP) \u3092\u7d39\u4ecb\u3057\u307e\u3059\uff0eWP \u3067\u306f\uff0c\u30e1\u30c3\u30bb\u30fc\u30b8\u306f $\\{0,1\\}$ \u306e2\u5024\u3092\u53d6\u308a\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u610f\u5473\u3092\u6301\u3061\u307e\u3059\uff0e<\/p>\n<ul>\n<li>$u_{a \\to i}$: \u5909\u6570 $i$ \u304c\u7bc0 $a$ \u3092\u6e80\u305f\u3059\u5024\u3092\u53d6\u3089\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u304b\u3069\u3046\u304b<\/li>\n<li>$h_{j \\to a}$: \u7bc0 $a$\u3092\u7121\u8996\u3057\u305f\u3068\u304d\u306b\u5909\u6570 $j$ \u304c\u3069\u3061\u3089\u306e\u5024\u3092\u53d6\u308b\u50be\u5411\u304c\u3042\u308b\u304b<\/li>\n<\/ul>\n<p>\u3053\u308c\u3089\u306e\u30e1\u30c3\u30bb\u30fc\u30b8\u306f\u4ee5\u4e0b\u306e\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059\uff0e<\/p>\n<p>$$<br \/>\nh_{j\\to a} = \\sum_{b \\in V(j) &#8211; a} -J_j^b u_{b \\to j} \\\\<br \/>\nu_{a\\to i}=\\prod_{j\\in V(a) &#8211; i} \\theta\\left( J_j^a h_{j\\to a} \\right)<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\uff0c \u5404\u5909\u6570\u3084\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e<\/p>\n<ul>\n<li>$V(x)$: \u56e0\u5b50\u30b0\u30e9\u30d5\u3067\u30ce\u30fc\u30c9$x$\u3068\u96a3\u63a5\u3057\u3066\u3044\u308b\u30ce\u30fc\u30c9\u306e\u96c6\u5408<\/li>\n<li>$J_i^a$: \u7bc0 $a$ \u3067\u5909\u6570 $i$ \u304c\u80af\u5b9a\u306a\u3089 $-1$, \u5426\u5b9a\u306a\u3089 $1$<\/li>\n<li>$\\theta(x)$: \u30b9\u30c6\u30c3\u30d7\u95a2\u6570 ($x \\gt 0$ \u3067 $1$ \uff0c $x \\leq 0$ \u3067 $0$ \u3092\u53d6\u308b)<\/li>\n<\/ul>\n<p>\u4e0a\u306e\u65b9\u7a0b\u5f0f\u3092\u4ea4\u4e92\u306b\u89e3\u304f\u3053\u3068\u3067\uff0c\u5404\u30e1\u30c3\u30bb\u30fc\u30b8\u306e\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\uff0e<\/p>\n<p>WP\u306f\uff0c\u56e0\u5b50\u30b0\u30e9\u30d5\u304c\u6728\u306e\u3068\u304d\u306b\u53b3\u5bc6\u306a\u89e3\u306b\u53ce\u675f\u3057\u307e\u3059\uff0e\u9589\u8def\u3092\u542b\u3080\u4e00\u822c\u306e\u30b0\u30e9\u30d5\u3067\u306f\u53ce\u675f\u306e\u4fdd\u8a3c\u306f\u306a\u304f\uff0c\u53ce\u675f\u3057\u305f\u3068\u3057\u3066\u3082\u53b3\u5bc6\u89e3\u3067\u306f\u306a\u3044\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u304c\uff0cWP\u306f\u591a\u304f\u306e\u5834\u5408\u306b\u53b3\u5bc6\u89e3\u306e\u826f\u3044\u8fd1\u4f3c\u3092\u4e0e\u3048\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">Warning Propagation<\/span>\n<span class=\"sd\">\u8fd4\u308a\u5024:<\/span>\n<span class=\"sd\">- u: \u8a08\u7b97\u3055\u308c\u305f\u30e1\u30c3\u30bb\u30fc\u30b8<\/span>\n<span class=\"sd\">- c: \u5404\u5909\u6570\u306b\u77db\u76fe\u304c\u3042\u308b\u304b (0\u306a\u3089\u77db\u76fe\u306a\u3057, 1\u306a\u3089\u77db\u76fe\u3042\u308a)<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">warning_propagation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">100<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span> <span class=\"n\">J<\/span> <span class=\"o\">=<\/span> <span class=\"n\">build_factor_graph<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"c1\"># \u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316<\/span>\n    <span class=\"n\">u<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[{<\/span><span class=\"n\">i<\/span><span class=\"p\">:<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]}<\/span> <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)]<\/span>\n    <span class=\"n\">h<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span>\n\n    <span class=\"n\">factors<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">))<\/span>\n\n    <span class=\"k\">for<\/span> <span class=\"n\">t<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_iter<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">converged<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\n\n        <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">shuffle<\/span><span class=\"p\">(<\/span><span class=\"n\">factors<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factors<\/span><span class=\"p\">:<\/span>\n            <span class=\"c1\"># j \u304b\u3089 a<\/span>\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                <span class=\"n\">res<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n                <span class=\"k\">for<\/span> <span class=\"n\">b<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]:<\/span>\n                    <span class=\"k\">if<\/span> <span class=\"n\">a<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">b<\/span><span class=\"p\">:<\/span>\n                        <span class=\"n\">res<\/span> <span class=\"o\">+=<\/span> <span class=\"o\">-<\/span><span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n                <span class=\"n\">h<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">res<\/span>\n\n            <span class=\"c1\"># a \u304b\u3089 i<\/span>\n            <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                <span class=\"n\">res<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n                <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                    <span class=\"k\">if<\/span> <span class=\"n\">i<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">j<\/span><span class=\"p\">:<\/span>\n                        <span class=\"n\">res<\/span> <span class=\"o\">*=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">h<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">res<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">converged<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\n                <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">res<\/span>\n\n        <span class=\"c1\"># \u53ce\u675f\u3057\u305f\u3089\u7d42\u4e86<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">converged<\/span><span class=\"p\">:<\/span>\n            <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"converged in <\/span><span class=\"si\">{<\/span><span class=\"n\">t<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"si\">}<\/span><span class=\"s2\"> iterations\"<\/span><span class=\"p\">)<\/span>\n            <span class=\"k\">break<\/span>\n    <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n        <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"did not converge in <\/span><span class=\"si\">{<\/span><span class=\"n\">n_iter<\/span><span class=\"si\">}<\/span><span class=\"s2\"> iterations\"<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"c1\"># \u77db\u76fe<\/span>\n    <span class=\"n\">c<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">pos<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n        <span class=\"n\">neg<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">pos<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n            <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">neg<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n        <span class=\"n\">c<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">pos<\/span> <span class=\"ow\">and<\/span> <span class=\"n\">neg<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">u<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0b\u306e\u4f8b (\u6587\u732e [1] \u306e \u56f33) \u3067\u6b63\u3057\u3044\u89e3\u304c\u51fa\u308b\u304b\u8a66\u3057\u307e\u3059\uff0e\u4e38\u3044\u9802\u70b9\u306f\u5909\u6570\u30ce\u30fc\u30c9\uff0c\u56db\u89d2\u3044\u9802\u70b9\u306f\u56e0\u5b50\u30ce\u30fc\u30c9\u3092\u8868\u3057\u307e\u3059\uff0e\u5b9f\u7dda\u306f\u80af\u5b9a\u30ea\u30c6\u30e9\u30eb\uff0c\u70b9\u7dda\u306f\u5426\u5b9a\u30ea\u30c6\u30e9\u30eb\u3092\u8868\u3057\u307e\u3059\uff0e\u8d64\u3044\u6570\u5b57\u306f\uff0cWP\u3067\u5f97\u3089\u308c\u308b\u5024\u3092\u8868\u3057\u307e\u3059\uff0e<\/p>\n<p><img decoding=\"async\" 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kpQyVWaoyjKevqrF+TcV+tmRf7Q9mEG9DL5iIs0QAy9Zytn1Bif05CTUjZNy0xySLS95v96uXi\/4eKL0g8vOC+tfOkzaeUOd0l3+Zdz8MpqWWy913+tfHjsD\/\/wj9Jb3vLmdOONG9O9732v9PrXvyE9\/hcfv9Xz\/653\/nk67rnPK8\/p\/+gd75ie8fSnl++6v8+996qvL7+uvG26\/r\/97e+kv\/yLv0xvlr\/7iiuuKJ9rOfbZx6Y\/ftUflzcl2+vx39zXzznSNrSXNMbrX1vrb\/7l5g984APpDPmA6YUXfFIea7lMvl72e3TQBeY3YnLsd9t1t7Tvz+ybHnrAQ9Nh8uNwj\/uFo9JtdtypBDkr2riuJcXZ\/Pl3c9XfVU95Ykr\/dlna7XV\/nnY95HB9zfpC2j7qP+Z\/XH+t6etPuSMvt\/bkJZblq+za\/AeaoRHepHXts5O3vMiWTaNl74SI2zV8I7YQuW6zk7cYX\/PAl8IuUTUsZoZugk0g134L8\/\/N33xm2vif\/5HS1V9J6374g5Tucs90p1M+tokRfXiZ8S+77FNyp\/y30xlnnSUJWEmPPeIx6QT5gOw++9zXd74ZXj\/+1d+8Jj3taU9Np556aml9zDHHyHfdvybt\/iO3p7psHbv2jR6i\/M+kb33rW9Pxxx+frpc79PfdZ5\/0nve+Nx3wkIeofgvznxttyfijP8q1j\/E1RbH+1FLR6ih7Vyitkpj+qnzQ821ve1s66aST0te+9jWdLyLYWT74\/WD51pZ73PMe5V+w8jzIvyHxH1\/6Urr0ssvSD+XCP2857Xe72z3Sb\/zmMenoo49Od77znQq7uePnPrZ047+\/TKbcwVY6\/lf\/6hPTityR\/5HXyYdr5Y78aFvN8Ufj9VyM3x3unKCtdPz7XI\/8yH+X7rWYf1nwdMu35uc2+Xf8solZJBs1b\/qNi9s24bSbGP9Wn\/\/v\/vNHVr7xM3utfOMXHz2tjwVMK6vl6u99733vyt3uete8Fq7cdqfbrjz\/+ONXrrvuugUj+lA\/\/tVXX73y4Ac\/uPR397vffeUjH\/mINmhC30H2lqj\/L3zhCysHH3xwGWf33fdYOe\/cc2P+TTPbmK2cf3Tcul2u\/ko\/Sxz\/tTb+d77znZVjjj5mRT7kXWpaTs0rcnd9RS7qVy686KKVH\/zgBrxkZ3P+v\/\/9\/1r55Pnnr5z45jetPOIRj6jt04p869PKcccdtyKPpC0+sUn+v\/Wtb63IB8pX\/uWjH3X9b8pZ7eN\/1a88YeXrD9lr5frTPz78U1Z7\/OGgRMb4SEbM\/1YLyAnZRcFY\/zRRkqO5NKW5gF48zEZnOywj5mb4n45Vg7VfMRW1EFA5eLPR+Xa5fW6G\/9Gfs7VfMRW5aHFifEnDbHYWRGqz3HS2eQ2ImZfkSIt+75Pnr3xDTlhXPf4I4TlSXL9D09bcx9GvxOcl6GRl5bvf\/e7Ki174wpXb3va25SIgX9i\/+6\/f3fVJLpp2ndtFvPwDmPwQ1co13\/zmZo1PPRvsuja+gDr+xh9uXDn22GPlb163ssfuu6+cd955VVdbi5ntJ+pfcjWbnQWR2iw3nW1eA2LmJTkyG10QWXvjf1Qunu+1555l7u22224rv3HMMSuXfepT8kJnNqRuJn0XXXThytOf\/vQVuYtf+pR\/ZVs5++yzfWdU\/5\/+9KdX9tl776KVb4gqupmutY9NjG\/HVXSz\/dD4\/g9rQ2R01VOeUNbF60\/\/WJNtw\/HboIRifD2w8wdXkyXxeQmSSHklONsua9B0VlQDYuYlOTIbXRCJ8W+O\/MtTA3SwCOZ6yJunqgcSVqW01wDCsCZwBDkEofVU9UDCQmxWAwjDduHqUpQgtJ6qHkhYiM1qAGHYLlxdihKE1lPVAwkLsVkNIAzbhatLUYLQeqp6IGEhNqsBhGG7cHUpShBaUBv+H3vXAahHVaznJpQEQkkoIk1ECCUghJYAApKAAhakWJ4iTelNuoBBuoQSBAVFRfQpVjr4EAkgKEUTQAGTAAJBgkoJBBIglNz\/zSnfnJmzuzc3N\/emXM5Cdr6Z+c6Z3dk5Z\/ffu\/\/+fCH\/\/KZrtl7adadUlHCCLDI44IbM3FFVXgXB1aYnnni89clPfNKf0N0d+o9s\/ZHWQw89BKqSoRXaOunu4vOf\/n3bYVsMb\/GbaSIfLFYVRGfWFDUYIUEWGRxw8\/vxfVx3Z\/6BBx\/M4oDVc\/FVhLCFxqAUBbEr1hQ1GCFBFhkccENm7qgqr4LgWlPUYIQEWWRwwA2ZuaOqvAqCa01RgxESZJHBATdk5o6q8ioIrjVFDUZIkEUGB9yQmTuqyqugc7a3z2odceSRLX6jjK\/fHT+2Y2vKs1NS\/WZ86T8OJLghxR8N\/q9W237E992nT5\/WSV8\/iWNa9vU33NBaaqmlPGf7Edu3pr40tdvih+1R8RTEtlpT1GBkWXsh38n974742E4rwwaqzaxzRxtYrCqIBtYUNRghQRYZHHBDZu6oKq+C4FpT1GCEBFlkcMANmbmjqrwKgmtNUYMREmSRwQE3ZOaOqvIqCK41RQ1GSJBFBgfckJk7qsqrILjWFDUYIUEWGRxwQ2buqCqvguBaU9RghARZZHDADZm5o6q8CoJrTVGDEZLJ6Y48jJDoqUYGSjOx6sktSRcEAFkTF6ZAaSZWPbkl6YIAIBGsRgZKM7HqyS1JFwQAWRMXpkBpJlY9uSXpggAgEaxGBkozserJLUkXBACZxQ0X8vxoDd+RD5QGIrerenJL0gUBQGbxtXrTzTe31lrrQ+57cq2+bX1bhxxySGsq313HUu2ivcXP4\/qLgc0337zFX6gFNW0rGkEKowoCpZlY9bS3Dj\/8cB9\/\/fXX50cN3pROhQsAKYwqCJRmYtWTW5IuCACyGlYsgdJMrHpyS9IFAUBKtCoIlGZi1ZNbki4IALIaViyB0kysenJL0gUBQEq0KgiUZmLVk1uSLgggSv4htNZeX\/oS12xba6kBA1qXX365bEigoIGYBVQ9uSXp785qb40ZM6bVv19\/P54PPuhgfzHvLujPOP10tvVxb6JuHckfKPgLtj5GaJ36kMARVD25JemCACDzTpUeKGH90ud2C4\/W3Jke+al2kVuSLggAUsXLYaA0E6ue3JJ0QQCQeVClB0ozserJLUkXBACp4uUwUJqJVU9uSbogAMg8qNIDpZlY9eSWpAsCgFTxchgozcSqJ7ckXRAAZB5U6YHSTKx6ckvSBQFAqng5DJRmYtWTW5IuCAAyD6r0QLFE98uN2QKCkworiAYwBR0aJFhWitcD0RQJNicVVhBkmIIODRIsK8XrgWiKBJuTCisIMkxBhwYJlpXi9UA0RYLNSYUVBBmmoEODBMtK8XogmiLB5qTCCoIMU9ChQYJlpXg9EE2RYHMy4Tf4GVf\/aM2nw6M1rgG8oTE0yGDN1+L1QDRFg81JhRV05Ldmzmydfc45rSWXHOAvAJZbblCLv2TamjXrXdVXgO45eHcHf2l+vOWZfz0TjL4\/dKqbwOakwgqCDZPqULUBK0j+NVv\/OI\/bjhNOOD52bXuo9gM\/SwXRM0zVdmBUpbTxQDRFhM1JhRUEGaagQ4MEy0rxeiCaIsHmpMIKggxT0KFBgmWleD0QTZFgc1JhBUGGKejQIMGyUrweiKZIsDmpsIIgwxR0aJBgWSleD0RTpHYeQ7NaX\/rSF\/2YWWGFFVqPPPqw2RSQbWtokGBZKV4PRGuNGzeuteyyy\/qL9gMOOKC1++67+fjuOfofX3lFj8dPW4ltclJhBWe9PqP1zpRnWzMff7z1wjabtF7Y7EOtV8ac13p78uTWuy8+n7qqQegmdC2aYsLmpMIKggxT0KFBgmWleD0QTZFgc1JhBUGGKejQIMGyUrweiKZIsDmpsIIgwxR0aJBgWSleD0RTJNicVFhBkGEKOjRIsKwUrweiKRJsTiqsIMgwBR0aJFhWitcD0RQJNicVVhBkmIIODRIsK8XrgWiKBJuTCisIMkxBhwYJlpXi9UA0RYLNSYUVBBkmp7c5Lt\/04PO7fI2acXWpZ8AKadtx\/\/41eHztwP+ll0+6b+7LD275pvXtdW\/1DFghdQuOUeL3mvy\/wa+Ye\/2QL1LbqmvR8tf\/Ph5oHHfIeX\/8p0x5jo477lj69a9\/w0OojTbh975\/h99us9XWW\/v64y\/p0YYbDKFnn3uOrvjRFbT\/\/vu74TBf6v\/xxx6joUM3If4QQnfzu+e33mpLvy1l\/NfXj66megaskLpFmX+6Ov9+9YADeaz8kN8osyLdeecdNGTIEDdkas5QsELOXf7Hjx\/PP+i0I0175VV+O9VaNGPG63TttdfQ8OHD50l8u\/VW03v42o9\/RG9dNpoJ\/MMTPivwtlGfVT9Iy13\/B9+4q\/m3kYOGCNYHK2TmLeffXnP+bTjCfMDddWODtxz\/eXb8wy+7xsPhh6EcEwHe3NEKTD5u7lqGL2CClDYgiMEC4xZFgCXXaGAiLqRQQRCDBcYtigBLrtHARFxIoYIgBguMWxQBllyjgYm4kEIFQQwWGLcoAiy5RgMTcSGFCoIYLDBuUQR48pt8IT\/jUL6QX0VfyId+wERcSIkCghgsMG5RBFhyjeaYd\/3xj3TEEUfRo48+7Bl77bUXnXfeef41eaefdjrtvMvO9Lvf\/a6mdTYNSlgBtW20EUzsN6RwQGDDRReNoWP43fVbb7UV\/fmeezxFudXGGKt0VQfARFxI4YIgBguMWxQBllyjgYm4kEIFQQwWGLcoAiy5RgMTcSGFCoIYLDBuUQRYco0GJuJCChUEMVhg3KIIsOQaDUzEhRQqCGKwQLuvveZa2nPPPWjgoIF0991\/8hfxll3V0B5xIYUJghgs0O7x48bTyJEj6LXp0+mX\/NrWL3zhC5Zco6E94kIKFQQxWGDcogiw5BoNTMSFFCoIYrDAuEURYMk1GpiICylUEMRggXGLIsCSazQwERdSqCCIwQLjFkWAJddoYCIupFBBEIMFxi2KAEuu0cBEXEihgiAGC4xbFAGWXKOBibiQQgVBDBYYtygCLLlGAxNxIYUKghgsMG5RBFhyjQYm4kIKFQQxWGDcogiw5BrNM\/lTu5OyhOa2E2OrbKU0bQCpL494JXfja1qYWNFvbCV+9impJonGFLLnTB7xamHM\/8xxf+E78l8iWnlNWv7GcMfJ7GajMu\/2v33WLP5Bpsvom6eeSq9Mm0YDlhrAvyjZh9yPNT3M77LeYMMN\/c3v+Zn\/We+8Sx\/44Afo38\/9mx568EHaeOhQk7mQrZQz5zS2Mv7ek+Mv\/egfV0PDT92bQhIl1ZJHvGqq\/xf5F5XXX38IvfTii\/wXrl\/T5z73Od9L6CH2Mw\/qz\/014IADDqJVV1vNfzDnL4nzfcd5F19ixRzO6\/0v8eOxLvmfL+Ov1N+c15+\/Ix\/rlYXqQKAAdVBDC8ypnmFpqctKq8xlVNWJQAGVnkr8cE71GbJpMlk1xzXzWFV1IlDAfMn\/rP\/+m9rfmUWvX\/0beueq71FrwLK0zGU\/pb7LLEN9lluB+vRbXD6g1PztPe6e3Qe7z1pTPIECOr3\/L\/KFyMknn0xXXHGF\/+vUdtttQ3\/84106UANWsQQK6HT8aue2j7POPJtGffMb\/jEf97hPWhRPoIBui5\/i5UjFEiigxOcM6Gz0tvnvs3wn\/mq+I+8u4H\/9q1\/z5OYOud5jq\/Xk\/u+y8y50y+9vof3225d+\/OMrfe3lW9OT8dNuz5\/9L\/H5aM\/H+iv5L\/mfs\/qrvSMf5i07hQRbWgdvx5xmtm9X01ibNE49AQVvxxxwcQJIbI+SKkRt0lgIAoK3Y46Q47hMbI+SKkRt0lgIAoK3Y46QF9r4L23Dd4zfnME7wnvqJla3w160aMD5P6D+248M9R7Mjes8W14PRtNGmzQ2JK8Eb0ecTfnXVB\/ku95X\/\/a3tPuee\/J2JrZHSZXutUljIQgI3o45QjbH\/4UXXvB3Gxdp60NT\/v0cDRo0SIi6P42FIKDr8V0XvnVNAG3SWMIKCN6OOUI2+++svl1NY23SOPUEFLwdc8CN8eJWOKtvV9NYmzROPQEFb8cccBf8+O75dH6jE62w4oo0ceIEWm7QcipbaT8S6tn9f46\/0zJkgw3otVdfpcf4uyVr8y8k26Vn47tYHR\/bEt+dEDrOUTpieba8XtNYmzROPQEFb8cccHEsE9ujpApRmzQWgoDg7Zgj5JinxPYoqULUJo2FICB4O+YIucTnVOhq9XmrSZ42aZwyCRS84MgdeRhASxJfVFUMgQIS3aMmu3PCBxmaWi3Y4AlflFUMgQJ0A8ZNdkeDDzI0tVqwwVPiuy8qqwwJFKATxrjJ7mjwQYamVgs2eBbG\/L\/KX3IduOwgvkgeSP99\/r+0SN9F4k5hTyGxl\/EGkN51j3tm\/LnnkK+55jq6+urf0h577CFHpRKePQtj\/puy+V6pv4Vt\/\/feZx\/62f\/+jM4++yz\/16xUh\/Ov\/r7+9a\/T6NGj6fAjjqTvXPJt3iR\/izaVUOOosWM77YtD8EEGr9V0i\/m3\/9iyMv7L+a+c\/9UIFShAD1jGTXZHgw8yNLVasMHTmfHHF\/Lt3EecoFxL6VGA7tVgy8CEEynGyUp8MBJ\/jkwdGWKJL+kQkFKVIcso+Q8Fv2DU3x2330EjdxhJO+20E91yy\/8tcPU\/ZsyFdOxxx9HXTzyRvvWtc1NlSVEJSL4MWUapvwWp\/tI87g4aH6kFeP596aWptOqqq\/rtfPZfU\/iu\/Aphm\/V5ye1GtvR0\/f3rX8\/SmmuuSfxrsvydkudoyQEDzBb0dHxzXjaRg1Li6wyV+afMP\/bNiGn6WLDnP13Fad62o7tm+CcqO+WOvLqC9m3SsEio0llDrNwMPUi91j2CFWwpakKa7bFtIu7cDD1IvZYmDMAKthQ1Ic322DYRd26GHqReSxMGYAVbipqQZntsm4g7N0MPUq+lCQOwgi1FTUizPbZNxJ2boQep19KEAVjBlqImpNke2ybizs3Qg9RracIArGBLURPSbI9tE3E783l8J8\/d0Rv1jVF0+pln+DlFR642tZYUNSEEcF+cfeCBB2i\/ffczcwD8tqe0Zzr+XfxGkI9uty2\/oWMkjR07lpvaVilqQuhfpG3SaAZNx4dNGpX4nIp0QyVlPaGUq4iqSfSO3Aw9SL3WPYIVbClqQppdGygSbE+psnRkzXF3vd1Y2XvvvemnP\/1p7BqXJT0fP2y23iK3zSH+brt9hvjXXemyS79HhxxycNzDhh1tMKPnpv3vKH7aEhvaa+g4c+Vm6CW+G2E6CzpxyFKw4fiX\/KdM6Gx5bFMm7twMPUi9liYMwAq2FDUhzfbYNhF3boYepF5LEwZgBVuKmpBme2ybiDs3Qw9Sr6UJA7CCLUVNSLM9Vk38hTzukpsmiqRDe6x8fgO8zichY3eh2ND0igK1VSU+TzA+fTh5hdThvB7SqtYmzy7HzA8d6GuBkv\/5WH+f\/eye\/NjKNXTD9TfQp3f9tKr2KuxM\/f\/twQdo\/PgH6c\/33kNX\/ewqGrrpxjTur+PiMWYxh8d\/xowZtAx\/YZh\/pIqmTn2F+OU6nK1Sf3JPR42xANVa+cIcN+f511XQmeNvLkB6WfwRI0by++LvpDvuvJ22\/+j2ITVqH1Xmw1SnfHn+Z7XP4r7+6J+zX3311bi\/EbT0MkvrdFdwR\/m\/8cYbadddd6Xd+YL+mmuvm218zNmyE+X8l52TKumX11WX+afMv2X+5QtBt6g5rjPzn7ojH9rLWnUUbNoQh5w2qYZSjuIXEDdQ6dIuAxWKNpT4Psc6JZI+NR2KX0DJv0+FyofkLQMVijbMvv622GwzGs93zR9\/\/HH\/4zJyNuti\/AMO+Co9+o8J9OQ\/\/0nurTgf3X57upMf37EXDm4fOn\/8P\/jBD9LkyZPp5ZdfpoEDB9oE6N31Hm2Y\/f776UiaCCj151Oh8mGznrQKRRt6T\/7duxZc7c14fQa9Nu1VWoIfY6mUW8VQv\/\/uS6l77L4bve\/9K9O6gwfTDTfcSM+\/8DwddNCB\/CNtl4a3Zs5h\/p9\/\/nlaaaWV+NGfVejZZ6fE41MfHxtezn\/xckxKVkAZ\/3NYf7HgWKgcYo7XJiHG2nS6+AWU\/PtUqHxI3jJQoWjDgjf+1YV82FC7ufE6QRv9\/iqDh0F3a7fEzxSMEg8I0hPNKni0X7AANFAGD4Pu1m4p8UMeSv5TnQBBIkNJBo\/2CxYAtjJ4GHS3dourP\/drlBMnTPC\/6LrKyivLSFAtPTetUh+oX+EKIPrzn\/5E22y7LX3sYx+jW2+91UzMjuYWtJ\/d8V9\/yPq8jZPoueem0Morv9+3VKFkmxPw3fNKsTwMulu7pbPxAxvr1AfaBwv7BViu17wvtXU2tNcN0QUkekoy9YH2whUAtjJ4GHS3dgval\/gpT0CQIVPEH3SfoHXWGUwbcC0+8ug\/zKEWrgC0UgYPg+7eMrPzzjvTBeef74ktvju\/Mf+S8SP8KNoll36XDj\/0MNM\/egsy9KF6Fu7q\/D75Z6dMof\/wl9ZXWvF9TFcsD1Nb11c5\/iGjOk\/IGCQYSaYcIn\/CFQC2MngYdLd2C9qX+ClPQJAhU3odPNovWAD4yuBh0N3aLSX\/IQ\/ztP7cD0K1u5VbBAS11Z4MggREDkRur9VhjNKKEh\/pkZwmgyABIEWZ22t1GKO0ouQf6UFq56L+B689mOe1thbf0Qu9+b4RwCYe1s6Mv0cefsTNly3+Ei22UvWvTNJptHkdxiA\/vOGHW\/xETmvyM8809AG+Ko1kUsEY5vZaHcYorajpA3zlSqYSX2cgz0utDmOUVqgkx47nov7r66Ea\/xe\/\/IWv53333W+u4v\/ziSf5IZa21j777NN65513pa+zzjrL9\/\/xj7nxUo3v9hTWBOz+77bbbr6Pm2++WZEjB0I6QVs4tA5SlFZU+54H+Xdbh61KANssnuRKpkgC16qpgfajcZRWqA1BG\/CVK5lswNxeq8MYpRUqSInvM1DqT2oMlVOpazCEgNqBQ+sg2cKDtdL3HOSfn09DIOkOFi9hhTRONBVjM8t7Km5lUBst3TEAA1L7gJMvIfggvafiVoYSH6kyEhmCNM6oJF9COc97Km5l6GX53+jDH\/Yn\/2fiRXJ37f+jj7gL+TZzIZ+ymFBn8r\/22mv5bfQfNnpZ\/juz\/2l2YXbZ\/zxlXkdFQdaRki+hnOc9FXd769xzz\/U1eDZfcNctaALZxOHHzVp9+rT5vn72s58J7Wtf+5p70qW11dZbm8MdCKrXDo7\/iV8\/0ff7ve9\/T\/rVIPWSkPY77D0VtzJ0EF\/a551GPfWSUE71nopbGUr8PGVeR4Yg60jJl1DO856KWxlK\/vOUlfxzBlAhkHVJcr50Ia8ZeatcF27VUbUIOQEmtcsmJrOgvJNcbySmHRdKHSjxS\/57uP622WYbfwHBP3RTrcC5qL9H\/IW8uyO\/M\/dbHRhVSzW8a+bGH\/\/oDt+Rb2u98cYblpR3kuvCrjqqFiEnwKQy\/jvIVO7Kdclk1VG1CDkBJi0o+T\/ttNP8RfJF377IbF9SGDXulHWcc\/bZrWHDh7cmTpzom7\/9ztutwYPdX8aoxb+0nLqcw\/0\/\/bTT3VdWW2MuGpP68MjGd6aqJWsSSQtK\/mu2rroTjTtVdVQtNRGYVPa\/g0zlrlyXlFYdVYuQE2BSyX8HmcpduS6ZrDqqFiEnwKTuzr+9kPcBUrymu1TCUFsdoDI4ElQv3SpufrTDrfsztoZPqZoPHNqZ1iU+0uGlW5X8Syp8NlA9UbLT+2Gei\/o77LDD\/AXED3\/wg9hp9+T\/kUfDozU7u0dr1MYGqAxuH6B66Vbp+D\/11FP+g8bgwWtjbz0fTbxxLvY\/tI9d18R3HhMrGoytxI8JbBAqWQEqQ8ynb+nNbpWOv3Z7TjSYHuZB\/keN+oYfJ9+55DvdXn\/HHH2MvwBfbdXVWi+\/PLXL+4\/Hc84\/73xJlQcqWQEqQ8xn4jnfgpd\/v31Y8SaaPZgHxx+hvSzxS\/5DGz0nAABAAElEQVR1QZT609moYjVYw4W8MoBtTUpTENwuS\/QFqTqyJqUpqOhdg+gLUvViTUpTUNG7BtEXpOrFmpSmoKJ3DaIvSNWLNSlNQUXvGkRfkKoXa1KagoreNYi+IFUv1qQ0BRW9Aq+88kq+QGlrHXDAARWfGNAXpDiyE6qa3uUZ+Z2zZ+RV287A3\/7mN\/4C6otf\/GIezDe3m6Q0BTsTp0MO+oJUZGtSmoKK3jWIviBVL9akNAUVvWsQfUGqXqxJaQoqetcg+oJUvViT0hRU9K5B7utsvovuxsl5559n+rBhlKagaZAp11xzje937bXWaj3xxBOZN6roC1KxtOnkb5zsx8p3L\/1u7VhRzeYMIgikam1NSlNQ0bsG0Rek6sWalKagoncNoi9I1Ys1KU1BRe8aRF+QqhdrUpqCit41iL4gVS\/WpDQFFb1rEH1Bql6sSWkKKnrXIPqCVL1Yk9IUVPSuQfQFqXqxJqUpqOhdg+gLUvViTUpTUNEbHq1RFw5CbuggUJVToADpLVlmNx9qZtyCGpP3eLtyChRQ4tekMGVHjrACNd4aU8k\/Z8DnRSUnwn\/EO+dDhw7t1vpzj9a4P\/PvtNPHw\/FqiK9HGLYO0jU87oTj\/cXJRRepRxpCj7zWzGisMXmPtyunQAHSW7LURpDotV7dWDGb8q\/7QFNI11xj3V3ANd4ak+d6u3IKFCCxkqXERy4uu+wyX4fHHHOMOgzwdmxqyv\/Ysbe3+vdbvPXxj3+89corr8x1\/r\/61a\/6Mffzn1+lNihCv6lqewUKmOv4aT+r4UPnKZYES0CQYomtpkc2aWZk1Ji8x9uVU6AA6S1ZaiOoTdHMEj\/lWaUI0KdK5UuggJL\/mhJK2UEitazx1ph8C29XToEC5kn++fWTLiB\/3z++M8jNqun1QeE1OrBBOiswZGDWrTVDY3Ddh4kSv+Q\/1EN9hYSa1D5gSFRTVWqGxmD2TP21t7fToIGD+P3Y0\/ld7c\/IT9DXja45qf9\/PPoobbjhhvSxj3+cbv3972UcYm+qUu9zwhtuuAE9yq\/7u5d\/YGr48K3K+C\/zny+dVCGpkmCDdB5gyMTOkWZoHHj33XcvbbXV1rQdv1L1j3fdJf3qXtAK0vmAIcH\/61\/\/6n+t+Ctf\/SqNueBC6tO3jSZNeow++9nP0iOPPMy06tltduPPvcLy739\/yI+XIeuv70MhLiTiV6VmaAxmz8w\/6D1lyllK\/K4cf2QNUmdS21LONdIMjcEpx3924w9Zgyz5TyMZOam8Rz6MdbhVysQkAJU4R1JaM3C3OdK0Gj1eCIv71na1PXMUNZGlZwYlfsl\/T9bfYYcfxj\/tfhmd8o1T6Kwzz\/JF2NX6m\/XOu\/Qufzi45prf0l5f2ouGbjKU3yP\/B\/\/rrIsusggfyLQnqdqryMW\/649\/pO35B6UGr7MOPTZpUiTFLfNCtpJ92u6o2hebzoGQ1gzK+Cvj762ZM2nppZaifv370TT+Qag+bfwTw\/7lM6jnztffU089RVtsMYyOPfZoOumkk6Uqzx19Ll17zXX017\/+JVVvJ+tv5ltv0lJLLU39F+Pte+01\/wvI+qhJkE6CUv8xe53Mv8w3OnHqqqGTaRea7qbMP7qSY2a8kCxx3rTdpVH7JK2dBtKaQcl\/9+VfXcjbYyEJhzlLPH7W2rkDV7UA9JI\/cfLAw7QcugMBnVdlhcEGfeBLfC6CmNSQK5UxQC9L\/udX\/U2cMJHcjy4tv8IKNOXZZ2nxxRePhY4DVK17WHLGuoP5ovufT7CbPc7pR5QHdLf7kaiPbB1tgSJuvijK93+PPXen6\/jC5tsXX0xHHnmk66yy5PF9WK43jOMy\/sr46675Z+ONN+Y73n+nCfwDauutt56vxTmtv5lvvs4X8cP5rvmjtO466xJ\/IiBqb9Hrb8zwv8j6yU9+km666aZY55XeG+v\/\/vvvpy233JK222ZbuvPuu0r9I4Ocwu46\/pXks6FyhNhQzv9l\/i3nnzBa8vOvvLUmfp8+PSg0m28MV\/ipJSM8HwQZnVAhhedaiDGQS3yT0Vyp5MsQkEvI6IQKqXJe6a\/k32Q0Vyr5MgQkuL01cuRId05q\/fiKK2qGBXjzrv6fevrpVt8+fVsDBgxovfrqNNnqyv6U4y+5qQOVfBkSjitkdEKFLOPPJ+aQQw7xY+Tsc85JWZzD+hszZozvI14DMg7vlIf+lf3379L4+\/pJJ\/l+TzzxxLRtjMrxlyI2eQkKfJCRAhWy1L\/krlJPc1j\/0pEHSDBkyX99WlJ+Fvb8t7mxJLcZwsW++TTMCeBP3uFzkJvR8IkoUkVUfJkhU307b6txaFOJX\/K\/MNffLbfcQrvs8glabvnlaMI\/HqUV\/U+8h2Ezr+ufP7XTDjvsQHfccQcdffTRdOGYMfYphjiay\/hL81yZf3p+\/hn\/wHjaYvMtaNXVVqWnn36an2vvK+eZ+Zn\/mW\/NpFVXWZVeefllmvjYJFp77cGyXXLiqxkz3qQHERsyNVFqHNo0P\/ffbWSJ3\/P1nxdVOf5l\/sV1dmfHX\/ZojS4hP4x5JV0q7Hy85HRlDC5e67+Heb9rx3b8XQ421TaZdACNI6PGhI0KLl6X+OkQIrEl\/\/O0\/r601xfpF7\/8JX1m193ouuuunW\/1fyk\/r38EP7f\/gTXWIH4fPQ1YcgAqomFA6QGmcQPdm2Xk8cxRxl+Zf\/j8gVMIqq1m\/hm+5XD6y\/1\/4e+AXEO77757TYHN+\/r7yU+upP3225+\/WP4x\/8Xyyo7UbFI5\/5Tx7+pEslCuPyrDplz\/cXV08\/Wvv5DXV\/1hInLzaJx9fUVKWfoJFvNyslpLnIWTcERX2rUb765r0qfeEt8ni\/NV8u8LyBeZX\/nJ0dlstQWf58bpM2C19inl1Xyqv5envkwbbDCE\/vPf\/9KVfHGw7z77qo2bN\/X\/+OOP0SabbkpvvPkG3XnHnbTddtvJNpTxV+Yf\/NVrfs2\/v7jqKtrry3vzG2yG05\/v+TOPcf7Sq1v88PareTr+Z\/EXyzfdZDN6+O9\/oxtuuoE+9clPz9P4MsvNp\/0v8cv5d36Ov1J\/c1Z\/4Y58Nln4pwvdUcQVkz+iHa9cF27xTYwS7HpdcZf4nDifhHTekmTqzDVjk1OjVNtU3D60X5X4nK6eqP+bb76ZPvWpT9Giiy5Kv\/ntb2nXXXdNw6uH8\/\/U00\/RR7f7KH\/p71k66qij6KJvf9sXhQzvHo6fV6AL55YSP+QhDbp4J6+SoMjrQJgmRqk2qridYT7PP2+\/+xZ\/SXU9frRmMl363e\/SoYceqgqkug+5xeyTUXJm5aNK5cOCS8W5555LJ518Eg0ZMoQe5tdW+rfpVLsSiwlpFKEIqLidYT7nv8T3ByENRXe0ZIKSQ9cIzDE1SrVJxe1D+1WJ79JeSVA1h7nFNDFKzuzc+PetFqLj3+Ye97fbGwoq7L7KSDRrr+MEvcEZOvGkFh+d9O4a9FJ9owZ6LPGRXSf5CDWkuOTfZachOaGIFpj6G3PhGDruuONo0cUWod\/+9mra9dPuLl8aFWFzMTac5rBbun78n+JX8vmL+Oeepfe\/byXafY896NRTR8Vn9cv46+n8+8PHh7HMfzrTqHFbf3feeSeN3GEELdF\/Sf8Wmw99aE2fvrmp\/67k3\/2+wqabbkLutyDuu+8+2myzzcv8Gw8Zjlw8MHHmbXAqUqn\/2dd\/SJfOsMNu6fr875tzNyX\/vTv\/fEee39GFSyFdQ74CwqrBrBgdQ9PeKW6RTw\/B69eGGGhu3WBOhNkg094pbinxQx70VGwSFd0sGsyJMBtk2r\/H8+9+pObY44\/nO\/OLEP\/kOx14wAGcPXUnVuoyJdXkL5lni9yr8z7\/uc\/Rv\/hOvPuS6913303vvP02LbHEAPra0UfR8SccT8ssvXSPxccGmu1\/jx9\/P5hcYuQ4h+z4tUkUstf7x9\/f\/vZ3OubYY2m3XT9D\/+RXrF7yne\/QRz6yDd1x+1j+0LvYPJ1\/Zs58k7b+yEfowQcfolH8+w9nnHnmPI2f6uK9c\/x7av5DBs2wcopbyvgLeYjV\/V6ef3pF\/fEN+bCkN\/HAkiRehcScjmipQUKJX3nBTyI5lIjW7n3RyaIjWrWh5pf4HeauI2c5\/qG0uqn+LrjgAjdv+n877bRT67kpU3ShVst4DvPPb9tonXDCCa0+ffr4GJ\/+9K6tt9g2+V\/PtPbbb79W3759vX3QoEGt0aNHt958441uja93IJVVGX8pFzpDEXfknMPjr3tP3S54+Z\/y7JTWPvvsw69DDXU6dOjQ1uuvv95ae\/BgX5\/8KFrr7bfe4tqMe8Ei7Y\/ey2ac+LPff\/7+SGvE9iN87I022qj19ttvh47nUfzGvSjx43Ho2eNf8t+QgVJ\/C3z98W9mNCz+4DV6O55QXTP8q+0+9ssioiqrxI9JrKbGWRrzBqcjNJKig0UzxXkavR14YrMOm8d+WTRG6OXH\/w9\/+ENrtVVX9RcNyy47sHXxxRe3Xpv+mjt6YenC\/s+aNat1ww03tIasP8T322\/x\/q0LL7ygNWuWzfLESRNae+yxh+e4DxQrr7xK66GHHkLkLseXDlw4\/BOjBnF7WESknQF3Yf+lE8Ru7jzGKPGbU4QkSlYNaGznWGjaQJrx+vTWqFGjWkv07+9rkH85tXUOv0P+zZlv+hhPPflka\/XVVvM+dzH\/lruYz5aGrgNrNvHlqDMP\/bzBH2ZHjAwX8YPXXrvFP+DGfcGbBe\/QE53YhmrT1FrFr9BK\/ac8VZLT0ZGJzUr+O0hSrOtSf80jfCEbf\/zGmHhQ3WBREGPHmqIGIyTIIoMDbsjMHVXlVRBca4oajJAgiwwOuCEzd1SVV0FwrSlqMEKCLDI44IbM3FFVXgXBtaaowQgJssjggBsyc0dVeRUE15qiBiMkyCKDA27IzB1V5VUQXGuKGoyQIIsMDrghM3dUlVdBcK0pajBCgiwyOOCGzNytadOmtfbbf1+5oF6aL2gOO\/zw1qRJk3Jq1GNP6DDKqVOnts4777zWGmus4fvil\/O0tthii9aEiRN9O9DzTseNG9fa8WM78IX8yi13IVPGv2RIgM1d1GCEFDZAcMANCa\/Ns\/IqCK41RQ1GSJBFBgfckJk7qsqrILjWFDUYIUEWGRxwQ7oPlD\/84Q9bK73v\/fzAapv\/y9BBBx\/Yev7550NLEFl78smnWh\/4wOq+nt2Pqj3r\/mqFxIEHKXEBggNuSHjRTdDbW0899VRr66239rHW4ov4EAteacUg9oQOITXF4+CAG1JoxqAUBcG1pqjBCAmyyOCAGzJzR1V5FQTXmqIGIyTIIoMDbsjMHVXlVRBca4oajJAgiwwOuCEzd1SVV0FwrSlqMEKCLDI44IbM3FFVXgXBtaaowQgJssjggBsyc0dVeRUE15qiBiMkyCKDA27IzB1V5VUQXGuKGoyQIIsMDrghM3dUlVdBcK0pajBCgiwyOOCGzNxRVV4FwbWmqMEIyeT0ZVc3jbnnxiAZNi2B0kysenJL0gUBQDYFZ3ugNBOrntySdEEAkCV+YwZCipoTVfXklqQLAoBsjN77jv+f+Nn1i8ZcRDf97iaa9e4sv+err7Y6bb75ZrQp\/1DOZptsQgMHDaR+\/frRW\/yM+4wZM+gf\/B748Q88QOP\/Op4mTJxAfDfet9uUXzF5+BFH0Je\/vBfxL7jGLOZJTbpDL77wAq24wopl\/Jf5D4Mr1k29CNWTaihnVT0tuu22sf6L3g8\/\/LCn77zzznT++efT+vxWGP+4MhpBMutp\/qL29iN3oH9NfpqWWXZZuviSS2jvL3+5W+f\/71\/+Azr+uGP9mFpn3XXo9ttup1VWXSXfJaOHTVQbarx1Kcy5SRcEAJn1qdVAaSZWPbkl6YIAIHXADAdKM7HqyS1JFwQAmcXUaqA0E6ue3JJ0QQCQOmCGA6WZWPXklqQLAoDMYmo1UJqJVU9uSbogAEgdMMOB0kysenJL0gUBQGYxtRoozcSqJ7ckXRAApA6Y4UBpJlY9uSXpggAgs5haDRRLzH4QytFBcNIt8eyGHzaAmz0KKs1aXQ96Ea8HoikKbE66pcT3mS75l1IIZ\/7eV3\/\/euZf9P3vX0Y\/+\/lVNGXKlFD+dWseEu4VXWGEtNHSyyzF77n+JB12+BG05fBhcczUNVQ588PMrzIibKF3SXqpP0lFb62\/UAjde\/wnTJjgL+DdLxy7ZcMPf5jGXHgB7TByx1DESGYIzmsb\/9VXX+NfIf4aXXnlTzzjE7t8kr5+0on8ZdiPCDM01e38R4NgztZg3XH7HXTOt86m21m29WmjQw85lPj7IrTkkktwi3jO8W3L+ccfkzL+U1nE8kIthRKDBpkVXlTF64Foigybk24p9Vfqj2thNuOvzf21EO+QDYVTv0Z5WS+skJlXfujJvmbMzcDYrjAb17fXvdUzYIXULThGic9\/wQ4TgX75Usn\/gl9\/\/\/nPf2j8+Ado3Li\/0qOPPkqvTZ9Ob82cSYvxWzz69+9Pa621Nt+x39S\/Gm\/w4LX5OMcf0FFDoDvqn7\/wRwcddBAdceSRtMnQoap3BzHuIK27O+Kjx4YI7I4nusoFYRn\/8zP\/L7z4Ar\/1ZRRdccUV1M5\/LXrfyu+ns8440\/9Sah\/37BcfNnfkOjv\/3\/y73\/k3PLlx4ZahQzehww47hD73uc\/TUku5Xyj2vXkfVvn+vzptGv3yl7+i7\/JbcfixM9\/kA\/yXrx9f+SMaMWIHNKuVpf5qM8y5KuMvzYO2dPL6kwrlYprT+i\/1V+pP6kfKDFXhLuHdEoej94siQJo1ATBdR+66EVL4IIjBAuMWRYAl12hgIi6kUEEQgwXGLYoAS67RwERcSKGCIAYLjFsUAZZco4GJuJBCBUEMFhi3KAIsuUYDE3EhhQqCGCwwblEEWHKNBibiQgoVBDFYYNyiCLDkGg1MxIUUKghisMC4RRFgyTUamIgLKVQQxGCBcYsSwOWXX06HHHywH9h7fnZPOpMvxtZZZx3TAZogLqSQQBCDBcYtigBLrtHARFxIoYIgBguMWxQBllyjgYm4kEIFQQwWGLcoAiy5RgMTcSGFCoIYLDBuUQRYco0GpovLb0eiC\/n3EkaPPpem84fPJZZYgo4\/9ng6\/sTj+W73kjWts8sgdCYfElOTV197ja740Y\/osssuoyeffNJfQrbx42OD1x1Mm2+6GX+o3YJWW30V6t9vCfa16E3+4Dt58mT\/+Nm4B8bRPx9\/gtp9v8Q\/PrUO\/wXrcNp3331pyQED0seADuKnLbEITZB3SGGBIAYLjFsUAZZco4GJuJBCBUEMFhi3KAIsuUYDE3EhhQqCGCwwblEEWHKNBibiQgoVBDFYYNyiCLDkGg1MxIUUKghisMC4RRFgyTUamIgLKVQQxGCBcYsiwJJrNDARF1KoIIjBAuMWRYAl12hgIi6kUEEQgwXGLYoAS67RwERcSKGCIAYLjFsUAZZco3lmvI4Xd2huOzG2ylZK0waQ+vKIV\/JptKaFiRX9xlbih09LNbmrN4XsOZ9HvCr5r\/t0H7Jnai0m1NjeY\/XHr+Sjiy++hM47bzS9+so04lda0r777UenfvObxG8WiRnqSITsOYZHvCr11\/vqz\/3N9Rc\/\/zn\/GuopxG984cdV+tDe++xNZ\/F72FdZZVVfIN11\/N0vn9zy+\/+jH\/CHzD\/96c\/0yiuv+ITicTPcI5abxbE8By23HH102+3ooEMOph35dxXCXyujMwq\/jaFSxWFs77Hx75JQ9t+VV8hC9S6llEkDiO2QR1bL\/Nf75r+Gg4+j7t2+Enro+GfPyKeiQ91iGGNDFUNqGhuYbmuADalbwVYnFU+gAN9Aa5hTvU07Kl136FRsxRMooMTnDOhslPzzhOT+AsV5cRcRvbn+p\/FF\/Pn8bPO3v\/1teuP11\/mLt4vTwQcf6i\/wF1l00V6\/\/37wl\/qvHf938Ze1jzvmWBr\/4Hg\/GEaMGEEX8g+fbTx045i2DgcHUmuzK00EeJ7WMP888c8n6YFx4+iBhx7gL26\/SDP5Trxb3CNo7+NfM95006H+EbQPfvCD3t68Ur0LFOCbaQ3xvU07KgE6dCq24gkUUOJzBnQ2Sv7fO+cfDJJy\/NNlhq3\/8GQN8mQHClvd3Y36JaRUJ7aeF6w52+s1jbVJ42rfwdsxJ7XK2V6vaaxNGqeegIK3Yw64mIAS26OkClGbNBaCgODtmCPkeFwT26OkClGbNBaCgODtmCPkEp9TIXd1GPu81SRPmzROmQQK3o454HZf\/fGrAunss86iy39wOW211dZ0x513djBHdH\/85h6Tpw7l2fJ6TfK0SeNqn8HbMSe1ytler2msTRqnnoCCt2MOuN13\/HWPTzzxT\/514BPohuuv9yeKddZZly7gN9F8kr94nS\/51nq9ZuO1SeO8v+oeVRnaEvpKPXqUVKFqk8ZCEBC8HXOEXOY\/TkVvmP+aj2jy1KG8WrxeUzzapHG1z+DtmJNa5Wyv1zTWJo1TT0DB2zEH3Opo9e1qGmuTxqknoODtmANu748vd+SbE4IvqiqGQAEpYx412Z0TPsjQ1GrBBk\/4oqZiCBSgGzBusjsafJChqdWCDZ4Sv81MwpLCBHTCGDdnM\/ksx2q6u1J\/C2L9PfPMM\/TGm6\/Teuutrw9WxM1Hsxx\/5AYypMxqOqULXv2\/PPVlOuOMM+iy711K7777Li2\/\/Ip02mnfpAMPPJAWWWQR3vjmvUk+y7Hagr3\/afeatrrJ7vYLPsiwr1Yr+58ysODVvxzCBNLmetR8NMvxR24gQ+qsptNZjn9nzv98Ie+eOFT33SWjAnRWDbYMJDxSjJOV+GAY\/hyQOjLEVOeNg6SpZYkfDnjJv8+AKatSf2X88RzH\/5f5h9Ogpns14YaJQ8aNAJlw3RuMLuE3vri\/yPCPmdFiiy9OXzvqKDrllFNo6aWX4hnbfeCPi2lexl8Zf2X8lfmnzL89df6RO\/L5hJ4uixPCHC3STNZirVyCgxakXqc2JT6yFHKSsp6QzpbHtom4czP0IPVamjAAK9hS1IQ022PbRNy5GXqQei1NGIAVbClqQprtsW0i7twMPUi9liYMwAq2FDUhzfbYNhF3boYepF5LEwZgBVuKmpBme2ybiDs3Qw9Sr6UJA7CCLUVNSLM9tk3E7cz\/fu45+vOf\/0yf59cD4stdOnK1qbWkqAlJAADbBNZsT9Kelfjp8YZq6qwlZT2ga66+hk488QR66umnfEK\/8IUv0LnnfIs+8ME1JO8AtqeSf+QjSL1GxpwEK9jy\/MsHpOYm4rE9pZ515JyTWCW+y0DJPz6Wp0xIgQFUi8h7cjP0IPUaHTkJVrClqAlptse2ibhzM\/Qg9VqaMAAr2FLUhDTbY9tE3LkZepB6LU0YgBVsKWpCmu2xauIv5PEpwTRRJB3aY+XzG+B1nmqM3YViA87ila1IhhI\/3CUr+cfkEUoHt\/dCWam1qTNXY8yXb52muir153IT7oTprOS4J8bfgQceQD\/84Y9o6MZD6exvnUM777RTHlb0nogfOp9\/+99b4v\/lL\/fTMcceR\/fdc48fZltutRVddOFFNGz4FvH4lfFX5h8uhTL\/xvNQHBZelPlnfp1\/wlF47+Rf3ZHXBciYc4ALKUmKGOIlZ4XjmOpyVPwCYr9KD51X1xWKNpT4\/pJXp0QyWPIvHwckPwJK\/flUqHxI3WSgQtGG2Y+\/m264gU466WT+4Z0JvuNtttmWvsUX9FvzF2Rn84qbsCE6nLdow+zj+zuY0kRAOf4+FSof2WGHOvnpyfwqyZPp17\/+FT+O1KI11\/wgnTv6PPrsnnsypeS\/zL\/8GFVtGZXzTzn\/xEfspD4ElPnXp0LlAxNuLisUbajOv+pCPhAtPV7La6MPqAweBt2t3ZL+DJh4QJCBqdfBo\/2CBYCvDB4G3a3dUuKHPMRR4xVkDBKMJFMOkT\/hCgBbGTwMulu7Be1L\/JQnIMiQKb0OHu0XLAB8ZfAw6G7tlgUl\/+2z3qX\/\/flVdDq\/c34yfznWLbt84hN0ztln00YbbeT1tEr7gO0PFmYIAFsZPAy6W7sF7XVDtIAMTL1OfaC9cAWArwweBt2t3YL2C2P8aa++yo\/MnEPfvuRi\/nGnt2jQsoP4GfiT6YgjjqBF+VeFw9J791\/tWSo7bfQJUAYPg+7WblmYj7\/as7L\/OJY6Kf4IK4OHQXdrt5TjH\/KwMM5\/6sguVPUfHq1B8em9cMcCf\/N2sInjeG4RQlDrdZCitKKmDybEb2ahZaXfGK5ilwZ6e2CM0ooSH+mRnLKh5N9nQ1IjAEnS9aVsOc\/rMEZpRa+tP\/clycu\/\/wM66+wz6AV+z\/cRRxxOl1zyHdlfZKU6htlT6m+e1N+sd2fxMfo+nXb6afTSSy\/RovzbAIcecoj\/4a9BgwalQyMHS9W6g7m9VocxSitq+mBCOf7z5Pj7i08cHhzacv4v9VfG30Ix\/tIdeTVoMY6dxNiG1D7g5EsIPkjvqbiVocSXSQM5cxIZgtQ+4ORLCD5I76m4laHkv+Q\/TtqoGSdRIZDaB5x8CcEH6TxvzHjd3+k94KtfpRVXXJEtil\/qb77V30033UQnHH88TXrsMX838TO77Uaj+TGatddeS46QOlI4pCKTLyFxRuA9FbcylOM\/346\/P0Ql\/yX\/PTz\/Vx\/FKuOfiy7MkHM7\/vj5R5dNu6j8ekeuC7vqqFqEnACTWnxU1cvKks+hvJNcF3bVUbUIOQEmlfgl\/6X+0h+B0+BglA+iXBdy1VG1CDkBJpXxN\/\/H398f+jt\/kfUYupN\/1MudTzbbdDO68MIxtO0228j5xR+0xoNadVQt6bALYlI5\/vP\/+Jf5r8x\/MiY1yAdxrgu36qhahJwAk8r4797xn+7IuzT7BKs5vOFTghwRddQCVIbYn\/\/A4c1u5ULw9BFpGbvE54SYl4yU\/HMxNky2ur58Xbm6zSoKqpduVepvQR9\/\/3zqSVrpfe+jAQMG8MHiY1aOv6\/b2hXq29d15+v\/31Oeo1O+cQp\/f+Fn1JrVTquttiqd+63R9D\/\/8z9EfdTlXcl\/qb8y\/mqHnjd2cfyV6x\/OHp\/WVfpCjtlQrn98amI+OCGdHH\/hQr6S0TzJiqBgiDYXa\/QFqbqyJqUpqOhdg+gLUvViTUpTUNG7BtEXpOrFmpSmoKJ3DaIvSNWLNSlNQUXvGkRfkKoXa1KagoreNYi+IFUv1qQ0BRW9axB9QaperElpCip61yD6glS9WJPSFFT0rkH0Bcm9DB8+nJ5++mn\/xpRDDj6YFucfHTKzkeJ2Lahqhb4ga1zBpAgKKnrXIPqCVL1Yk9IUVPROwddff4MfmTmX77pfSG++8QZ\/WFqK83wSHf21Y6hff5fntNgwSlMwsbuI0Bek6saalKagoncNoi9I1Ys1KU1BRe8aRF+QqhdrUpqCit41iL4gVS\/WpDQFFb1rEH1Bql6sSWkKKnrXIPqCVL1Yk9IUVPSuQfQFqXqxJqUpqOhdg+gLUvViTUpTUNG7BtEXpOrFmpSmoKJ3DaIvSNWLNSlNQUXvGkRfkKoXa1KagorON8frHq2pflYy51LdQaCq3gUKkN6Spbm70Ldmxmg1Ju\/xduUUKKDE50S5+9opIxbHDCuhmdFcY\/Ieb1dOgQIkbrKU+DoXKvHNyW5q4O3KKVDAQpP\/6dOn05e++EW66eabfb2utvrq9E1+480+++xDffv0VbcqVMZ60f6nvUrHTmw1Ju\/rxP7Pam+nK3\/8Y\/rGqFH0\/H\/\/S3379qWvHPBVOvP0M+J3FSRKBDXBakydjY+mkK6dxjGoEjXeGpNv4O3KKVCAxEqWEl\/nQiU+whpvjanknzPg86KSI1BAqT9OU7n+sHNOqo445Iyo8daYfBNv57+zt1rtfCnPf06NTzDU8WGDdB0AQ5rtMIpmaAwSvxOzxC\/5L\/XnB0T9CGmeCOv4GFlBaobGYC144+++e++lk\/kd5nffdRdvZBsNXnddOuusM2j33ffgJz9CoWBPILE3VakZGoO54O1\/HArYwNq5FnsCKeQM3HbbH+i4446nhx9+2BfRzjvtTBecfz6tP2RIZPbu\/U9nKre7ddkq+1\/Ov+X6p1z\/hemwfoZY8M+\/6o583AUv9O5oe9NkGJLQmbX0zMA8D4VJ1hOExV1GLCYBnQlX4UhrBiV+KNCQpJgZLyRLJf+l\/rgG+NJSSkKAGVtvPfIIvTn2Vmrruwgt8enP0KJrrGH8UKQ1g9mNv1v\/cCtf0J9EDz74kP9ezW9+czXt+dnduav8Uhe9z17OSfzQW2yhGy4E8SdMmEDHHX8c3fJ\/t\/h0fXjDjeiCC86nHXbcMWx9J\/K\/MO9\/UyXowzi7+iv77zKwcNZ\/Of71GSj1H88evWz+Uxfy9sDLAYc523H9PajAVS0AveQ7HnzqsKdeENB5VVYYbNATb4nPBRmTGnKlMgboZcl\/qb+eHX+vXDCaZv36h9Q2eCi1pj5PrZf+S0uccREtufMnuEjnrv7ck3+\/vfpq+vlP\/5euvfEGWqRPHz9ZlPFfP\/5feOEFOnXUqfSjH19Bs959l97\/\/pXo9DPOpK\/svz\/1ibmTi7PqtCsWTCHaUObfeBHASSn1V19\/vl5QPOX8M9fzXxl\/MQNcS2X+6WD+wTPyldOtnqmkmhKo8JOLkRnJyVMxw+BaZJdbJX6aKVMGBVXyJR4HkFfI6IQKKbyS\/0o+S\/11qv5ev\/F6euOM42iRj+1OA885j9r5S5RTPzWC6LVXaNnrx9Kiq6yWKhN1B1nqj3MTPo3Pbf3NnDmTxowZQ+eeey657xosscSS\/EjNMXTCCSfSkksuGY4B8g5Z8t9t+U9F7hASDBm9UCGFV+bfua3\/kn+dARQYZKk\/nwGkA7IXjb8294h8drtc7R5PMM6dPZeqSwZYctNgqPiZ5201Dm0q8Uv+S\/3hYg+XfRhkSeox462ZIVMTpcahTbMbfy99akdq\/edpWua6O2mx1cJF+7SLL6R3\/vd7tNie+9AyJ41KsdLmJpsOFv3aNLv46PJNvpDt368f1HQtVdMnSD6ODlbD7Wz8SjeZIVN9JG+rcWjT7OI7\/1VXXeXf8vPcs89SG99133ufvemsM86iVVZdBbtq5nQYuyO+6QuKk3onqqpnlvg8nrM85amb3fH3iazLb9Zvppb8I2c1idGmkv9y\/bEwXH9kj9boEnZjXesa+3nAuqMJxsDmtf57CDiNdzvzGFrXuMT3GahJScl\/SIqsS\/1Vr\/67afy988y\/aNoefPd9sX60wr2PyqB88557aPpR+1LbssvTCrfd32PxMT3NmDGD1l1nXfrMZz5Dp4w6hd6\/0vuji6ugFx\/\/u++6m4497lgaP368z\/2Ij46g88ecT5sM3eQ9sf84\/rHwpP5cwZXxH7PQi+u\/HH8uefvMMhuk8sMoKMe\/mqNuOv8tSPXnL+T1p85QCG5O1A9gp+JQHlMyzo4iClitXXPHxkPdyuU9nFh86inxfbI4LSX\/vkx86fmVrzdnw9yVrNbi2+mVTymvSv3prAju6vh\/\/e4\/0pvHfIVaAwbSCn90F5PhiLz12ER67Uuf8l98Xf4vk+KQ7rn8jx17O33qU5+it9xd+SWWoCOPOpJOOP4EGjhwYNjHXnb8\/\/nPJ+hEfmTmuuuv83d0B6+zDp1\/\/gWcA\/5OgowOObw9nv8UMxx\/FblX5t\/ONnqfNVZZ6GX1V\/Y\/lTU+MmqLOvLJXK5\/yvm3B68\/wh15P\/+ESUigK0GM2EplVg1+rkITo8yG69wSNA6L2bSv9hjPVezwmzyb9hV3ic+J80lIh8IluRz\/ulKrtZmaMkqVXnH71PvVQpX\/6Vf9L8286EzqM\/B9NOi2P\/sddSXz9hNP0qtf+Di1+rRoubEPUN9lljVJ6In9f3bKFDrjjDPoJ1deSe++O4uWXWYZOu7E4+hrR34tPSMet6In4ps+jWJ23SsVtzN0Yvy9\/PLLfh+\/d9ml9PY7s2j5FZaj0755Oh180EHUZxF+z77rxq0qAZwxLRV3J+OnHqrI9GmU2XCdu8Tv1PGvZjJZTMqNkjhAFXfJf8l\/J+Yf1E+dNDVllCq74i71N9f11xbeIq+T7bMaDSrl0ay9jhT0Bie6ZXeLCyW9OwO9VL7iIj2Gpo7nFj49NYQI5gZnaOzblvgl\/6X+8MksjhceVLoqwnCBz2kOu6V+\/E3\/9S\/pzfNG8YX8CrT82PtkjL79+OP06hd38U+1LH\/HQ9SHf0F0Xo2\/J\/hu9Sj+4aPf\/OY3fu9Wet9K9I9H\/0EDlxu40M4\/b7\/9Dn33O9+ls84+i16ZNo36LbYY\/9XhKP+u\/aX5A4vcFdSHLhy4sGb7nOa\/ffpr9Mbtt9E7f3+IFhu2NS0xYgdqW2xRXxGoItd5CBkDd2N82XAP6uuvxC\/5L\/XnZucy\/vQ5Kswdas3pmdP5L7R2eXXLgj\/\/8B35dt5adSdcz9JhL1AmUZtzEcssNFS5SYYS3+fIJCrlucGcCLNBpr1T3CLHOXj92hADza0bzIkwG2TaO8UtJX7Ig74UMomKbhYN5kSYDTLtuzH\/M+\/jZ+GP3IdoiWVphbvCc9puU2b+\/W80\/St7Ei2yGK1w\/wS7\/d0Yv6Pdfuihh+iUU07xX4C9+tprbbm5hgtJ\/V19zTV04okn0tNPPum3+fOf\/wJ961vfojXWWKOj3Te+OT3+70x5lqbtxe\/rb59Ffdb5MM36+33UZ9UP0fK\/uIaoX3\/Td2eUOY2f92na585O6Ka9U9yykBx\/t6lm+51hDhfTvux\/yF45\/rGKQnX4tSmUVGQN5kSYDTLtneKWkv+Qh246\/6cvu5psxxgQ+HIAc+q+OwFanUzd1t39Uy0SURkjLPG58LnyS\/5L\/XEZyBxYHSkVSxpW3T\/+3n3xBXpll635EZq+tOK9E4j6hne8v\/77\/6M3vnEktb1\/DVruprFxe7s\/fmVnawwz33qL+i2+OHvmT\/yu5v8vf\/kLHXvssXQvf3HY9bHVVlvRmAvH0BbDh\/Xs8ee59sWPb8OvD32Zlv3trbQov4lo+s9+SjMvPpP6bvsJGjjm4p6NX3MM5aXtZf4r898CNP\/VlWpu6+r4N\/2U659y\/TOb67+aR2tiCfnicbj+siEVqCm5oDgnltrmsTWLxg8GJX5MfW0C4+c4JDmTJf8pIbXpK\/Xni6sbxt\/Ufb5A7f8YTwMu\/gn13\/ojPu+vfPMb9O7Nv6J+h59CS+23XzoWghas\/L\/Cz57feuutYbxh7GTzjysjuBxuZy09qhV3DATZT2a2tbMWmMntEPs4xnIrrEAf419bxTJ58mQ6+aST6Fe\/+pWPt+aaa9Lo0aNpzz35LxxqiT0oi4IpUNgn5QoQ8avz75u3j6UZJx5MfYePpEHf\/T7T+a+lb79NU7fdmDe3nb\/zMJ76LDWgzD8+M5XEpvTC5YqlsjTnX6hZ\/Yk9gp46\/hKnxI9jp\/YAlvrnQqnPDDvmYv4p9RczMIfjTx6t8c1rZgdrihqMkJJ9gOCAGxJeOwqUV0FwrSlqMEKCLDI44IbM3FFVXgXBtaaowQgJssjggBsyc0dVeRUE15qiBiMkyCKDA27IzB1V5VUQXGuKGoyQIIsMDrghM3dUlVdBcK0pajBCgiwyOOCGzNxRVV4FwbWmqMEICbLI4IAbMnNHVXkVBNeaogYjJMgigwNuyMwdVeVVEFxrihqMLGc+MI6mH7oXta2+Ni33i2vp7aeepOn77katfkvRcrfcTX3697fD3XWM9j6IUhTsbPz6s0noCN1Bok\/EnzRpEn3t6KPof77wRdp3333FHQBffPP3etx8qhd3Se7u7Xe0+JsnkeJOdokNjaWHLRq+5TC679776dVXX6Vzzj6Hvn3JxfQ2\/xVh2WUH0qmnfoMOPexwWpyfiQ+L64kbRiEyepMIhEYaHL6BUhhOPeIgmnX\/7dTvoBNo6QMOlBAv7vlJak2eSEuecj4t+Rl+7EbtSooLFPpEz5DwSqc18X2\/Qky7GkyxJ3QIqfiaBzek0IxBKQqCa01RgxESZJHBATdk5o6q8ioIrjVFDUZIkEUGB9yQmTuqyqsguNYUNRghQRYZHHBDZu6oKq+C4FpT1GCEBFlkcMANmbmjqrwKgmtNUYMREmSRwQE3ZOaOqvIqCK41RQ1GSJBFBgfckJk7qsqrILjWFDUYIUEWGRxwQ2buqCqvguBaU9RghARZZHDADZm5o6q8CoJrTVGDERJkkcEBN2TmjqryKgiuNUUNRkgmpzvyMEKipxoZKM3Eqie3JF0QAGRNXJgCpZlY9eSWpAsCgESwGhkozcSqJ7ckXRAAZE1cmAKlmVj15JakCwKARLAaGSjNxKontyRdEABkTVyYAqWZWPXklqQLAoBEsBoZKM3Eqie3JF0QAGRNXJgCpZlY9eSWpAsCgESwGhkoifj6H26lN755LF918d3nWe8QrbAqDfzxVbTISivH1okbDEkXBABZExemQGkmVj25JegHHngA\/fCHV3C3TueFL04PPvDgcJEaVL7z3kbugSF98R5a85qv2Nv4T4ra57rxfneh6xbfdWgRDME4ceIkuuuuu2jYsC35EZqj6dBDDqWXXn6JFu27KF+8H0qnjjqVBi03KDVRKPSW95kIVU9uSbqgCF76zM7UmvIE9Tv2DFrqf74onU79ypf9s\/KL730YLX3k0ZwVaSkcgKontyRdEAAkOquRgdJMrHpyS9IFAUDWxIUpUJqJVU9uSbogAEgEq5GB0kysenJL0gUBQNbEhSlQmolVT25JuiAASASrkYHSTKx6ckvSBQFA1sSFKVCaiVVPbkm6IABIBKuRgdJMrHpyS9IFAUDWxIUpUJqJVU9uSbogAEgEq5GB0kysenJL0gUBQNbEhSlQmolVT25JuiAASASrkYFiiekZeWkAgpNuibde8AwM3OxRUGnW6nrQi3g9EE1RYHPSLSW+z3TJv5SCLwmuDFSKLxPRrDX40lq8HoiWCKYfZy7116n64y9Gznz4Yeq7\/HK06Kqrq3xaKBlfAPI\/86036dJLL6MzzzqTXp32Ko0cMZLG8pta5Jj7Te+Z4z9xwkRaf8j6NHz4cDr1m6fSLjvv4n\/Q6vzzRtNaaw\/myC5BbumZ+KHM5WiEULx+cduhRG9Mp\/6jzqMBu+4m8aceuD+1P\/gn6rvDbjTo3PM937aGBildGiBeD0RTHNicdMu83f80q5T4Jf+l\/sr4WzjmnzZ+aQ0\/7InJMwzdunU9A1ZI2zL90Iy7ZxWeE\/UMpuO6tOmEYntK06u1Iy5k5nW75v7OzUFK\/JJ\/Vwl+KfVXxh8Xg68HroW77r6TPvrRkTRy5AgaO3YsqsTIhhmGOWF+ib3ZNh3MPxP4sZ4h7kJ+C3605v576W9\/e5g23ngj014r3R2\/af59cfvNqTV9Gi3xjdE0wD1CE5eXDtiHWg\/dQ4t8fA8aePboaMVWQYIdZJn\/y\/mnnH\/D\/FCuP8r1hz\/fuKmRp8um+dfOoElrmGGZEOrL35E3JFEEpN4aEJjueVI8H+qvn8EHAXomjVsUARm7qoJZ4pf8l\/rjSYIHRBl\/ap7ABKFMGo4bP5622HxzvpDnO\/K38YW8n3Fn00h1ACbyDikUEMRANGniRFpv\/XBH\/t777gshnV+4AlSreggm4kIKGwQxWKDdL+35aaLJE2jxY0\/jR2v2EuLUL3+e2ic9QIvtfzQtc8hhYncA7REXUkggiMEC4xZFgCXXaGAiLqRQQRCDBcYtigBLrtHARFxIoYIgBguMWxQBllyjgYm4kEIFQQwWGLcoAiy5RgMTcSGFCoIYLDBuUQRYco0GJuJCChUEMVhg3KIIsOQaDUzEhRQqCGKwwLhFEWDJNRqYiAspVBDEYIFxiyLAkms0MBEXUqggiMEC4xZFgCXXaGAiLqRQQRCDBcYtigBLrtHARFxIoYIgBguMWxQBllyjeSbfNXFSltDcdmJsla2Upg0g9eURr+TTSE0LEyv6ja3Ez67SapJoTCF7zuQRr0r+47WayVNQTK1Fv7GV+ut19TeeL+Q3dxfyO+xAt912G19UhyOO8uiJ4+8u5IfwhfwwfrTmPr6Qx2JizYf6m3rCMdR+xw206JcOoWWPPs5vgduml3bejtpefI76f+syWnLHj2FzOyFTLj3iVZl\/yvwjdyezCgrVkmrGuY2tzL+9bv7VJWCOdXQYWzn+tcc\/e0ZeDSCBAnxatYacept26CNTaVVxKoPqRKCASk8lfjimPkM2TSqnDnboVFzFEyjA87RW8l\/y7\/8CwpXR8dN5umpUuVWg4gkU0GP1hwv5HfjRmtvG3h62SsIK6Nb4EyfxM\/LujvwwfSGvYgkU0K3xw07m65b\/nsP0\/fegtg+sS8tfczMTWtQ+fQZN3X5T\/uGvJWn5P46nNv7dALeU8V\/Gf28Y\/76YQ0XzOn7EkGEnIGeU+ufUlOMfr65smaSSqlRN5jKq6kSggEpPdv6tvSMferddmIisBG\/HnNQmZ3u9prE2aZx6AgrejjngVrfWt6tprE0ap56AgrdjDrglfp4tr9ckT5s0TpkECt6OOeCW\/OfZ8npN8rRJ45RJoODtmAPugp1\/XMi7L7vexu9Rx93Cjvdt7vZ\/At+R36DxjnzIW0\/G933XBHCml\/d1vw3wAN99v5QGjNiBXj72SJr1p9\/T4oefTEvvu388qKFxTRfpoCuUs71e01ibNFZdlfg+AyE7HecoZS1ne72msTZpnHoCCt6OOeAu2OM\/bSW2M1g63rey\/+5DT8c5SpnNs+X1msbapHHqCSh4O+aAi+Oa2B4lVYjapLEQBARvxxwhV66WfbuaxtqkceoJKHjBkTvyMICWJL4oqhgCBSS6R01254QPMjS1WrDBE74oohgCBegGjJvsjgYfZGhqtWCDp8R3X1RRGRIoQCeMcZPd0eCDDE2tFmzwlPyX\/Pdk\/Y0f\/wA\/WrMZPyO\/A3\/Z1b21Ri89M\/9NnDiB78hvwG+t4S+78qM1C1T9z5xJUw\/aj9onjOdf613E33lcfO+DaZnDjgqJkY0VoBPGuMnuaPBBhqZWCzZ4yvgv478nx7+rs1J\/8rcIPfh8Zsr4W\/DHH1\/It3MN4x6Urujm0saRtgyc8KLXOFmJD0bizwHoozKEpJ2ARM2QZZT4YcCV\/PsMmOJgpdSfH+Zl\/HEa1HTn5p9wIe++7MpvrbmNH63xflNA2cwTVMuYs\/lnIt+R96+fHOYu5O9P\/UunApIvQ5YxZ\/FTV7aXdEXTollTp\/IPfD1F\/TfamEh+lKqpZffHN+elFFaQ3fISv8z\/7oIrLqY4WCnzf5n\/uTh66\/lP7si7E5qeONO0mBDGiEjbpNEMWpB6LU0YgBVsKWpCmu2xbSLu3Aw9SL2WJgzACrYUNSHN9tg2EXduhh6kXksTBmAFW4qakGZ7bJuIOzdDD1KvpQkDsIItRU1Isz22TcSdm6EHqdfShAFYwZaiJqTZHtsm4s7N0IPUa2nCAKxgS1ET0myPbRNx52boQeq1NGEAVrClqAlptse2ibhzM\/Qg9VqaMAAr2FLUhDTbY9tE3LkZepB6LU0YgBVsKWpCmu2xbSLu3Aw9SL0OTeTRGvfWmvj6yRQ1IQkAgI6hR5mboevIE\/gHoYasv55\/j3z4sitYoZMUNaEsTJ4ycdueEk3HzzmJVeK7DKSsJyQJBqgm0XtyM\/Qg9RodOQlWsKWoCWm2x7aJuHMz9CD1WpowACvYUtSENNtj20TcuRl6kHotTRiAFWwpakKa7bFtIu7cDD1IvZYmDMAKthQ1Ic322DYRd26GHqReSxMGYAVbipqQZntsm4g7N0MPUq+lCQOwgi1FTUizPbZNxJ2boQep19KEAVjBlqImpNke2ybizs3Qg9RracIArGBLURPSbI9tE3HnZuhB6rU0YQBWsKWoCWm2x6qJv5DHpxTTRJF0aI+Vz2+A193HHe5ePhK7UGzo6BUFfmuYwrTwpQl1T0H1FaBaK1+I4eKW+CX\/rg5iUXnBhVLqL8uJzk\/A7\/XxN24cv35yiy1oxMjt6fbKl139DMNlVZ1\/nn\/+ebrxxhvoicefoG2324524Edz+vXvpxLcXH\/+jjxeP3kvv37ST19l\/pN7qmqOV5kPR0H5yvzvaoxLrpz\/MFA7Nf4UqVx\/cP2U+ceVz8I7\/6o78rq0GZvJ0vm0Ie6yNklzlQ7xC4jdKF3aZaBC0YYS35ecTomkr+RfhqPkR0CpP58KlQ+pmwxUKNrQu8afvyO\/BT9a437ZFT8IpXfXp0YbWvTne+6lPXfbnZZdbiDtv\/\/+dPnll\/PFfhv9\/W8P0RIDlgqfJ6WJAKm\/iXxH3r+1Jnv9pBwF1STYtKF35V\/2WQO9u96uDWX\/y\/zPo02XhNROOf+V81+8HSD1IUDm39nf3eKCym8KimHBm3\/UhXzYWbXL6dJdG\/NJ1ftSW+dO+58aAkH6bswq9YH2whWABsrgYdDd2i1oH4+at6EFpDeaVeoD7YUrAA2UwcOgu7Vb0L7ET3kCggyZ0uvg0X7BAsBXBg+D7tZuKfkPeSj1l+oECBIZctJdyLsfhNp+h\/CDUKgf4QoIrd5++y2+CB9CTz35JE2e\/Ayt\/oHVaJWVV6F\/\/+c\/dMedd9L2H\/1oIKYZVBC68hfyQ\/jRmmFb8jPy9zI\/eOB3HQgWELtNnkhKbR0D2696kBaVrtBlie8zp\/MjWACSpQweBt2t3VLyH\/JQ6i\/VCRAkMpRk8Gi\/YAFgK4OHQXdrt5T6C3l4L9VfeLQGB1\/Vh08F\/ubOirgEIFlR5vZaHcYorVBB0CcT3N98eEHLBCIHQgjRUKvDGKUVKgj6YEKJ75OBzJX8czrSTBkLhYUkKJpqdRijtKKmDyaU+vMJReYqecYREMKc5z\/8susWfEeev+zKr5+UpWH+u+X3t9Auu+xC6667LrlHZNxy+GFH0IQJ\/6Abb7qRBgwYUHMsmSS3EFvcLtyR33LL4XSPe7TGdVLZh3L8S\/2X858ZGvkYcU635PZaHcYorajpgwll\/rXpRQq9Va1ye60OY5RWlPwjPUhrw\/mn7voj3ZFXjdCPk+gbUvuAky8h+CC9p+JWhhJfJg3kzElkCFL7gJMvIfggvafiVoaS\/5L\/eNJCzTiJCoHUPuDkSwg+SO+puJVhPtZf3ZddzXazoraULhwzho479ljad5996cqfXKl8moUegvQe5dbPyPsvu87H\/fdbWOKX8f8eHf+l\/jkDZfwv3OOffw\/KnV7sok443pHrwq46qhYhJ8CkFt+dki82JU9AeSe5Lvyqo2oRcgJMKvFL\/kv91f1pgYdJPohyXUZS1VG1CDkBJi1I46\/yjHy+E5n+ox\/9iA444EDacceR9Ic\/2PfOZ9S0zxoxacJjE2iD9TagYfE98tr9Xsu\/2Xen5EnMdWlQdVQtQk6ASQtS\/aUNiyjfiVyXBlVH1SLkBJhU9r+c\/8r5r\/ec\/9IdeTfM\/QDnDyYY8g2f0uDWE26YQLJpBKqXbuVCcPlEO9y6P\/OSkRK\/9lOizhcOVshlllGoXrpVyX+pvzL+8vln\/Phx\/Iz8MBrBj9boX3Ztukv1zDPP0AfXWIP691+Cpr06jRZddFE\/FZ43ejRtuMEGtMsnPhGGaAfjb+KkmvfIM7\/Mf+X8U86\/Yfg0jb\/o9dcr5fynpxpMOMgfS1dM3uxW5fzfW8\/\/4UI+O\/7hgKsJtXrF7otirleIC6k6tCalKajoXYPoC1L1Yk1KU1DRuwbRF6TqxZqUpqCidw2iL0jVizUpTUFF7xpEX5CqF2tSmoKK3jWIviBVL9akNAUVvWsQfUGqXqxJaQoqetcg+oJUvViT0hRU9K5B9AWperEmpSmo6F2Dsa\/x4\/iXXYfxL7uqt9bYMEqL8MMbfZgeefgROvLII+n444+nO\/lLrgcdeCA98uij9KEPfWi22zOJn61fL75+8j5+Rh4XJGioIrJJaQqC22WJviBVR9akNAUVvWsQfUGqXqxJaQoqetcg+oJUkcu3NAAAQABJREFUvViT0hRU9K5B9AWperEmpSmo6F2D6AtS9WJNSlNQ0bsG0Rek6sWalKagoncNoi9I1Ys1KU1BRe8aRF+QqhdrUpqCit41iL4gVS\/WpDQFFb1rEH1Bql6sSWkKKnrXIPqCVL1Yk9IUVPSuQfQFqXqxJqUpqOh8c7zu0Rp94gC7oYP0aS\/eRxCeAOktWcypCRGU1MxorjF5j7crp0ABJT4nSj6YzyadwZ1yF+nNB8xTFV+ggJL\/kv8Fuv7cl12H8VtrRsgPQqXabar\/J554gvbcc096mC\/m3Tvm37\/yyjSa78jv9aW94kV56gMI0vU5ge\/ID1lvffWDUBKJgWZGe43Je7xdOQUKkN6SpTaC2gDNLPFTnlWKAH2qVL4ECij551yV848dc6k6UEha1nhrTL6FtyunQAGl\/t4D9ccX8u18Kc9\/bs+vw1VdoSQgnQsYUtEzqBkag8bv5CzxS\/5L\/fkBUT9Cmk+EdXyMrCA1Q2Owyvgbx3fkh\/F75N2F\/G38HvlYikhQ7VznMun+9P\/oPybQu++8QxtvvBGP4bylJ\/EK9pT\/9GXXYXTvvfeX8V\/GvysWqTWvxBWqBlLztE23SVgzNAajjP9y\/VGu\/zB114+QBf\/8q+7Ix13wQu+OtuspBBPBnEnpmYF5HhRTmCcIizuPWEwC5ixwZEtrBiV+usSweZYslfyX+uMa4KssKQkBvWb8PcB35DfjO\/Ij3R352\/j1k3iI3u9h3F\/ZbQFztf8TJ4Rn5N3rJ+91j9Ygwb57HSNiMQmYq\/guXJn\/yvyHj5il\/vQ402NM292Q0745H4LSmkEZf2X8ddf4Uxfytiil4GDOCk9\/DzVwVQtAL\/kTP18IpA12HYKAzquywmCDLvwSnwdBTGrIlcoYoJcl\/6X+yvjraP6pe\/0khpDMTGzozvlnEr9HPjwjjx+Ekkge9HR8fQq1kYNW4mcZ6ubjn\/VeOQQl\/1mGSv67df7JslvqL8vAQjf+8Ix85XJPXylnO+nUCt9wkAbI6IQKqS7oK\/2V+DzW7OWHTnElX9opeZVEBy9USOHVHM+S\/5L\/90j9jR83njaPj9bczo\/W+KWH638SPyMvX3a9777qfNrD8cOdFZkISnzOgPm4W\/Jf5r\/3yPzn5rvK9USp\/4Wq\/tvcI\/LZ7XI+qLwP\/mzGB9i5Y0Fre3SLqPgyQ6b6dt5W49CmEr\/kv9RfGI16XMjAi6DiywyZWsYfZ8DnhFfjHxjPr5\/cgp+R51925Qt5nauemn\/CL7uuR8OHDaf77neP1qRlXsR30bD\/MtnHTSjxy\/mvnP\/DYOip8V\/GX5l\/unP+zR6t0VO4lFrN9N5siocnngy5P\/336Nis+f2wJX46hZT8o5ZC2eS1wdYaE4zBxetSf7akfFlxXmrvNuUJ1brG4Yj0lvy7t9ZswXfkR\/J75MeOvT3unE8Ur+SSRuFIqUlJZ+tv4mOTaP3KW2vyDrWu8dzHL8cfxzXm0os8x1rXuOS\/Nl3KGLLF6zL\/pikklk25\/uG6KOcfVIOS+RyjdY1jE2XyF\/L6U2c4ETlinOg8ObRwa7dgCkxWawkstfYNeVV78Diiuutf4mdZ9kn2K3\/dVPJf6s+OtlAbYbRpXMafZMClxY2ehvln3Lhx\/NYad0eev+w6Fr\/U2rPzn9yRd192vede3jR9VN329mx8FwFLmX\/TXz3L+ccPFi6NUn9+fPgp1a\/K+TdOGHqmcq\/elVoxOJKd8CXFK5njlM+5y\/XfXM\/\/4Y68PxbhgAh0ucYRs3mv1Vw7t\/gmRgl2va64JWgsiwpBt67HpolRqvyK2xnimyoEumZl\/6vJa7CYnBql2qDilqSX4y+pcGkr9VctngaLqSmjVBvkbv+M\/DB3Rz6+fjInVLuoWEwTo1So\/rzmXj+5Af8g1LDh\/GXXe+8t80+Zf7lQyvznho4vBTdsyvznstCpxUw5Rqk2r7gl6aX+JBUubQtR\/bWFt8jrg+13JRrUIY9m7XWkoDc40S27Wzw605eJ0EvlKxbSY2jqeG7hjDaECOYGZ2js25b4Jf+l\/jAzxfHCg0pXRRgu8DnNYbf07vHnXj+5Od+Rd3\/yvuHG61nqPGX7z3eV+jAPmQnZijmLIrYI3bDNXZi092lxu3CidAZ3R\/6kE79OWwwfTvfzl13TojqRKL07\/8h2yEHZ\/3QF4XLhlnL8\/VBIaQhp4XWollgzunSEEUjl\/K9neiSqzP86K6FkkBunOeyWVHja6zxBj9bc6QhuYXtP1x\/fkW\/nMOqTmJ1VsR1uV7q8mP1zilukw+D1a0MMNLduMCfCbJBp7xS3lPghD7oUTaKim0WDORFmg0z7kv+QrVJ\/sWpCdfi1KZRUVA3mRJgNMu2d4haV\/\/HjH6DN+T3yMAeK+9jHJzr352D3p9\/oZGgX52BbFNbHWm4PerIOHz6M7rvv\/jDGXN\/OlS0N5ozVrJr2TnGLxAlevzbEQHPrBnMizAaZ9k5xS4kf8hCz63NkEhXdLBrMiTAbZNo7xS0l\/yEPJf++GHyNmEKJ6WHRYE6E2SDT3iluKfUX8tBN9Ze+7GqyHWNAuLOXP6HxQeUDIMcA\/g5k6rbu059qmIjKGGGJX\/Jf6s\/PqGX8df\/888zkyTRq1KlEfXi+cfOQWtxc557hrM5\/3kPP\/\/d5mvH6DFp55VWo\/xL9Qvvg8r2EaY0NrXZq9eEPB1n\/a6+9Nsceldqp2AJr44u3QxDiO0qZf6t331TqUqKUMcKS\/5r6r6apzpLSWuqv1F\/6m3ilVlKhVFzuRkp1\/q3S6iyp295dfzWP1sR0+OQ57M5K1SUlqOozJ8Pa5rE1i8YLkxI\/pr42gfFzXE3uncmlF0tt85J\/n9xSf2X88fioHyJcHN5R65Xxt\/vuu9N1111Ht99+O43gt974pYw\/zD5NyWU\/57WMvzL+uAxqR1g5\/3dq\/kkDTaEy\/6Rk1BdXr5t\/5NEav+euALIdt6aowQiZ0hZRcMANKTRjUIqC4FpT1GCEBFlkcMANmbmjqrwKgmtNUYMREmSRwQE3ZOaOqvIqCK41RQ1GSJBFBgfckJk7qsqrILjWFDUYIUEWGRxwQ2buqCqvguBaU9RghARZZHDADZm5o6q8CoJrTVGDERJkkcEBN2TmjqryKgiuNUUNRkiQRQYH3JCZO6rKqyC41hQ1GCFBFhkccENm7qgqr4LgWlPUYIQEWWRwwA2ZuaOqvAqCa01Rg5Hl7nvUXMjHy3xFs9MqHD6IUhTsbHzbsW2F7iDhlU8hJT5nQGVHQeTKmqIGIyTIIoMDbsjMHVXlVRBca4oajJAgiwwOuCEzd1SVV0FwrSlqMEKCLDI44IbM3FFVXgXBtaaowQgJssjggBsyc0dVeRUE15qiBiMkyCKDA27IzB1V5VUQXGuKGoyQIIsMDrghM3dUlVdBcK0pajBCgiwyOOCGzNxRVV4FwbWmqMEICbLI4IAbMnNHVXkVBNeaogYjJMgigwNuyMwdVeVVEFxrihqMkExOd+RhhERPNTJQmolVT25JuiAAyJq4MAVKM7HqyS1JFwQAiWA1MlCaiVVPbkm6IADImrgwBUozserJLUkXBACJYDUyUJqJVU9uSbogAMiauDAFSjOx6sktSRcEAIlgNTJQmolVT25JuiAAyJq4MAVKM7HqyS1JFwQAiWA1MlCaiVVPbkm6IADImrgwBUozserJLUkXBACJYDUyUMJ6j932oGuvv9bcka92kVuSLggAsiYuTIHSTKx6ckvSBQFAIliNDJRmYtWTW5IuCACyJi5MgdJMrHpyS9IFAUAiWI0MlGZi1ZNbki4IALImLkyB0kysenJL0gUBQCJYjQyUZmLVk1uSLggAsiYuTIHSTKx6ckvSBQFAIliNDJRmYtWTW5IuCACyJi5MgdJMrHpyS9IFAUAiWI0MlGZi1ZNbki4IALImLkyB0kysenJL0gUBQCJYjQyUZmLVk1uSLggAsiYuTIFiiekZebDkDoUjusXdomeMZ2BUewUDB9z620SuM+k9ANuDJwjD+dxS4pf8cy2U+pOhgOFlRw80yDB68rV4PRBN0WBz0i1l\/HU0\/vZwj9Zcz4\/W8C\/CjuDXV6oZzmcvXyG7Zf5zpSXZUGmCrdRfSEoZfx2NP5edsOi6SVZ4IcEq448zUsafSwJKI0pUyMI1\/7TxS2v4OxjY+GyflFrPgBVSNWCYXvSffdGA6bguax5QWV+s5ilPJ80SvzY77tC6L4lyks0XbUr+S\/1xWfjx5IdO\/fjRI7CeASukbvHeGP+7775H9Rn5mIYy\/5X5p8y\/5fxTzr\/l+qOnr7\/8HXlzGhZFgD0712hg+u+n8LiFFCoIYrDAuEURYMk1GpiICylUEMRggXGLIsCSazQwERdSqCCIwQLjFkWAJddoYCIupFBBEIMFxi2KAEuu0cBEXEihgiAGC4xbFAGWXKOBibiQQgVBDBYYtygCLLlGAxNxIYUKghgsMG5RBFhyjQYm4kIKFQQxWGDcogiw5BoNTMT9f\/a+B\/iyoyqzJ0AIgciCskZACRFQXBdCCIj8kUwiCCqrmaCClEJpFgoUCjAJrrrlFmqVJFAuggqFClStWC4hGbeUEJgEFHAFEghIgpIlYROUrfIPIQFCAkn2dJ\/+zvlO375vZn7MTGYy50Lu+c53vu5+99zTfe+78977wZoUAiMiCGFzDETxxIMS48KaFAIjIghhcwxE8eC1G\/n60ZpdF5ft20\/RH1eQpu39M7S76SqEzTGAXlYtlDhuWGsAgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOJBiXFhTQqBERGEsDkGonjiQYlxYU0KgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOJBiXFhTQqBERGEsDkGonjiQYlxYU0KgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOJBiXFhTQqBERGEsDkGonjiQYlxYU0KgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOJBiXFhTQqBERGEsDkGonjiNaU8NarWNm0eOwnc4lVa0xXgfTUkO3saP2kRxurxwOX4w13CJImB0uxVqiHZZf5n\/36hSQu11vMYuKy\/rD+6S7dfrblEfrVGbuSXm1ZP5RuSXc6\/nH\/tX8OWxaI10vcI5\/pT66XPo1x\/c\/2l9RdzZN32uhFBQ7K7M66\/w2fk\/aAxb\/rhW55IYU\/ekaDJZ196O25lXU0A6QwaaHr2MKcbx4FFzxuDpCadQQM5vmSAs5H51zW15YQTQxWlcGOQ1KQzaKDp2Mv83\/H5P739as1O\/Yz8qbMb+Xra+KzR6V5A0hk00NTs5fm\/489\/vado54RPzKbzuogxQZ0YNJDnXzLA2cj6z\/rP+Yf1Z\/pEXhcXnjS83HB0s8Zbqc7VDblrQqYYm8CARjdrTNwXAFc35K4JmWJsAgMa3awxcY4vqbCnKoJb3ibJY4qxZxJIo5s10OIC4OqG3DUhU4xNYECjmzUmzvMvqbgznv\/TTttRdtYvu64+kdcaGKul+ZPiYYqxVxKQRjdroM36H7PV\/EnymGLsmQTS6GYNtJn\/MVvNnySPKcaeSSCNbtZAm\/kfs9X8SfKYYuyZBNLoZg20mf8xW82fJI8pxp5JII1CY0\/kQUDmFl9UIIVBAy5vaI2vQcRgtWn0lENEvyhACoMGuIHgNb7KEIPVptFTDpEcX\/9cfb0Va5slywAnTPAaX2WIwWrT6CmHSOY\/889vAqyEHHDBCF6vJo9FTfS4u83r3+mny89Pni9P5C+uv1qDJ\/Lrve3r8W1O8ks+gMef488+JJPnf14XtUiRG1gt3OhxMW+ef\/Nx1nvL8ZEb2Mx\/zUDMxqFXf3Ijf5scAy1GdkQG+KgCjgpMuC4JQXH6B5Pwz2HeURBSRgfeGxiKihx\/\/Ga0n9bMf9afzHH5f84\/SQMtd7Tg6Lpii4oBW29GUBXt5yfbX3bdVbbLz09a16G5OLn+Zf3l\/Mv1R5aCfbn+2Hojt6J5\/a8PvPp2mK2\/9kR+vKB5WThCjsyGZBm7eHcDmVree5scH1nSnHjWHXG2Go5NLDzS8NXy3poIgEo5H9URqxuOTSw80vDV8t6aCIBKOR\/VEasbjk0sPNLw1fLemgiASjkf1RGrG45NLDzS8NXy3poIgEo5H9URqxuOTSw80vDV8t6aCIBKOR\/VEasbjk0sPNLw1fLemgiASjkf1RGrG45NLDzS8NXy3poIgEo5H9URqxuWJvqXXeMT+diT98wjjxpX7d34fuXyVzf2DT\/Hr+8lOAues8w\/qiTrr2bAZ70jrpaGY8osPNLw1fLemgiASjkf1RGrG45NLDzS8NXy3poIgEo5H9URqxuOTSw80vDV8t6aCIBKOR\/VEasbjk0sPNLw1fLemgiASjkf1RGrG45NLDzS8NXy3poIgEo5H9URqxumJu1GHk\/pQhMS8dANU6y9gObXxw3Svb0lqkMJsekrwu3ViERk+qUFek9JfSmkPcV0jDpujp\/5r3XQi6oZKZSsvyEnnB\/FOf+wfOz9+rNjx2nyO\/L1Rr7\/ak3WHxVYzr9cf2RChDlB5dFhrj9bX3\/y\/qeuMVJIh\/n9Hz2RHyZYSw5zTPRbfqZMSm8HLG6gJ518azeAhYSJHL\/dcnBKLH2Zf7sds\/wYyPprqaB8WN0MYCFhIucf5t+OZ8pfdm0frcHPT+b8y\/nX\/4nfpoyBXH9aKigfw7Jj7kLCRK4\/WH+Wb5Jy\/Tkc1x+6kdeJEqdLfzPNZJtpRDSoft3Xzd+Auw4IVpW81wjHDRuAnogG1a\/7uuX4mod+1WgOMgYLhVvPIfJnWgNQE9Gg+nVfN7TP8T1PQLCaKd5rhOOGDUBPRIPq133dMv+ahwNRfzvkV2sukF+tuUSeyJ\/cv+ya+T9w+dencVn\/ddbn\/Ne6y\/mX808zoOtCxUCwyJBbjXDcsAGoiWhQ\/bqv2x1Rf\/rRGgxOr6+9IvyblzgWMtAUvhv5qQ+y22hokN5tji9VoWWBzPmJ8NQ3ZALkTqxXVM8tRDHxYBd9Z\/4z\/1l\/cXrZZNF5Zn8Qatcl5ZRTt\/fJJ2bQqQ+y22gmbUSQ+d+Yf0s4Ugti6oPsNprMP9JjORQi6y\/rTzJgpWEARdLtyE99kN1GQ4OgTxFk\/bVkIHN+ImL+\/Yk83bSxBB3AcgzYY44Qg22RRZiIHN+KFjmrFhmC5RiwxxwhBtsiizARmf\/Mf180UTPVokJgOQbsMUeIwbbIIkzEIVp\/diNfPyN\/Sr2R53fPOPqeRzpcjRBxiB5\/PQ4\/Ckd+5HSkizARefy5\/uT6M04bm1s0U1Y1PBNHUWu\/6ISInH+H9vyTvwdVz2bc6Py2wOibehlYMiZ2IKLbt9knmZwHGjsZfeiszI2YMB4zlONn\/rP+5JZzftO5mEQ5\/1buz2+XX605vezsvyO\/XT5as5oqW3wE5PqT60+uP7n+5PrLq6LjcREdfVMuA0vGxA5EdGe7\/\/Qn8vUw2wHSNWvlXZplhLKmkIjeX6vVRtddHUJuH7psUOf4kpDwIyuZ\/+m75FZIWkxWrFpLQ0XBbbbusv5y\/u3b9Qc\/P7lL\/iDUqacMT+Sz\/nR+5vyTPOT6k+tvXn\/y+rNvrz94L6g38rjgtFsd3UWKPIIk3xpEX7DUS6TII0jyrUH0BUu9RIo8giTfGkRfsNRLpMgjSPKtQfQFS71EijyCJN8aRF+w1EukyCNI8q1B9AVLvUSKPIIk3xpEX7DUS6TII0jyrUH0BUu9RIo8giTfGkRfsNRLpMgjSPKtQfQFS71EijyCVR4\/WoO\/7EodbYLoC5a0kSKPIMm3BtEXLPUSKfIIknxrEH3BUi+RIo8gybcG0Rcs9RIp8giSfGsQfcFSL5EijyDJtwbRFyz1EinyCJJ8axB9wVIvkSKPIMm3BtEXLPUSKfIIknxrEH3BUi+RIo8gybcG0Rcs9RIp8giSfGsQfcFSL5EijyDJtwbRFyz1EinyCJJ8axB9wVIvkSKPIMnlOcHsozWzfyBe6UClFDRowHpzpj18x5sJfj0ds3KdapEmJb1BAzm+JKp+iMIzEnHPMBlWdnpCtUjjKWjQgI3rTI7PuaDEryd7rUHjKWjQQOZfsrq\/6n\/HafLRmp3nl13tM\/JyI29pN2CUMyRbnnxhWLleEi3SpKQ3aMB6c2Y6Ar0SVub4nmdKEWBLFeXLoIHMv+Rqf80\/Ta7n2pLtwBCpjMNpjJaVPTKhWqTxFDRowMZyJucf5yLmvnqT6ITK\/CNV8u8ct99+m9zKy+P+OtPAK7Q9cgjLOuasQQCsYAyR\/O5pjp\/5z\/prE2I+Q9YvhDM9ZpZaVjCGKuffN7L+nLZjR9nZ\/iDULvmy6+yJPOecceYf9fmN5H+WUWQW\/evsqd5MnfWf+c\/7n7z\/W64WyviqwasHMCy0S8sKxlDum\/WHnsj3QZrhAZmvg3MML2bPrbUWED4Pjn6bwFQ+nlEG9nxQUlprATm+X+LsvLYEWZYy\/6EuayFxbqiw9hBaawFZf4d+\/dWP1uyUPwi162L5+clTtu+2Csbzf9Ou95SvfeLycu+Xnylt5d1sE5hKuI6NMrDbsWYCay0g6+\/Qr7\/ZOd7E5fnv5zzrP+e\/LLf9+aFMmT4zmrFZMvB1ZnGs+nu3WWsB+3L9pRv5+IJsQNDDwPw9TNVSC8Bm5R2HpMsTVjuEAJ0v7UIhBB94ji9F2JOquaKMATab+c\/6y\/m3v9YffEb+kkt2le3bT9WFbDfz78u7Lipfv+yy8rVL\/7bcfs2nSrn3t5T7Xfy\/wyKILowUItc\/v\/Dm+p\/rf17\/eLmhFQOw2bz+HxbXf3xGfnG6eaW0q4mDhd5DgkIleWRBg6gthnTn+L5SewYNLfJlkQqQV9gehAtrusz\/Ip9Zf1l\/uFMIc0sd1Atu5C\/GZ+RbGBMMNs6\/f33Bz5Xb\/+nacvu\/\/FMpX7ulbPvW7yjf\/JcXx8cdWX9Zf3tQf5PSFAp1Bxvrz8IOBOX1NzzuyPmX8+8Qmn\/b6kfkh8flNL1lSajhfkDDshDWkEVsIAa3tW3cJMBUjp\/5z\/rT58k8L8LkE2cRG4jBzfmHnE0Sw9Tu1h\/cyNcvu57Kn5HnTjBWy7rvvvSed5ebfvlFZdsDjy\/f8ufvtgA33d34aMRtGjcQg+uSSYCpHD\/X31x\/c\/2tCwavC20Bod0iNhCD21o2bhJgKtefPVt\/ho\/WcAprrtln3M\/ghEIbDcme\/z24N5N3Byvv9sYO2Wec47cMTFKS+dek2D7rT+YaJh7mjWRn+rRhLCj2GaMfsWPffc1Qtezv5PnX35G\/oPgTeTtySc3m47\/pIx8uX3rhT5fy7Q8p97vgXZJMbduzO\/hjbAhboz0f35oYGMdgn3FvMKFwDBqS\/Z38\/B\/u9Z\/Hb5MnTIqs\/3ppyPl\/oNa\/diPP73p0Ia412a\/QrSKtLFux4trtbGR6RbupwnpSpzcPEqGn\/jl+S5bkK\/PfCqgVWdu125zKxWrTWNMuboSU1Yaiy\/rrCYkm558\/9djb9eeZO04r57dfralfdj1ZEovqFIitluhk\/bvpwx8qX\/qF55Ry\/+8s9\/vzi7q6iQXn\/G8JadO77XL+9wpBhXlWItNlblpJyS7XP88JoVz\/tr7+tZt1rFV5\/ZWqwlzkAqt4\/84\/fSLfVoS201NRYd0mr0kDy31oEpzdaGu4Dd12Diuf49cs7NEWUh6cZfNFuKW+7TL\/kq7+Rxiz\/nL+LSfPwOzYIb8jL79a8x75y6715ydbyhYTLDZC+GZ5In\/jC59Ttj3gO+WjNRfWysv5V7OABGX9xcLZ4IWUBWfZaBGuRP9z6wZrs8z\/MnkrTMhpcJYNFmFLes5\/S0VNW9bfsnhWmG36K\/IcbansBJVcpzlaReqvBNGthG+XhcK\/TIJeFl+xsR61adXVTc7oyhBKrwS1cWub42f+s\/6wMvb5IpOKq0KnC2LVq7huOf\/W1p\/TTpOfn9zZP1qzXX5HHinWxOle0jhbf776kQ+VG+RG\/ogHPqR8y8760Zq6Zf49iVl\/WhM5\/zAteHb4bOnsGNTk5fVf8jJbf2picv33uwItFy6iiut28M8\/eSJ\/m7xaeic4uRDxoemB7d0+tKfcaC8abfsg9DFWaBfsBoX21ambHadG2z4IVVb3K7QLdoNC++rULcfXPPTsthyFRPWwmBXaBbtBoX116pb51zxk\/lsxtBoJhdLTI2aFbgJ82fUS+bLrdv6yqzeP7an+6mfkb3zhs+VG\/qHlm+VGvj8UpZYKN42\/EE+I0J7G596bJgi9oxXaBbtBoX116pbzT\/OQ868VQ6uRUCg9PWJWaBfsBoX21alb1p\/mIeuvFUOrkVAoPT1iVmgX7AaF9tWp2z6uP\/+yaxhNx7I9vpwqmtl3l0w3Ad7t7N0fNXAhkR3m+HLi5cxn\/rP+pAxsDVjOlAXj0yrn3\/LpE6XLE0VkhxvWnx3yRP6C9kR+\/gehvNtl\/m\/6sHzZ9UU\/3Z7If3P9suvaid0w\/vLFRmbT+EHpwkA3J8fP9TevP3n9lTUi7\/\/Wl+nlwtlKpi\/ry\/U\/6L\/B9Xfy0ZrefVu8K55fXTaN297C4FVOm\/fWmwojx++pnyZw87vEml5s0+aZ\/5bcrL\/1hTnn3x7NPzyR91+tkYm3h\/Ovftn1xhfJR2vaZ+TxZdc+cTP\/e5R\/LHPB7mH+Nz4Yyfxn\/tu1c3oBzeuvTLh5ZiSQ88+Xo2mSaoIkIGb1jdFerj\/20Zo2cu\/fX4WeE38t\/gLaWZzota0GEIa1fgNBDkFoI9U9kLAQm9UAwrBDuLsUJQhtpLoHEhZisxpAGHYId5eiBKGNVPdAwkJsVgMIww7h7lKUILSR6h5IWIjNagBh2CHcXYoShDZS3QMJC7FZDSAMO4S7S1GC0EaqeyBhITarAYRhh3B3KUoQ2kh1DyQsxGY1gDDsEO4uRQlCG6nugYSF2KwGEIYdwt2lKEFoI9U9kLAQm9UAwrBDuLsUJQhtpLoHUuzy5ydrSxWQLFz0vv75\/1duv\/Xr5cvn\/Vn52p\/8fin3vE\/5pt9\/aznim+5d7nq\/+5Vtd787hh9uGHqPax0PrVZlCDQ9OQTRVaS6BxIWYrMaQBh2CHeXogShjVT3QMJCbFYDCMMO4e5SlCC0keoeSFiIzWoAYdgh3F2KEoQ2Ut0DCQuxWQ0gDDuEu0tRgtBGqnsgYSE2qwGEYYdwdylKENpIdQ8kLMRmNYAw7BDuLkUJQhup7oGEhdisBhCGHcLdpShBaCPVPZCwEJvVAMKwQ7i7FCUIbaS6BxIWYrMaQBh2CHeXogShjVT3QMJCbFYDCMMO4e5SlCC0keoeSFiIzWoAYdgh3F2KEoQ2Ut0DCStifyIPEhY9TaxK1oXLyMi4bwgAdjIuKJWsC5eRkXHfEAAsBptYlawLl5GRcd8QAOxkXFAqWRcuIyPjviEAWAw2sSpZFy4jI+O+IQDYybigVLIuXEZGxn1DALAYbGJVsi5cRkbGfUMAsJNxQalkXbiMjIz7hgBgMdjEqmRduIyMjPuGAGAn44JSybpwGRkZ9w0BwGKwiVWJ7k8\/7fRy\/s7z6XfkcRvPDWOn\/\/ykE0q56UtNcLs8ktlWPxxfJUfIPf2r3liOPuVUbrzA2lvsk0XLyMi4bwgAljscsErWhcvIyLhvCAB2GJNdlawLl5GRcd8QACwPOGCVrAuXkZFx3xAA7DAmuypZFy4jI+O+IQBYHnDAKlkXLiMj474hANhhTHZVsi5cRkbGfUMAsDzggFWyLlxGRsZ9QwCww5jsqmRduIyMjPuGAGB5wAGrZF24jIyM+4YAYIcx2VXJunAZGRn3DQHA8oADVsm6cBkZGfcNAcAOY7Krkij0z8ibEoJq61afxwvGvwEgrCw9aUIAtrZdbhZtwDwSgqu2bjl+5l9qIevPpgImHWaKzhN4sMqOe4s2YB7JwFVbt5x\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6jz\/+OXf6xsP3l7u4l\/0YteVF4vn2ffdkTtE6+st+CGFtu7sasa3Vz9mavLyadsL5+77tr2ZP6CnRfIL+HIm4cmgIpaGGVg7wen8es4uf75WbYz09LLOe7YKAOZ\/y1kwLInIOsv6w+rbM6\/PjOasVniK7ZRBsLsoxv5wNsFx1hpzxOPvwegXdMAgM3KOw658PkJqz1CYL0vwEIhRI7vEz\/zL7noRaW1QhUD2GzWX86\/+fpz0003lRNOeFT59Kf\/obywPon\/vd+TmtKiQgnZwiTEvl5\/rr5abublTcR1cjN\/7rnnljPPPJOHi2vmfhjfBpuAA3H8k2GNyvF9rW9JyfO\/z+efFdsEZP1l\/YV71oN9\/uHnJxe3O3ynOC305e2ByzANYHsELizd0Of4Qz4z\/36n7oVlaFEvFqkABQbbg3BhTVdbZP7D7e5hUH8vf\/nLyu\/8zn8vT3jCE8pf\/fVflbvUJ+LYDtDx\/+3ffqg88YlPLHeVL9R+7KMfKw\/H5\/IP0Pi4XGf95\/w\/3Oa\/Xydy\/c\/5f2jP\/231I\/Lx0Q+Xt+AaXntKhYueWLs3AjcQg9tUjZsEmMrxM\/9ZfytPiTHXcv7t9fpTfx\/+ySefXO5x96PKxz\/x8fKQhzzEsnmg159f\/i+\/XM551TntS7Z\/8zd\/U46Qz+fjaVCuf7n+5fqX619dnHhdssWqg0VsIAa3tWrcJMBUrj+HxvozfLSGT2E91+wzXqseb6Nq2fO\/R\/dm67+PO47BPuMcv2VgkhKcMw3JPvOPh46oPsmJ5AWfy3FW0JhQ9hn3RhMKfWhI9pn\/gzL\/J5706PYE\/Hdf+9ry4pe8ZOWE8glmvCJvtJ15uRnfs\/N\/8y23lEc\/+sT2x6Pe\/OY3l+c973mTAfbf+H0wMeMY7DOevDzrRHW2z\/o\/KOs\/1z+8VbbCzfrP+S81wHXBax7jXjMTCmvogV7\/2o08v+vSF1JfaD+g9orsZbUjwKE6G5l+mG6qsBbJ9OZJIvTUP8dvyZJ8Zf5bAbUia7u2zFQuVpvGmnaxECmrDUWX9dcTEs3hNv8++MEPysdZnlSOf\/CDy1WfuUrqSf5ntVHrqW4Hdv5d+M53lh+Rn6M88cQTymWXXXbAx7+jjz\/H51XtwNdf5j\/zX6su77\/umPX\/G51\/+kS+3Qu1nd4KDceiJ3jzPjQJzrLdIlyJ\/udeDdZmmFvLLhZM6DM4C+nihtAPuv9txt20X\/Y4lP9u2i\/Clcjjr0nwU1GTnOe\/ZmGPtlBTwVk2X4QPs\/r7qWc9q\/zPP\/uz9tdbf+mXfkkn7x08\/24rt5aHPuRh5eqrrykf\/MAHyuMf\/\/is\/5z\/y8m7woQ5HZxlg0X4MJv\/efxaEza98vwf8vdf2\/RX5Hmyt7PaCSr5TnO0itRfCaJbCd8uF0r\/Mg16WXzFwnrUplVXNym5lSGUXglq49Y2x8\/8Z\/1h6e7zRSYVV4VOF8SqV3Hd7jzz7\/Of\/3x50HHfIX+t9cjyj9ddV+59n\/sO7xfvuON\/zWteU84868zy7Gc9u7ztbW+TvN\/58t\/KqR1XrcXDr\/7y+GsGMMfy\/B9u62\/W\/\/6pf3kif5vMKnoSimu9ZrztMe2I2isY2lenbjaORts+CFVW9yu0C3aDQvvq1C3H1zz07LYchUT1sJgV2gW7QaF9deqW+dc8ZP5bMbQaCYXS0yNmhXbBbhC3f\/Mf\/XH5uTPOKM997s+Wt7zlLdb7gRq\/HUx9vZP6v\/7fvlC+9Vv\/fTnqHvco11\/\/RfldeRXx669N93YL7atTt8n4\/R8lNE770J74PYWhfY6vacv89\/LR6mj7UCheXSu0C3aDQvvq1C3zr3nI608rhlYjoVB6esSs0C7YDQrtq1O3fVx\/\/mXXMJqOZXt8OVA0s+8umW4CvNvZu29q4EIiO8zx5cTLmc\/8Z\/1JGdgasJwpC8anVc6\/+vTrRfJ78W94wxvKH\/7hH5af\/\/mf93x5opwDOoDrzwmPPKH9is6VV165\/CnKnP85\/3P+5\/qHdWkPrC9ruf4v\/\/WDEuiJIrLDA7j+LwcXZg\/Gn3y0hl98xfPbhk3HbU+dVpv31mJW3xi0F7\/aweZ3SbV7bNOXn+O385r5z\/pbuzG4k86\/xzzmMeXSyy4tl3\/s8vLIRzzyoDv\/Z8i\/FvzxH\/1Reetb31p+5md\/Rlax6QKW699qZiSQ6z+ufivlk9e\/vP7JupLX\/4Nu\/beJu5fXX\/toTeugz2\/rTECkfAFo15cYpGYaQBjWBIEghyC0keoeSFiIzWoAYdgh3F2KEoQ2Ut0DCQuxWQ0gDDuEu0tRgtBGqnsgYSE2qwGEYYdwdylKENpIdQ8kLMRmNYAw7BDuLkUJQhup7oGEhdisBhCGHcLdpShBaCPVPZCwEJvVAMKwQ7i7FCUIbaS6BxIWYrMaQBh2CHeXogShjVT3QMJCbFYDCMMO4e5SlCC0keoeSFiIzWoAYdhbbvlaOeaYe8kffrprueFLN5S7yu+1hxUOQusnRF0LHSzpFWoAYViTBYIcgW944xvaX5l98YtfUn73d1+b668kzd\/K9FwhZbCWWAANIAyLaEwqRQlCG6nugYSF2KwGEIYdwt2lKEFoI9U9kLAQm9UAwrBDuLsUJQhtpLoHEhZisxpAGHYId5eiBKGNVPdAwkJsVgMIww7h7lKUILSR6h5IWIjNagBh2CHcXYoShDZS3QMJC7FZDSAMO4S7S1GC0EaqeyBhITarAYRhh3B3KUoQ2kh1DyQsxGY1gDDsEO4uRQlCG6nugYSF2KwGEIYdwt2lKEFoI9U9kLAi9ifyIGHR08SqZF24jIyM+4YAYCfjglLJunAZGRn3DQHAYrCJVcm6cBkZGfcNAcBOxgWlknXhMjIy7hsCgMVgE6uSdeEyMjLuGwKAnYwLSiXrwmVkZNw3BACLwSZWJevCZWRk3DcEADsZF5RK1oXLyMi4bwgAFoNNrErWhcvIyLhvCAB2Mi4olawLlxFlPvOZz7Q\/\/PSoR51QPip\/RbVupgWAxWAT+\/Vbby0X73pP+YdPf7oce79jy2Mf99hy3HHHmXLZxci4b6iDD7z\/A+VJP\/Ck8vSnP728U36Scrap1FouJMvIyLhvCAB20asTKlkXLiMj474hAFgfboFUsi5cRkbGfUMAsItRnVDJunAZGRn3DQHA+nALpJJ14TIyMu4bAoBdjOqEStaFy8jIuG8IANaHWyCVrAuXkZFx3xAA7GJUJ1SyLlxGRsZ9QwCwPtwCqWRduIyMjPuGAGAXozqhknXhMjIy7hsCgPXhFkgl68JlZGTcNwQAuxjVCZWsC5eRkXHfEACsD7dAKolC\/4y8ySGotm71eYhgfAYGYWWXT0v80lgbLzZr3oB5pANXbd1y\/My\/1ELWn00FTDrMFJ0n8GCVHfcWbcA8koGrtm53nvn3d3\/3yfKIR\/zH8gNyo\/xX7\/trOTQcqx6p7sHNj\/+6a68rT33aU8vRR91DbuAfVy5610Xlms9eXX7jla8sv\/Zr\/1W6QHvu07FFGzDPBJdf\/rHyqEedWE4++cnlve99r\/B3nvzXg7QjXjl+V1RB3fL4W05y\/bNSyPVPZ4bNpebCg1XNuLdoA+aRDFy1dcv5dyjMv23yozXyHQCcPD11s\/1cARY2tvQ\/NDN80ULkWJd0ZZ+3597mCrCw3ELGqIfW\/tBLjh++6CHpyvzrEpX1J3PmMJn\/H\/voR+UvqJ5Utm\/fXi6+5GK9H2hLx3z94NUEih07dpSLLrqo\/PM\/\/0s5+uijyq233la+7duObf4nr7ii\/Ifv+R5rtpX158pPXSl9fK\/8jvz3l\/qHq7BhfPhqwcIO0Vz\/cv3P659Mirz+5\/Xff3y6XvPvbPc\/7Yl8uAyYYyBeHSYelO3z+fIGDtakEBgRQQibYyCKJx6UGBfWpBAYEUEIm2MgiicelBgX1qQQGBFBCJtjIIonHpQYF9akEBgRQQibYyCKJx6UGBfWpBAYEUEIm2MgiicelBgX1qQQGBFBCJtjIIonHpQYF9akEBgRQQibYyCKJx6UGBfWpBAYEUEIm2MgiicelBgX1qQQGBFBCJtjIIonHpQYF9akXXBlvdH+3u8tT3jCE8oH5I8uYUP75ptjALJmH\/nIR5ZPfOIT5U1velOpX0yt2+k\/8cxy\/nnvKG9845vK859\/xje0\/n30so+Wk056dNl+irzZuPiS1v\/udnilOG5YaweBERGEsDkGonjiQYlxYU0KgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOJBiXFhTQqBERGEsDkGonjiQYlxYU0KgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOJBiXFhTQqBERGEsDkGonjiQYlxYU0KgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOJBiXFhTQqBERGEsDkGonjiQYlxYU0KgRERhLA5BqJ44kGJcWFNCoEREYSwOQaieOI1pTw1qtY2bR47CdziVVrTFeB9NSQ7ezc0aRHG6vHA5fjyBLX+c9eebpq9qm5Idpn\/\/jR+ksJQaz0euKy\/Q7b+\/u+115bjHvSg8t0P\/+7yqSs\/NTn7fY7oTLE4n\/+L3vWu8ib56cpzzj2nHP\/g45um3dz\/3SfKlZ+8ojycnshrB9q64oZkt2n+vWfXrvLUpzyl\/NiP\/3jZecEFrQsef\/kuQUdZ3+\/d+GGs3mngsv4P2fpv51F2m+ovnOs8\/y0DISdZ\/1n\/B+H91\/AZeS1Zql6BxA0earopoqx14buNQZfxWNbEQNOxl+PrnGo54cRQRhVuDJKadAYNZP4lA5yNrL9Dq\/7qP7Df99\/dp9z4pS+XL95wfbnn0fek2q+Qzq5BA00L79Zbv15uuulm+ZnIt5RflF+Y+eGnPa385Tv\/cugPLlrBX7O3l3POObe84hWvKL\/6K79afvO3flOEsS17WX+HVv2tnXXn6ewaNNBk7OX5z\/Nf7ylbTXBheEF1tDFIatIZNJD1JxngbBxc82\/6RF7PLb9oOtsdanSzxluN6uZPGjPF2HsC0uhmDbQ4Aa5uyF0TMsXYBAY0ullj4l4Arm7IXRMyxdgEBjS6WWPiHF9S0f9+cUtKy9skeUwx9kwCaXSzBtqsvzFbzZ8kjynGnkkgjW7WQOv5\/8FTf1A+H39J+ev3v7886QlPrK3T3NwAAAQqSURBVEURNu6PMYtu+spXyoOOe1D7XHzlv0eewn9MvqR65N2OZFnA46tt\/mSAn\/jJnyznnfd2eRq\/s\/ynH\/ux8eVRn2OPFJrAUb02Pr8kxssuxx6XCmZGdfMnAzDFmPtSrNHNGm81qps\/acwUY+8JSKObNdB6\/aHgWrtJY6YYe09AGt2sgTbHH7PV\/EnymGLsmQTS6GYNtJn\/MVvNnySPKcaeSSCNbtZAe+fPvz2RX08IvihCCoMGPGMNrfE1iBisNo2ecojoFzVIYdAANxC8xlcZYrDaNHrKIZLj1y+KUIYMGuCECV7jqwwxWG0aPeUQyfxn\/vdV\/b3iFWeXc889t7zmNa8pL3vZy63Q9rb+brzxxnLL124uf\/qnf1p+5Vd+rRx\/\/IPLX\/zFX5QHPvCB0ud6bx6LGnjHH398+ew115TrPve58oAHPKD1lfWf9b+v6n939WcTwkBe\/3P+5fw72Oef3MjfJtcQeiyFK8rGi5HOcpM2FxO+rwAhKE7\/YB7+OcLWiXEca2fApQOKihxfF5zMf8tAKA5xsv7aND\/c5995551ffkK+nPq0p\/1QufDCC6VUQqGQO\/B9Wv393\/99ueWWW+RnLB9hLX9SnqK\/\/e1vL7\/9qt8urzj7FaoMzfes\/q666qrysIc9rNz\/\/vcv\/\/iPn5N+aF3u47MJQ8iryflfbzj6FpKzZ\/lvLa2dAfS4sFGR+c\/6y\/rL+XfHrD\/2RJ6uYH09w7QcFihezuJKZpGRhq+W99ZEAFTK+aiOWN1wbGLhkYavlvfWRABUyvmojljdcGxi4ZGGr5b31kQAVMr5qI5Y3XBsYuGRhq+W99ZEAFTK+aiOWN1wbGLhkYavlvfWRABUyvmojljdcGxi4ZGGr5b31kQAVMr5qI5Y3XBsYuGRhq+W99ZEAFTK+aiOWN1wbGLhkYavlvfWRABUyvmojljdcGxi4ZGGr5b31kQAVMr5qI5Y3XBsYuGRhl\/tzV\/9itwoP7B84fovlqs+\/Q\/tD0RpQ6jgLde\/T8sfgKpflL3XPe9VPvvZz5b73ue+7V773HNfXc4++6z2JdWL3v3u4Uj8yHQE3ttLFnB7eelLX1Ze+9rXlrPOOqu86pxXyU1pvSzu2+PHk6V4tPV1RMZHdVRVYYtNLDTS8NXy3poIgEo5H9URqxuOTSw80vDV8t6aCIBKOR\/VEasbjk0sPNLw1fLemgiASjkf1RGrG45NLDzS8NXy3poIgEo5H9URqxuOTSw80vDV8t6aCIBKOR\/VEasbjk0sPNLw1fLemgiASjkf1RGrG45NLDzS8NXy3poIgEo5H9URqxuOTSw80vDV8t6aCIBKOR\/VEasbjk0sPNLw1fLemgiASjkf1RGrG45NLDzS8NXy3poIgEo5H9URqxuOTSw80vDV8t6aCIBKOR\/VEasbpib\/HwAA\/\/+vKCIVAABAAElEQVTsvQmgHkWVNlw3YQ17AMFlZFU\/URRZ\/AAHBEEFcSQBRPY1QDZXkgDO6PwfjisgqBBIcBQICahsLgiyuAGiggiKy4w6MopsWVBIWLL1f+pUPafOqeq+ufcmgeTeeiF9nvOcp+p0na7ut9++\/fbb0\/DLuZ4e5xr6r4f+41dDSwMDwUsV8638\/7EDaSOdNNRJ7Cdw5bKh9jV\/rX+df3X\/eyGOP5MmT3bnnXuu+9CHPuTOP\/9819fjz\/XX3+AOOeQQ98p\/2sr96sEH3EYbbkQHs8Yd\/t7D3TeuucadeMKJ7itf\/Yo6wPljY9+Of88884x72ctf6uY\/Pd\/96U9\/cltvtbUcN\/nwGg6yYRmImMfnIBgOoNImBH2sb\/nr8deXse5\/L8T+FyeumL7uf35y81TnBZr7OU64zv9YB9TFW1+buv8PhfPPHn8erze9YN45xAuTQioSD3mFxuvV4VDiAuJkU75OoXEh0UTNz285uiRSu1p\/eTuW+gio849Loeoh8yYDhUQTq\/f+99BD\/+O22\/5VboMNNnB\/+ctf3IYbbpgNnlw9XI427onZc9y222zjPv3pT7mJ7\/+A6yHN3T\/\/qXvnO97h\/In492\/\/vtt7772oaTwdkj4EdM6\/i6Ze5N4\/YaL7l\/e8x33zm99szZ\/O0lfv+nPh5L2kLH0sdxpuQdTx1+M\/7WNqt0qzqL7\/DeT4k+oXUVFbTdT9b1Xb\/9SJfNhQdnPFY6km84Mqx1JbH04X4FNDINg4XZRJfaC9aAVArgiGwfdL\/0J7\/W6IFrBBqZepD7QXrQDoFcEw+H7pX2hf86c6AcGGSulliOi4YAHQK4Jh8P3Sv2r9Qx3q\/EvzBAj2kEMOddffcJ0bc\/Ip7tJLp1PBQgRxX0HBApz70Q9\/6D728Y+5\/6UPAOuPWM\/99ne\/c6985T+5c889zx323vdy4fs7\/x555BG34+tf5+b9\/e\/u+9\/\/gdt3n324H0krgGlaKIJh8P3Sv\/qbP7RKfaB9YCgqICgNwbHU1ivQXuvQBSx6Sjb1gfaiFQC1IhgG3y\/9C+1r\/lQnINhQKb0MER0XLAB6RTAMvl\/6V61\/qEOdf2meAMGiQsmGiI4LFgC1IhgG3y\/9ayjOPz6Rl7IICAWRvzmTKyEBUQOT860+yGitUUlqfq4A\/uZIDiqXAAqPWpFNM1g10HH0YgsPtui75qeahqJ21gibQQS63giS5ThE0VrTss1IUPNzEVG5Yo6ixCKIRKsPsnF\/\/evDdPK8o3vq6X+4G797kzvwgAP6Vf8FCxa4Bx54wL30pS91W221lRvWM2zA+9+7DjrI3UTrcPxxx7nLLr8MI6L1ofWt25\/rgS23orY\/b6zYaWfftf51\/tX9r+5\/VIHOYwSO1iKIRKsPMlprVBL0QYI+zr90RV4dtLBu3mapdUgwNEktIQGsScLIK6Lml40mRSOACsHqGHCKJYQYLEeKsCJq\/Wv940EDc8ZbzBBYHQNOsYQQg+VIEVbEizD\/vkr3s5900snu5S9\/ufv1r37lNhk5EqsrFmsIKwEFUiwhFWbIkSLcuP\/8z6+6MWNOdq+gdXjwN79xG23k77tPLzSBTZGEUiyhFA2II0VYES9C\/dPsonWs+evxZ4gdf+r8r8cf2unjAZpqsTzzv\/UeeVVfzpL7IbU\/+tI\/fRm4jRFxAtSsoRvc5Is1KRJQ3m3ui74MlIyIEyBRzV\/rX+ef3XdlB8l3otzvFK4++\/\/tP7zd7f2Wvd3oQ0a7G2+80e325t3crbfcGk6k8\/Hm\/goa\/43fvtEdetihbuHChe7m791M99q\/M\/Sc58v9FZS\/zv+hO\/\/r+199\/6v7\/+DZ\/9MVef\/mQG8Y5kvOHVdJ2t5HwntN9o4Dl61f+BQ0fSKPsO6v5lcfjWr9Wz+l6vmCz5FhLmUzCi5bv6jzb6jvf88+97ybfPpkd9HUC93pkye5j555pttvv\/3cA\/f\/yu26667ulttudRvjqvhK3P++\/Z1vu0Pfe5hb9PxC99nPfsZNmXJGPf7SLlqP\/\/X4L6dXK3H\/8+8beHvQ7yd1\/tX5tzrOv3AiX8zofJIrgYKyAwwUoC9Y1Y+llKegkg8Moi9Y1YullKegkg8Moi9Y1YullKegkg8Moi9Y1YullKegkg8Moi9Y1YullKegkg8Moi9Y1YullKegkg8Moi9Y1YullKegkg8Moi9Y1YullKegkg8Moi9Y1YullKegkvcJPvjgb9yRRx7hHnzwQbfB+uu7Cy+8yB13\/HFu7px5bv937Ofu\/+X9fDJ\/DT1K8pV037sc0PVb\/nLkx0rOmDHDnTJmjHuersR\/9rOfdVMmT1HvnkFl0yhPQfQ3YIu+YFVHllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegko+MIi+YFUvllKegkpOF8dbHz\/Zom6huCPmVVCgAHkbTEz+QUGvksdaGWMtFEeYV0GBAqS3xLRmiIm80cpIt1AcYV4FBQqQ3hLTmiEm8kYrI91CcYR5FRQoQHpLTGuGmMgbrYx0C8UR5lVQoADpLTGtGWIib7Qy0i0UR5hXQYECpLfEtGaIibzRyki3UBxhXgUFCpDeEtOaISbyRisj3UJxhHkVFChAektMa4aYyButjHQLxRHmVVCgAOktMa0ZYiJvtDLSLRRHmFdBgQK4twu\/9CU3ecoU9\/xzz7k3v\/nNbuZVs9z2224XO3du7ty5bv\/996cr8\/e79TdY353\/+fPdyXSyLa\/UnVAMmFdBgQJkNI8\/8YQbP26cu+666\/jE\/d8\/\/u\/uySefdJ\/5zGfcuuuuq\/pNbYVsofqbX3ehseQQ0BJtoWp+qgDXRRVHoADZ\/olpneFS\/daobqyUNT8VA3\/i93WROgkQKjFKpmspWCsj2UJxhHkVFCig5qdC+YsiqSIWxworo5WRbqE4wrwKChQgeRMz+PLTifxSOpWn213i5Sc9WFQWHKzngWGh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\" alt=\"Screen Shot 2023-08-29 at 10.39.21.png\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">8<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">9<\/span>\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">1<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"o\">~<\/span><span class=\"mi\">6<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">7<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">)]<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">u<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span> <span class=\"o\">=<\/span> <span class=\"n\">warning_propagation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>converged in 3 iterations\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">u<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[{0: 1},\n {1: 1},\n {0: 0, 1: 0, 2: 1},\n {2: 0, 3: 1},\n {2: 0, 4: 0},\n {3: 1},\n {3: 0, 6: 0},\n {4: 0, 7: 0},\n {4: 0, 5: 0}]<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">c<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[0, 0, 0, 0, 0, 0, 0, 0]<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6b63\u3057\u3044\u5024\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>WP \u3092\u7528\u3044\u308b\u3053\u3068\u3067\uff0e\u5404\u5909\u6570\u304c\u3068\u308b\u3079\u304d\u5024\u306b\u95a2\u3059\u308b\u60c5\u5831\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\uff0e\u3053\u306e\u60c5\u5831\u3092\u7528\u3044\u3066\u5b9f\u969b\u306bSAT\u3092\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092 warning inspired decimation \u3068\u547c\u3073\u307e\u3059\uff0e<\/p>\n<p>WID\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\uff0e<\/p>\n<ol>\n<li>WP \u3092\u5b9f\u884c\u3059\u308b\uff0e<\/li>\n<li>WP \u3067\u5f97\u3089\u308c\u305f\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u5143\u306b\uff0c\u3044\u304f\u3064\u304b\u306e\u5909\u6570\u3092\u6c7a\u5b9a\u3059\u308b\n<ul>\n<li>\u77db\u76fe\u304c\u898b\u3064\u304b\u308b \u2192 UNSAT \u3068\u5831\u544a\u3057\u3066\u7d42\u4e86\u3059\u308b\uff0e<\/li>\n<li>0\u3067\u306f\u306a\u3044\u30e1\u30c3\u30bb\u30fc\u30b8\u304c\u3042\u308b \u2192 \u305d\u306e\u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u53d7\u3051\u53d6\u3063\u3066\u3044\u308b\u5909\u6570\u3092\uff0c\u30e1\u30c3\u30bb\u30fc\u30b8\u306b\u5bfe\u5fdc\u3059\u308b\u5024\u306b\u6c7a\u5b9a<\/li>\n<li>\u30e1\u30c3\u30bb\u30fc\u30b8\u304c\u5168\u30660 \u2192 \u30e9\u30f3\u30c0\u30e0\u306b1\u3064\u5909\u6570\u3092\u9078\u3093\u3067\u30e9\u30f3\u30c0\u30e0\u306a\u5024\u306b\u6c7a\u5b9a<\/li>\n<\/ul>\n<\/li>\n<li>\u3059\u3079\u3066\u306e\u5909\u6570\u304c\u6c7a\u5b9a\u3055\u308c\u305f\u3089\u7d42\u4e86\uff0e\u305d\u3046\u3067\u306a\u3051\u308c\u3070\uff0c\u6c7a\u5b9a\u3057\u305f\u5909\u6570\u3092\u56e0\u5b50\u30b0\u30e9\u30d5\u304b\u3089\u53d6\u308a\u9664\u304d\uff0c1\u306b\u623b\u308b<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">updated_vars \u306e\u5909\u6570\u306e\u5024\u304c\u78ba\u5b9a\u3055\u308c\u305f\u6642\u306b\u56e0\u5b50\u30b0\u30e9\u30d5\u3092\u66f4\u65b0\u3059\u308b<\/span>\n<span class=\"sd\">\u7bc0\u306e\u5909\u6570\u304c\u6b8b\u308a\u4e00\u3064\u306b\u306a\u3063\u305f\u3089\uff0c\u305d\u306e\u5909\u6570\u3092\u78ba\u5b9a\u3055\u305b\u308b (unit clause propagation)<\/span>\n<span class=\"sd\">\u77db\u76fe\u304c\u898b\u3064\u304b\u3063\u305f\u3089 False \u3092\u8fd4\u3059\uff0e\u77db\u76fe\u304c\u306a\u3051\u308c\u3070 True \u3092\u8fd4\u3059\uff0e<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">reduce_factor_graph<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">J<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">remaining_vars<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">remaining_factors<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">updated_vars<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">value<\/span><span class=\"p\">,<\/span>\n<span class=\"p\">):<\/span>\n    <span class=\"n\">satisfied_clauses<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">set<\/span><span class=\"p\">()<\/span>\n    <span class=\"k\">while<\/span> <span class=\"n\">updated_vars<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"n\">updated_vars<\/span><span class=\"o\">.<\/span><span class=\"n\">pop<\/span><span class=\"p\">()<\/span>\n\n        <span class=\"c1\"># \u5909\u6570 i \u3092\u53d6\u308a\u9664\u304f<\/span>\n        <span class=\"n\">remaining_vars<\/span><span class=\"o\">.<\/span><span class=\"n\">remove<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n            <span class=\"k\">if<\/span> <span class=\"mi\">2<\/span> <span class=\"o\">*<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">==<\/span> <span class=\"o\">-<\/span><span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n                <span class=\"c1\"># \u5909\u6570 i \u304c\u7bc0 a \u3092\u5145\u8db3\u3059\u308b<\/span>\n                <span class=\"n\">satisfied_clauses<\/span><span class=\"o\">.<\/span><span class=\"n\">add<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">)<\/span>\n            <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                <span class=\"c1\"># \u7bc0 a \u304b\u3089\u5909\u6570 i \u3092\u53d6\u308a\u9664\u304f<\/span>\n                <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">remove<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/span>\n                <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                    <span class=\"c1\"># \u77db\u76fe<\/span>\n                    <span class=\"k\">return<\/span> <span class=\"kc\">False<\/span>\n                <span class=\"k\">if<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">])<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n                    <span class=\"c1\"># \u5909\u6570\u304c\u4e00\u3064\u3057\u304b\u306a\u3044\u306e\u3067\u5024\u304c\u78ba\u5b9a<\/span>\n                    <span class=\"n\">j<\/span> <span class=\"o\">=<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\n                    <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"k\">if<\/span> <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">0<\/span>\n                    <span class=\"k\">if<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n                        <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x<\/span>\n                        <span class=\"n\">updated_vars<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">j<\/span><span class=\"p\">)<\/span>\n                    <span class=\"k\">elif<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">x<\/span><span class=\"p\">:<\/span>\n                        <span class=\"c1\"># \u77db\u76fe \u2192 UNSAT<\/span>\n                        <span class=\"k\">return<\/span> <span class=\"kc\">False<\/span>\n                    <span class=\"n\">satisfied_clauses<\/span><span class=\"o\">.<\/span><span class=\"n\">add<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">satisfied_clauses<\/span><span class=\"p\">:<\/span>\n        <span class=\"c1\"># \u56e0\u5b50 a \u3092\u53d6\u308a\u9664\u304f<\/span>\n        <span class=\"n\">remaining_factors<\/span><span class=\"o\">.<\/span><span class=\"n\">remove<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">)<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n            <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">remove<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">)<\/span>\n        <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n    <span class=\"k\">return<\/span> <span class=\"kc\">True<\/span>\n\n\n<span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">Warning Inspired Decimation \u306b\u3088\u308b\u30bd\u30eb\u30d0<\/span>\n<span class=\"sd\">\u89e3\u304c\u898b\u3064\u304b\u3063\u305f\u3089\u5909\u6570\u306e\u5272\u308a\u5f53\u3066\uff0c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u3089 None \u3092\u8fd4\u3059<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">warning_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">100<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span> <span class=\"n\">J<\/span> <span class=\"o\">=<\/span> <span class=\"n\">build_factor_graph<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span>\n\n    <span class=\"n\">remaining_vars<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">set<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">))<\/span>  <span class=\"c1\"># \u307e\u3060\u78ba\u5b9a\u3057\u3066\u3044\u306a\u3044\u5909\u6570<\/span>\n    <span class=\"n\">remaining_factors<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">set<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">))<\/span>  <span class=\"c1\"># \u307e\u3060\u78ba\u5b9a\u3057\u3066\u3044\u306a\u3044\u7bc0<\/span>\n\n    <span class=\"c1\"># \u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316<\/span>\n    <span class=\"n\">u<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[{<\/span><span class=\"n\">i<\/span><span class=\"p\">:<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]}<\/span> <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)]<\/span>\n    <span class=\"n\">h<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span>\n\n    <span class=\"k\">while<\/span> <span class=\"n\">remaining_vars<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">factors<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"n\">remaining_factors<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># WP \u5b9f\u884c<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">t<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_iter<\/span><span class=\"p\">):<\/span>\n            <span class=\"n\">converged<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\n\n            <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">shuffle<\/span><span class=\"p\">(<\/span><span class=\"n\">factors<\/span><span class=\"p\">)<\/span>\n\n            <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factors<\/span><span class=\"p\">:<\/span>\n                <span class=\"c1\"># j \u304b\u3089 a<\/span>\n                <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                    <span class=\"n\">res<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n                    <span class=\"k\">for<\/span> <span class=\"n\">b<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]:<\/span>\n                        <span class=\"k\">if<\/span> <span class=\"n\">a<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">b<\/span><span class=\"p\">:<\/span>\n                            <span class=\"n\">res<\/span> <span class=\"o\">+=<\/span> <span class=\"o\">-<\/span><span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n                    <span class=\"n\">h<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">res<\/span>\n\n                <span class=\"c1\"># a \u304b\u3089 i<\/span>\n                <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                    <span class=\"n\">res<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n                    <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                        <span class=\"k\">if<\/span> <span class=\"n\">i<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">j<\/span><span class=\"p\">:<\/span>\n                            <span class=\"n\">res<\/span> <span class=\"o\">*=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">h<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>\n                    <span class=\"k\">if<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">res<\/span><span class=\"p\">:<\/span>\n                        <span class=\"n\">converged<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\n                    <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">res<\/span>\n\n            <span class=\"c1\"># \u53ce\u675f\u3057\u305f\u3089\u7d42\u4e86<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">converged<\/span><span class=\"p\">:<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">:<\/span>\n                    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"converged in <\/span><span class=\"si\">{<\/span><span class=\"n\">t<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"si\">}<\/span><span class=\"s2\"> iterations\"<\/span><span class=\"p\">)<\/span>\n                <span class=\"k\">break<\/span>\n        <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n            <span class=\"c1\"># \u53ce\u675f\u3057\u306a\u3044<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">:<\/span>\n                <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"did not converge in <\/span><span class=\"si\">{<\/span><span class=\"n\">n_iter<\/span><span class=\"si\">}<\/span><span class=\"s2\"> iterations\"<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># \u77db\u76fe\u3092\u78ba\u8a8d<\/span>\n        <span class=\"n\">updated_vars<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">remaining_vars<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">pos<\/span> <span class=\"o\">=<\/span> <span class=\"n\">neg<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n            <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">pos<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n                <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">neg<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">u<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">pos<\/span> <span class=\"ow\">and<\/span> <span class=\"n\">neg<\/span><span class=\"p\">:<\/span>\n                <span class=\"c1\"># \u77db\u76fe\u304c\u898b\u3064\u304b\u308b \u2192 UNSAT<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">:<\/span>\n                    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"a contradiction found\"<\/span><span class=\"p\">)<\/span>\n                <span class=\"k\">return<\/span> <span class=\"kc\">None<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">pos<\/span> <span class=\"o\">==<\/span> <span class=\"n\">neg<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                <span class=\"k\">continue<\/span>\n            <span class=\"c1\"># 0\u3067\u306a\u3044 local field \u2192 \u5024\u3092\u78ba\u5b9a<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">pos<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n            <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n            <span class=\"n\">updated_vars<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">updated_vars<\/span><span class=\"p\">:<\/span>\n            <span class=\"c1\"># local field \u304c\u3059\u3079\u30660 \u2192 \u5909\u6570\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u3093\u3067\u78ba\u5b9a<\/span>\n            <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">choice<\/span><span class=\"p\">(<\/span><span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"n\">remaining_vars<\/span><span class=\"p\">))<\/span>\n            <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\n            <span class=\"n\">updated_vars<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"n\">success<\/span> <span class=\"o\">=<\/span> <span class=\"n\">reduce_factor_graph<\/span><span class=\"p\">(<\/span>\n            <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">J<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">remaining_vars<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">remaining_factors<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">updated_vars<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">value<\/span><span class=\"p\">,<\/span>\n        <span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">success<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">return<\/span> <span class=\"kc\">None<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">value<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u518d\u3073\u6587\u732e [1] \u56f33\u306e\u4f8b\u3067\u8a66\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">8<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">9<\/span>\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">1<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"o\">~<\/span><span class=\"mi\">6<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">7<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">)]<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">warning_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\n<span class=\"k\">if<\/span> <span class=\"n\">value<\/span><span class=\"p\">:<\/span>\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span><span class=\"p\">)<\/span>\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">)<\/span>\n<span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>converged in 3 iterations\nconverged in 1 iterations\nconverged in 1 iterations\nconverged in 1 iterations\nconverged in 1 iterations\nSAT\n[1, 0, 1, 1, 1, 1, 0, 1]\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u78ba\u304b\u306b\u89e3\u304c\u898b\u3064\u3051\u3089\u308c\u307e\u3057\u305f\uff0e<\/p>\n<p>\u6b21\u306b\uff0c3-SAT \u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u52d5\u4f5c\u78ba\u8a8d\u3092\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">alpha<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">warning_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">value<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>converged in 7 iterations\nconverged in 1 iterations\nconverged in 1 iterations\n...\nconverged in 1 iterations\nconverged in 1 iterations\nUNSAT\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6700\u9069\u89e3\u306f\u898b\u3064\u304b\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u304c\uff0c\u6b63\u3057\u304f\u52d5\u4f5c\u3057\u3066\u3044\u305d\u3046\u3067\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$K=3,N=100$ \u3067\uff0c\u69d8\u3005\u306a $\\alpha$ \u306b\u5bfe\u3057\u3066 $50$ \u500b\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u4f5c\u6210\u3057\uff0c WID \u3067\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u308b\u5272\u5408\u3092\u305d\u308c\u305e\u308c\u8a08\u7b97\u3057\u307e\u3059\uff0e\u307e\u305f\uff0c\u6027\u80fd\u3092\u6bd4\u8f03\u3059\u308b\u305f\u3081\u306bHC, SA\u3082\u5b9f\u884c\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">n_shots<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">50<\/span>\n<span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">5e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span>\n<span class=\"n\">alphas<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">20<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ratio_wid<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"n\">ratio_hc<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"n\">ratio_sa<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"k\">for<\/span> <span class=\"n\">alpha<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">tqdm<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">cnt_success_wid<\/span> <span class=\"o\">=<\/span> <span class=\"n\">cnt_success_hc<\/span> <span class=\"o\">=<\/span> <span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_shots<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">warning_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">value<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">cnt_success_wid<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">hill_climbing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">4<\/span><span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">cnt_success_hc<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simulated_annealing<\/span><span class=\"p\">(<\/span>\n            <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">4<\/span>\n        <span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n    <span class=\"n\">ratio_wid<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">cnt_success_wid<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">ratio_hc<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">cnt_success_hc<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">ratio_sa<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">ratio_wid<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"WID\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">ratio_hc<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"HC\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">ratio_sa<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"SA\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"alpha\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"success ratio\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 20\/20 [02:32&lt;00:00,  7.63s\/it]\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Text(0, 0.5, 'success ratio')<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>WID\u306f\uff0cHC\u3088\u308a\u306f\u9ad8\u6027\u80fd\u3067\u3059\u304c\uff0cSA\u306b\u306f\u52a3\u308b\u3068\u3044\u3046\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"Survey_Inspired_Decimation\"><\/span>Survey Inspired Decimation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>SA\u306e\u7bc0\u3067\u3082\u8aac\u660e\u3057\u305f\u901a\u308a\uff0c$K$-SAT \u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u591a\u304f\u306e\u6975\u5c0f\u5024\u3092\u6301\u3064\u8907\u96d1\u306a\u69cb\u9020\u3092\u6301\u3063\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u4f3c\u305f\u4e8b\u4f8b\u3068\u3057\u3066\uff0c\u7d71\u8a08\u7269\u7406\u5b66\u306b\u304a\u3044\u3066\u3082\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u3068\u3044\u3046\u975e\u5e38\u306b\u8907\u96d1\u306a\u30a8\u30cd\u30eb\u30ae\u30fc\u69cb\u9020\u3092\u6301\u3064\u7cfb\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff0e\u305d\u3053\u3067\uff0c\u30b9\u30d4\u30f3\u30b0\u30e9\u30b9\u306e\u89e3\u6790\u3067\u767a\u9054\u3057\u305f cavity \u6cd5\u3068\u547c\u3070\u308c\u308b\u624b\u6cd5\u3092\u5fdc\u7528\u3059\u308b\u3053\u3068\u3067\uff0c WP \u3088\u308a\u3082\u3055\u3089\u306b\u8a73\u7d30\u306a\u60c5\u5831\u3092\u5f97\u308b\u3053\u3068\u306e\u3067\u304d\u308b\u30b5\u30fc\u30d9\u30a4\u4f1d\u642c\u6cd5 (survey propagation, SP) \u3068\u3044\u3046\u624b\u6cd5\u304c\u751f\u307e\u308c\u307e\u3057\u305f\uff0e<\/p>\n<p>$K$-SAT\u306e\u89e3\u7a7a\u9593\u306f\uff0chard-SAT\u9818\u57df\u3067\u306f\u8907\u6570\u306e\u30af\u30e9\u30b9\u30bf\u306b\u5206\u88c2\u3057\u307e\u3059\uff0e2\u3064\u306e\u89e3\u304c\uff0c\u5145\u8db3\u6027\u3092\u4fdd\u3061\u306a\u304c\u3089\u5909\u6570\u306e\u53cd\u8ee2\u3092\u7e70\u308a\u8fd4\u3057\u3066\u4e92\u3044\u306b\u5230\u9054\u3067\u304d\u308b\u3068\u304d\uff0c\u305d\u308c\u3089\u306e\u89e3\u306f\u540c\u3058\u30af\u30e9\u30b9\u30bf\u306b\u5c5e\u3059\u308b\u3068\u3044\u3044\u307e\u3059\uff0e\u5927\u96d1\u628a\u306b\u8a00\u3048\u3070\uff0c\u540c\u3058\u30af\u30e9\u30b9\u30bf\u306b\u5c5e\u3059\u308b\u89e3\u306f\u4e92\u3044\u306b\u4f3c\u3066\u3044\u308b\u3068\u8a00\u3048\u307e\u3059\uff0e<\/p>\n<p>\u305d\u3057\u3066\uff0c\u305d\u308c\u305e\u308c\u306e\u30af\u30e9\u30b9\u30bf\u306e\u4e2d\u3067\u306f\uff0cWP\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u308b\u5024\u304c\u7570\u306a\u308a\u307e\u3059\uff0e\u305d\u3053\u3067\uff0c\u300cWP\u30e1\u30c3\u30bb\u30fc\u30b8\u304c\u7279\u5b9a\u306e\u5024\u3092\u53d6\u308b\u30af\u30e9\u30b9\u30bf\u306f\u3069\u308c\u304f\u3089\u3044\u3042\u308b\u304b\u300d\u3068\u3044\u3046\u5024 &#8220;survey&#8221; \u3092\u8003\u616e\u3059\u308b\u3053\u3068\u3067\uff0c\u89e3\u7a7a\u9593\u306e\u3088\u308a\u8a73\u7d30\u306a\u60c5\u5831\u3092\u5f97\u3089\u308c\u308b\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>SP \u3067\u306f\uff0c\u30e1\u30c3\u30bb\u30fc\u30b8\u306f $[0,1]$ \u306e\u5b9f\u6570\u5024\u3092\u53d6\u308a\u307e\u3059\uff0e<\/p>\n<ul>\n<li>$\\eta_{a \\to i}$ (survey): WP\u30e1\u30c3\u30bb\u30fc\u30b8 $u_{a\\to i}$ \u304c $1$ \u306b\u306a\u308b\u30af\u30e9\u30b9\u30bf\u306e\u5272\u5408<\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u3067\u30e1\u30c3\u30bb\u30fc\u30b8\u304c\u6e80\u305f\u3059\u65b9\u7a0b\u5f0f\u3092\u793a\u3057\u307e\u3059\uff0e\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\u6587\u732e [1] \u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\uff0e<\/p>\n<p>$$<br \/>\n\\eta_{a\\to i}=\\prod_{j\\in V(a)-i} \\left(\\frac{\\Pi^u_{j\\to a}}{\\Pi^u_{j\\to a}+\\Pi^s_{j\\to a}+\\Pi^0_{j\\to a}}\\right)<br \/>\n$$<\/p>\n<p>\u5404\u5909\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\uff0e<br \/>\n$$<br \/>\n\\Pi^u_{j\\to a}=\\left(1 &#8211; \\prod_{b\\in V_a^u(j)} (1-\\eta_{b\\to j}) \\right)\\prod_{b\\in V_a^s(i)}(1-\\eta_{b\\to j}) \\\\<br \/>\n\\Pi^s_{j\\to a}=\\left(1 &#8211; \\prod_{b\\in V_a^s(j)} (1-\\eta_{b\\to j}) \\right)\\prod_{b\\in V_a^u(i)}(1-\\eta_{b\\to j}) \\\\<br \/>\n\\Pi^0_{j\\to a}=\\prod_{b\\in V(j)-a}(1-\\eta_{b\\to j})<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\uff0c $V_a^s(j)$ \u306f\uff0c$J_j^a=J_j^b$ \u3092\u6e80\u305f\u3059\u7bc0 $b$ \u306e\u96c6\u5408 ($a$ \u3092\u9664\u304f)\uff0c$V_a^u(j)$ \u306f\uff0c $J_j^a\\neq J_j^b$ \u3092\u6e80\u305f\u3059\u7bc0 $b$ \u306e\u96c6\u5408\u3067\u3059\uff0e<\/p>\n<p>\u4e0a\u306e\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u3066 $\\eta$ \u3068 $\\Pi^u, \\Pi^s, \\Pi^0$ \u3092\u4ea4\u4e92\u306b\u89e3\u304f\u3053\u3068\u3067\uff0c\u5404\u30e1\u30c3\u30bb\u30fc\u30b8\u306e\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\uff0e<\/p>\n<p>survey \u306e\u5024\u304b\u3089\uff0c\u5404\u5909\u6570\u304c\u3068\u308b\u5024\u306e\u5206\u5e03\u304c\u8a08\u7b97\u3067\u304d\u307e\u3059\uff0e\u5909\u6570 $i$ \u304ctrue\/false\u306b\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u30af\u30e9\u30b9\u30bf\u306e\u5272\u5408\u3092\u305d\u308c\u305e\u308c $W_i^{(+)},W_i^{(-)}$ \u3068\u3059\u308b\u3068\uff0c\u3053\u308c\u3089\u306f\u6b21\u306e\u3088\u3046\u306b\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\uff0e<br \/>\n$$<br \/>\nW_i^{(+)}=\\frac{\\Pi_i^+}{\\Pi_i^++\\Pi_i^-+\\Pi_i^0} \\\\<br \/>\nW_i^{(-)}=\\frac{\\Pi_i^-}{\\Pi_i^++\\Pi_i^-+\\Pi_i^0}<br \/>\n$$<br \/>\n\u3053\u3053\u3067\uff0c<\/p>\n<p>$$<br \/>\n\\Pi_i^+=\\left(1 &#8211; \\prod_{a\\in V_+(i)} (1-\\eta_{a\\to i}) \\right)\\prod_{a\\in V_-(i)}(1-\\eta_{a\\to i}) \\\\<br \/>\n\\Pi_i^-=\\left(1 &#8211; \\prod_{a\\in V_-(i)} (1-\\eta_{a\\to i}) \\right)\\prod_{a\\in V_+(i)}(1-\\eta_{a\\to i}) \\\\<br \/>\n\\Pi_i^0=\\prod_{a\\in V(i)}(1-\\eta_{a\\to i}) \\\\<br \/>\n$$<\/p>\n<p>\u3053\u3053\u3067\uff0c $V(i),V_+(i),V_-(i)$\u306f\u305d\u308c\u305e\u308c\uff0c\u5909\u6570$i$\u304c\u73fe\u308c\u308b\u7bc0\u306e\u96c6\u5408\uff0c\u5909\u6570$i$\u304c\u80af\u5b9a\u30ea\u30c6\u30e9\u30eb\u3068\u3057\u3066\u73fe\u308c\u308b\u7bc0\u306e\u96c6\u5408\uff0c\u5909\u6570$i$\u304c\u5426\u5b9a\u30ea\u30c6\u30e9\u30eb\u3068\u3057\u3066\u73fe\u308c\u308b\u7bc0\u306e\u96c6\u5408\u3067\u3059\uff0e<\/p>\n<p>easy-SAT \u9818\u57df\u3067\u306f\uff0c\u89e3\u7a7a\u9593\u306f\u8907\u6570\u306e\u30af\u30e9\u30b9\u30bf\u306b\u5206\u88c2\u305b\u305a\uff0csurvey \u306f\u3059\u3079\u3066 $0$ \u306b\u53ce\u675f\u3057\u307e\u3059\uff0ehard-SAT \u9818\u57df\u3067\u306f\uff0csurvey \u304c\u975e\u30bc\u30ed\u306e\u5024\u306b\u53ce\u675f\u3059\u308b\u3088\u3046\u306b\u306a\u308a\uff0c\u89e3\u7a7a\u9593\u306e\u69cb\u9020\u306b\u3064\u3044\u3066\u975e\u81ea\u660e\u306a\u60c5\u5831\u304c\u5f97\u3089\u308c\u308b\u306e\u3067\uff0csurvey\u306e\u5024\u3092\u7528\u3044\u3066\u5909\u6570\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e<\/p>\n<p>survey \u3092\u3082\u3068\u306b\u5909\u6570\u306e\u5024\u3092\u6c7a\u5b9a\u3059\u308b survey inspired decimation \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\uff0e<\/p>\n<ol>\n<li>SP \u3092\u5b9f\u884c\u3059\u308b\uff0e<\/li>\n<li>SP \u3067\u5f97\u3089\u308c\u305fsurvey\u3092\u5143\u306b\uff0c\u5909\u6570\u3092\u6c7a\u5b9a\u3059\u308b\n<ul>\n<li>\u30e1\u30c3\u30bb\u30fc\u30b8\u304c\u3059\u3079\u3066 $0$ \u2192 3\u306b\u9032\u3080<\/li>\n<li>\u30e1\u30c3\u30bb\u30fc\u30b8\u304c\u975e\u30bc\u30ed \u2192 $W^{(+)},W^{(-)}$\u306e\u5dee\u304c\u6700\u3082\u5927\u304d\u3044\u5909\u6570\u3092\u9078\u3073\uff0c\u5bfe\u5fdc\u3059\u308b\u5024\u306b\u6c7a\u5b9a\uff0e1\u306b\u623b\u308b<\/li>\n<\/ul>\n<\/li>\n<li>\u307e\u3060\u6c7a\u5b9a\u3055\u308c\u3066\u3044\u306a\u3044\u5909\u6570\u304c\u6b8b\u3063\u3066\u3044\u308b\u5834\u5408\u306f\uff0c\u9069\u5f53\u306a\u5c40\u6240\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u7528\u3044\u3066\u6b8b\u308a\u306e\u554f\u984c\u3092\u89e3\u304f<\/li>\n<\/ol>\n<p>\u672c\u5b9f\u88c5\u3067\u306f\uff0c\u30b9\u30c6\u30c3\u30d73\u3067SA\u3092\u7528\u3044\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">Survey Inspired Decimation \u306b\u3088\u308b\u30bd\u30eb\u30d0<\/span>\n<span class=\"sd\">survey \u304c\u3059\u3079\u3066 0 \u306b\u306a\u3063\u305f\u6642\u70b9\u3067\u306e\u5909\u6570\u306e\u5272\u308a\u5f53\u3066\u3092\u8fd4\u3059<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">survey_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">500<\/span><span class=\"p\">,<\/span> <span class=\"n\">eps<\/span><span class=\"o\">=<\/span><span class=\"mf\">1e-2<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span> <span class=\"n\">J<\/span> <span class=\"o\">=<\/span> <span class=\"n\">build_factor_graph<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span>\n\n    <span class=\"n\">remaining_vars<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">set<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">))<\/span>  <span class=\"c1\"># \u307e\u3060\u78ba\u5b9a\u3057\u3066\u3044\u306a\u3044\u5909\u6570<\/span>\n    <span class=\"n\">remaining_factors<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">set<\/span><span class=\"p\">(<\/span><span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">))<\/span>  <span class=\"c1\"># \u307e\u3060\u78ba\u5b9a\u3057\u3066\u3044\u306a\u3044\u7bc0<\/span>\n\n    <span class=\"c1\"># \u30e1\u30c3\u30bb\u30fc\u30b8\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u521d\u671f\u5316<\/span>\n    <span class=\"n\">eta<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[{<\/span><span class=\"n\">i<\/span><span class=\"p\">:<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">random<\/span><span class=\"p\">()<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]}<\/span> <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)]<\/span>\n    <span class=\"n\">gamma<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span>\n\n    <span class=\"k\">while<\/span> <span class=\"n\">remaining_vars<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">factors<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">list<\/span><span class=\"p\">(<\/span><span class=\"n\">remaining_factors<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># SP \u5b9f\u884c<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">t<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_iter<\/span><span class=\"p\">):<\/span>\n            <span class=\"n\">converged<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\n\n            <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">shuffle<\/span><span class=\"p\">(<\/span><span class=\"n\">factors<\/span><span class=\"p\">)<\/span>\n\n            <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factors<\/span><span class=\"p\">:<\/span>\n                <span class=\"c1\"># j \u304b\u3089 a<\/span>\n                <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                    <span class=\"n\">Pu<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Ps<\/span> <span class=\"o\">=<\/span> <span class=\"n\">P0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n                    <span class=\"k\">for<\/span> <span class=\"n\">b<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]:<\/span>\n                        <span class=\"k\">if<\/span> <span class=\"n\">a<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">b<\/span><span class=\"p\">:<\/span>\n                            <span class=\"k\">if<\/span> <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]:<\/span>\n                                <span class=\"n\">Pu<\/span> <span class=\"o\">*=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n                            <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                                <span class=\"n\">Ps<\/span> <span class=\"o\">*=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n                            <span class=\"n\">P0<\/span> <span class=\"o\">*=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">b<\/span><span class=\"p\">][<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n                    <span class=\"n\">Pu<\/span><span class=\"p\">,<\/span> <span class=\"n\">Ps<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">Ps<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Pu<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">Pu<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Ps<\/span>\n                    <span class=\"n\">gamma<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Pu<\/span> <span class=\"o\">\/<\/span> <span class=\"nb\">max<\/span><span class=\"p\">(<\/span><span class=\"n\">Pu<\/span> <span class=\"o\">+<\/span> <span class=\"n\">Ps<\/span> <span class=\"o\">+<\/span> <span class=\"n\">P0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-18<\/span><span class=\"p\">)<\/span>\n\n                <span class=\"c1\"># a \u304b\u3089 i<\/span>\n                <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                    <span class=\"n\">res<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n                    <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                        <span class=\"k\">if<\/span> <span class=\"n\">i<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">j<\/span><span class=\"p\">:<\/span>\n                            <span class=\"n\">res<\/span> <span class=\"o\">*=<\/span> <span class=\"n\">gamma<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n                    <span class=\"k\">if<\/span> <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">res<\/span><span class=\"p\">)<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">eps<\/span><span class=\"p\">:<\/span>\n                        <span class=\"n\">converged<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\n                    <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">res<\/span>\n\n            <span class=\"c1\"># \u53ce\u675f\u3057\u305f\u3089\u7d42\u4e86<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">converged<\/span><span class=\"p\">:<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">:<\/span>\n                    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"converged in <\/span><span class=\"si\">{<\/span><span class=\"n\">t<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"si\">}<\/span><span class=\"s2\"> iterations\"<\/span><span class=\"p\">)<\/span>\n                <span class=\"k\">break<\/span>\n        <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n            <span class=\"c1\"># \u53ce\u675f\u3057\u306a\u3044 \u2192 \u8ae6\u3081\u308b<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">:<\/span>\n                <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"did not converge in <\/span><span class=\"si\">{<\/span><span class=\"n\">n_iter<\/span><span class=\"si\">}<\/span><span class=\"s2\"> iterations\"<\/span><span class=\"p\">)<\/span>\n            <span class=\"k\">return<\/span> <span class=\"n\">value<\/span>\n\n        <span class=\"c1\"># \u975e\u30bc\u30ed\u306e survey \u304c\u5b58\u5728\u3059\u308b\u304b\u8abf\u3079\u308b<\/span>\n        <span class=\"n\">trivial<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">remaining_factors<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">factor_to_var<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">]:<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">eps<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">trivial<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\n                    <span class=\"k\">break<\/span>\n            <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">trivial<\/span><span class=\"p\">:<\/span>\n                <span class=\"k\">break<\/span>\n\n        <span class=\"k\">if<\/span> <span class=\"n\">trivial<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">return<\/span> <span class=\"n\">value<\/span>\n\n        <span class=\"c1\"># \u30d0\u30a4\u30a2\u30b9\u3092\u8a08\u7b97<\/span>\n        <span class=\"n\">best_var<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>  <span class=\"c1\"># (|Wpos - Wneg|, val, i)<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">remaining_vars<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">Ppos<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Pneg<\/span> <span class=\"o\">=<\/span> <span class=\"n\">P0<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\n            <span class=\"k\">for<\/span> <span class=\"n\">a<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">var_to_factor<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]:<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">J<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">Ppos<\/span> <span class=\"o\">*=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n                <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">Pneg<\/span> <span class=\"o\">*=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n                <span class=\"n\">P0<\/span> <span class=\"o\">*=<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">eta<\/span><span class=\"p\">[<\/span><span class=\"n\">a<\/span><span class=\"p\">][<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span>\n            <span class=\"n\">Ppos<\/span><span class=\"p\">,<\/span> <span class=\"n\">Pneg<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">Pneg<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Ppos<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">Ppos<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Pneg<\/span>\n            <span class=\"n\">Wpos<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Ppos<\/span> <span class=\"o\">\/<\/span> <span class=\"nb\">max<\/span><span class=\"p\">(<\/span><span class=\"n\">Ppos<\/span> <span class=\"o\">+<\/span> <span class=\"n\">Pneg<\/span> <span class=\"o\">+<\/span> <span class=\"n\">P0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-18<\/span><span class=\"p\">)<\/span>\n            <span class=\"n\">Wneg<\/span> <span class=\"o\">=<\/span> <span class=\"n\">Pneg<\/span> <span class=\"o\">\/<\/span> <span class=\"nb\">max<\/span><span class=\"p\">(<\/span><span class=\"n\">Ppos<\/span> <span class=\"o\">+<\/span> <span class=\"n\">Pneg<\/span> <span class=\"o\">+<\/span> <span class=\"n\">P0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-18<\/span><span class=\"p\">)<\/span>\n\n            <span class=\"n\">diff<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">Wpos<\/span> <span class=\"o\">-<\/span> <span class=\"n\">Wneg<\/span><span class=\"p\">)<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">diff<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">best_var<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]:<\/span>\n                <span class=\"n\">best_var<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"n\">diff<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span> <span class=\"k\">if<\/span> <span class=\"n\">Wpos<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">Wneg<\/span> <span class=\"k\">else<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># \u30d0\u30a4\u30a2\u30b9\u306e\u504f\u308a\u304c\u6700\u3082\u5927\u304d\u3044\u5909\u6570\u306e\u5024\u3092\u78ba\u5b9a<\/span>\n        <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"n\">best_var<\/span>\n        <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x<\/span>\n\n        <span class=\"c1\"># \u56e0\u5b50\u30b0\u30e9\u30d5\u3092\u66f4\u65b0\u3059\u308b<\/span>\n        <span class=\"n\">success<\/span> <span class=\"o\">=<\/span> <span class=\"n\">reduce_factor_graph<\/span><span class=\"p\">(<\/span>\n            <span class=\"n\">factor_to_var<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">var_to_factor<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">J<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">remaining_vars<\/span><span class=\"p\">,<\/span>\n            <span class=\"n\">remaining_factors<\/span><span class=\"p\">,<\/span>\n            <span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\n            <span class=\"n\">value<\/span><span class=\"p\">,<\/span>\n        <span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">success<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">return<\/span> <span class=\"kc\">None<\/span>\n\n    <span class=\"k\">return<\/span> <span class=\"n\">value<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u518d\u3073\uff0c\u6587\u732e [1] \u306e\u4f8b\u306b\u5bfe\u3057\u3066\u5b9f\u884c\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">8<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">9<\/span>\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">1<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"o\">~<\/span><span class=\"mi\">6<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">7<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">)]<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">survey_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>converged in 3 iterations\nconverged in 1 iterations\nconverged in 1 iterations\n[1, 0, 1, 1, -1, -1, -1, -1]\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u78ba\u304b\u306b\uff0c\u56fa\u5b9a\u5024\u3092\u53d6\u308b\u5909\u6570\u306b\u3064\u3044\u3066\u306f SID \u3067\u5024\u304c\u6c7a\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u6b21\u306b\uff0c3-SAT\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u52d5\u4f5c\u78ba\u8a8d\u3092\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">alpha<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">4<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">survey_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"n\">value<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>converged in 42 iterations\nconverged in 12 iterations\nconverged in 13 iterations\n...\nconverged in 5 iterations\nconverged in 11 iterations\ndid not converge in 500 iterations\n[1, -1, 0, -1, -1, 0, 0, -1, -1, 0, -1, 1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, 1, -1, -1, -1, 1, 0, -1, 1, -1, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1]\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SID \u3067 survey \u304c\u3059\u3079\u3066 0 \u306b\u306a\u3063\u305f\u3089\uff0c\u6b8b\u308a\u3092 SA \u3067\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"sd\">\"\"\"<\/span>\n<span class=\"sd\">SID + SA \u306b\u3088\u308b\u30bd\u30eb\u30d0<\/span>\n<span class=\"sd\">\u89e3\u304c\u898b\u3064\u304b\u3063\u305f\u3089\u5909\u6570\u306e\u5272\u308a\u5f53\u3066\uff0c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u3089 None \u3092\u8fd4\u3059<\/span>\n<span class=\"sd\">\"\"\"<\/span>\n\n\n<span class=\"k\">def<\/span> <span class=\"nf\">sid_sa<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">N<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">n_iter_sp<\/span><span class=\"o\">=<\/span><span class=\"mi\">500<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">n_iter_sa<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">eps<\/span><span class=\"o\">=<\/span><span class=\"mf\">1e-2<\/span><span class=\"p\">,<\/span>\n    <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span>\n<span class=\"p\">):<\/span>\n    <span class=\"c1\"># SID\u306e\u5b9f\u884c<\/span>\n    <span class=\"n\">value<\/span> <span class=\"o\">=<\/span> <span class=\"n\">survey_inspired_decimation<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter_sp<\/span><span class=\"p\">,<\/span> <span class=\"n\">eps<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">if<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">:<\/span>\n        <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SID finished\"<\/span><span class=\"p\">)<\/span>\n    <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">value<\/span><span class=\"p\">:<\/span>\n        <span class=\"k\">return<\/span> <span class=\"kc\">None<\/span><span class=\"p\">,<\/span> <span class=\"p\">[],<\/span> <span class=\"mi\">0<\/span>\n\n    <span class=\"c1\"># \u78ba\u5b9a\u3057\u3066\u3044\u306a\u3044\u5909\u6570\u306b index \u3092\u632f\u308a\u76f4\u3059<\/span>\n    <span class=\"n\">new_var<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span>\n    <span class=\"n\">new_N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">):<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">new_var<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">new_N<\/span>\n            <span class=\"n\">new_N<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n    <span class=\"c1\"># \u7bc0\u3092\u518d\u69cb\u7bc9\u3059\u308b<\/span>\n    <span class=\"n\">new_clauses<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">clause<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">:<\/span>\n        <span class=\"n\">satisfied<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\n        <span class=\"n\">new_clause<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">l<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">clause<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">l<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"n\">l<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">satisfied<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\n                    <span class=\"k\">break<\/span>\n                <span class=\"n\">new_clause<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">new_var<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">])<\/span>\n            <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n                <span class=\"n\">i<\/span> <span class=\"o\">=<\/span> <span class=\"o\">~<\/span><span class=\"n\">l<\/span>\n                <span class=\"k\">if<\/span> <span class=\"n\">value<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n                    <span class=\"n\">satisfied<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\n                    <span class=\"k\">break<\/span>\n                <span class=\"n\">new_clause<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"o\">~<\/span><span class=\"n\">new_var<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">])<\/span>\n        <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"n\">satisfied<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">new_clauses<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">new_clause<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">new_M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">new_clauses<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"k\">if<\/span> <span class=\"n\">verbose<\/span><span class=\"p\">:<\/span>\n        <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"original size: N = <\/span><span class=\"si\">{<\/span><span class=\"n\">N<\/span><span class=\"si\">}<\/span><span class=\"s2\">, M = <\/span><span class=\"si\">{<\/span><span class=\"n\">M<\/span><span class=\"si\">}<\/span><span class=\"s2\">, alpha = <\/span><span class=\"si\">{<\/span><span class=\"n\">M<\/span><span class=\"w\"> <\/span><span class=\"o\">\/<\/span><span class=\"w\"> <\/span><span class=\"n\">N<\/span><span class=\"si\">}<\/span><span class=\"s2\">\"<\/span><span class=\"p\">)<\/span>\n        <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"sa\">f<\/span><span class=\"s2\">\"reduced size:  N = <\/span><span class=\"si\">{<\/span><span class=\"n\">new_N<\/span><span class=\"si\">}<\/span><span class=\"s2\">, M = <\/span><span class=\"si\">{<\/span><span class=\"n\">new_M<\/span><span class=\"si\">}<\/span><span class=\"s2\">, alpha = <\/span><span class=\"si\">{<\/span><span class=\"n\">new_M<\/span><span class=\"w\"> <\/span><span class=\"o\">\/<\/span><span class=\"w\"> <\/span><span class=\"n\">new_N<\/span><span class=\"si\">}<\/span><span class=\"s2\">\"<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simulated_annealing<\/span><span class=\"p\">(<\/span>\n        <span class=\"n\">new_N<\/span><span class=\"p\">,<\/span> <span class=\"n\">new_clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"n\">n_iter_sa<\/span>\n    <span class=\"p\">)<\/span>\n    <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n        <span class=\"k\">return<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span> <span class=\"o\">-<\/span> <span class=\"n\">new_N<\/span>\n    <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\n        <span class=\"k\">return<\/span> <span class=\"kc\">None<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span> <span class=\"o\">-<\/span> <span class=\"n\">new_N<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>3-SAT \u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u52d5\u4f5c\u78ba\u8a8d\u3092\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">alpha<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">4<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">5e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span>\n\n<span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_decimated<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sid_sa<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">value<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy =\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">history<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"iterations\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>converged in 27 iterations\nconverged in 2 iterations\nconverged in 2 iterations\n...\nconverged in 41 iterations\nconverged in 1 iterations\nSID finished\noriginal size: N = 100, M = 400, alpha = 4.0\nreduced size:  N = 23, M = 27, alpha = 1.173913043478261\nSAT\nenergy = 0\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Text(0, 0.5, 'energy')<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SID\u306b\u3088\u3063\u3066\u554f\u984c\u30b5\u30a4\u30ba\u304c\u5c0f\u3055\u304f\u306a\u3063\u305f\u305f\u3081\uff0cSA\u3067\u89e3\u304d\u3084\u3059\u304f\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<p>\u540c\u3058\u554f\u984c\u3092SA\u306e\u307f\u3067\u89e3\u3044\u3066\u307f\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simulated_annealing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"mf\">5e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy = \"<\/span><span class=\"p\">,<\/span> <span class=\"n\">energy<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">history<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>SAT\nenergy =  0\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[&lt;matplotlib.lines.Line2D at 0x1241ba310&gt;]<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u4f8b\u3067\u306fSA\u3067\u3082\u89e3\u3092\u767a\u898b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u304c\uff0cSID\u3092\u7528\u3044\u305f\u3068\u304d\u3088\u308a\u3082\u975e\u5e38\u306b\u591a\u304f\u306e\u30a4\u30c6\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u5fc5\u8981\u3068\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<p>\u3088\u308a\u5927\u304d\u306a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u8abf\u3079\u3066\u307f\u307e\u3057\u3087\u3046\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">alpha<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">4.2<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1000<\/span>\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">5e-4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span>\n\n<span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_decimated<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sid_sa<\/span><span class=\"p\">(<\/span>\n    <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter_sa<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span> <span class=\"n\">verbose<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span>\n<span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">value<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy =\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">history<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>converged in 50 iterations\nconverged in 1 iterations\nconverged in 1 iterations\n...\nconverged in 1 iterations\nconverged in 4 iterations\ndid not converge in 500 iterations\nSID finished\noriginal size: N = 1000, M = 4200, alpha = 4.2\nreduced size:  N = 514, M = 1211, alpha = 2.3560311284046693\nSAT\nenergy = 0\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[&lt;matplotlib.lines.Line2D at 0x124c8df10&gt;]<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simulated_annealing<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"mf\">5e-4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">6<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT\"<\/span> <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">else<\/span> <span class=\"s2\">\"UNSAT\"<\/span><span class=\"p\">)<\/span>\n<span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"energy = \"<\/span><span class=\"p\">,<\/span> <span class=\"n\">energy<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">history<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>not satisfied\nenergy =  6\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[&lt;matplotlib.lines.Line2D at 0x124c3c790&gt;]<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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\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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\alpha_c$ \u306b\u8fd1\u3044\u5927\u304d\u306a\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u3082\uff0cSID\u3067\u306f\u89e3\u3092\u767a\u898b\u3067\u304d\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/p>\n<p>$K=3,N=100$ \u3067\uff0c\u69d8\u3005\u306a $\\alpha$ \u306b\u5bfe\u3057\u3066 $100$ \u500b\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u4f5c\u6210\u3057\uff0c SA, SID \u3067\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u308b\u5272\u5408\u3092\u305d\u308c\u305e\u308c\u8a08\u7b97\u3057\u307e\u3059\uff0e<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">K<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>\n<span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">n_shots<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\n<span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">5e-3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1e-5<\/span>\n<span class=\"n\">alphas<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">linspace<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">20<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">ratio_sid<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"n\">ratio_sa<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"n\">mean_decimated<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n<span class=\"k\">for<\/span> <span class=\"n\">alpha<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">tqdm<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">alpha<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">cnt_success_sid<\/span> <span class=\"o\">=<\/span> <span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">=<\/span> <span class=\"n\">total_decimated<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">_<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">n_shots<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">clauses<\/span> <span class=\"o\">=<\/span> <span class=\"n\">create_random_instance<\/span><span class=\"p\">(<\/span><span class=\"n\">K<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"n\">value<\/span><span class=\"p\">,<\/span> <span class=\"n\">history<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_decimated<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sid_sa<\/span><span class=\"p\">(<\/span>\n            <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter_sp<\/span><span class=\"o\">=<\/span><span class=\"mi\">100<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter_sa<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">4<\/span>\n        <span class=\"p\">)<\/span>\n        <span class=\"n\">total_decimated<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">num_decimated<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">value<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">cnt_success_sid<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n        <span class=\"n\">energy<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span><span class=\"p\">,<\/span> <span class=\"n\">_<\/span> <span class=\"o\">=<\/span> <span class=\"n\">simulated_annealing<\/span><span class=\"p\">(<\/span>\n            <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">clauses<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_begin<\/span><span class=\"p\">,<\/span> <span class=\"n\">temp_end<\/span><span class=\"p\">,<\/span> <span class=\"n\">n_iter<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"o\">**<\/span><span class=\"mi\">4<\/span>\n        <span class=\"p\">)<\/span>\n        <span class=\"k\">if<\/span> <span class=\"n\">energy<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\n            <span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\n\n    <span class=\"n\">ratio_sid<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">cnt_success_sid<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">ratio_sa<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">cnt_success_sa<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n    <span class=\"n\">mean_decimated<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">total_decimated<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">n_shots<\/span><span class=\"p\">)<\/span>\n\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">figsize<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">7<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">))<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">ratio_sid<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"SID\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">ratio_sa<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"SA\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"alpha\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"SAT ratio\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">()<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">alphas<\/span><span class=\"p\">,<\/span> <span class=\"n\">mean_decimated<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"alpha\"<\/span><span class=\"p\">)<\/span>\n<span class=\"n\">ax<\/span><span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"average number of variables decimated by SID\"<\/span><span class=\"p\">)<\/span>\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 20\/20 [14:04&lt;00:00, 42.22s\/it]\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>Text(0, 0.5, 'mean number of variables decimated by SID')<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea \"><img decoding=\"async\" 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w+Ef53l+0Q5z+4OzvyxYhOdG\/oR2pmDsNnbeSvw2cNCC0iInmYTLZDiEbcSljIAJo3b05qairZ2dl8+eWXTJ06lW3btuXetm\/fTp06dZg7d24p\/MsqPJUyKX+u3nDXFzDgfXB0g8MrYHo3OBJxxaZuzg58Pvw6ejWuyfmsHEbN\/ps1B1XMRETk2uLi4rjhhhv4+uuv2bFjB5GRkSxYsIC33nqL22+\/nSVLlnDu3DlGjx5Ny5Yt89wGDRpU7ocwVcrEGCYTdBgOD62Ems0gJQa+HAi\/vXjFnGauTg58+kAHbmhai\/QsC6Pm\/E3E\/lhjcouISIXh4eFBWFgY7777Lj179qRly5a89NJLjBkzhg8\/\/JCZM2cSHh6e7yHKQYMGsWnTJnbs2FFueXVOmRgvMw2WTYDNs20\/ewfZVgdomndW5cxsC499s4Xle2JwdjDzyf3tubGZf\/nnFRGpQiryPGXlSeeUSeXg7G6bImPIPPAOhsTjMG8ofHMvnDt2aTNHMx\/f155bWgaQmWPhka83s2x3tIHBRURESo9KmdiPJrfAY+uh+1O2KzMP\/AofhcHqdyA7EwAnBzPvD2nHra1rk5Vj5bH\/beGXnacNDi4iIlJyKmViX5yrQfgr8MhaCOkO2edhxau2ec2OrgFsxWza4LYMbFuHbIuVJ+Zu5aftxqxTJiIiUlpUysQ+1WoKI5bAwOng7gdn9sHs\/vD9I5ByBkcHM1PvactdHQLJsVgZO28r3289YXRqERGRYlMpE\/tlMkHbIfD439BhJGCC7XPhww6waRYOWHlrUGvu7RiExQrjvt3Ogk3HjU4tIiJSLCplYv\/cfWHANHjwdwhoBemJsOQpmBmOOWYHb9zRivs7B2O1wnPf7WDexiijE4uIVDpVbLKGIiuNfz8qZVJxBF4HYyKg75vg7AknN8NnvTEvG8\/rfYMZ0bUeViuMX7STr9Yfu+bbiYjItTk5OQGQlmbQskoVxMV\/Pxf\/fRWHY2mFESkXDo7Q+RFofjssex52L4IN0zHt\/oGJfd7A0dSUz9ce5aUfdpGTY2FEt1CjE4uIVGgODg74+PgQG2ubtNvd3R1TKSx1VFlYrVbS0tKIjY3Fx8cnzxqaRaXJY6ViO7QCfnkG4o8AYG1wA595PMqkDVkAvNi\/GQ\/2qG9kQhGRCs9qtRIdHU1CQoLRUeyWj48PAQEB+RbWwnYPlTKp+LLSYe0023xmORlYHVxYV\/sBRh7qTgbOPNe3Cf\/Xu6HRKUVEKrycnByysrKMjmF3nJycrjpCplJWAJWySizusG3U7PAfACS4BvKvpPtYZWnDuJsa868bGxkcUEREqiItsyRVT40GcP8iuOsL8AjAJ\/0EXzq\/yYdO7\/G\/5et5Z\/kBXT0kIiJ2S6VMKheTCVreaZvbLOxRMJm51WEDv7s8S0rE+0xZulvFTERE7JJKmVROrl5wy2R4KALqXoen6TwvO31Fv3VDmbNgoYqZiIjYHZUyqdxqt4HRy+HWaWQ4etLCfIxhu8ew453bSdmxBHJ0wqqIiNgHnegvVUfKGQ7PHUeDk4tzH0p39sWl3T2Y2g6FgNa2w58iIiKlSFdfFkClTHZuWsOB3z6lZ0YENU1Jl56o1Rza3Aut7gGv2sYFFBGRSkWlrAAqZQKQmW3hi1UH2LLyOwawipvMm3ExXTiUaTJD\/d7QZgg07Q\/O1QzNKiIiFZtKWQFUyuRyJ86l8criPWzce4R+DhsY4ryWNta9lzZw9oDmA20jaCHdwKzTMEVEpGhUygqgUib5Wb4nhlcW7+ZkwnmCTTE847+VfpYIHJOiLm3kHQStB9sKmp8mohURkcJRKSuASpkUJC0zmw\/+OMSMVUfItlhxdTIxqUMat5lW4bDnB8hIvLRx3eug7RBocSe4+xqWWURE7J9KWQFUyuRaDsYk88IPu9gYGQ9Ao1oe\/OfWhoRlboDt8+DQ72DNsW1sdoImfW3nnzW8CRydDUwuIiL2SKWsACplUhhWq5VFW07yxi97iUvNBODO9nV5vl8z\/EiEnQtg+1yI3nnpRW6+0OouW0Gr007Ta4iICKBSViCVMimKhLRM3lq2n7kbo7BawdvNief6NmFIx2DMZhNE74Id82DHt5ASc+mFfk1s5551GKHDmyIiVZxKWQFUyqQ4tkad44Xvd7HntG1es7ZBPvxnYEta1vW2bZCTDZERtsObe5dA9nnb4z4hMGIJ+AQbE1xERAynUlYAlTIpruwcC1+tP8bU3w6QkpGN2QTDu9Zj3E2N8XR1urRhehLsXQx\/vgUJx8A7GIYvBt9Q48KLiIhhVMoKoFImJRWTlM7rS\/awZMdpAGp5uvDygOb0b1Ub0+XnkSWdgtm3Qvxh8KoLw3+CGg0MSi0iIkYpbPfQTJgiReTv5cqHQ9vz5ahO1KvhTmxyBo9\/s5VhszZy9GzqpQ296sDIX8CvMSSdhNn94exB44KLiIhdUykTKaaejWuy9MmePBneCGdHM6sPnuXmaat4d\/kB0rMuTJnhGQAjfoaazSD5tK2Yxe4zNriIiNgllTKREnB1cuDJ8Mb89mRPejTyIzPbwnsrDtJ32ipWHThj28ijlu1kf\/+Wtis0Z\/eHmD3GBhcREbtjeCn76KOPqFevHq6uroSFhbFx48arbj9t2jSaNGmCm5sbQUFBPPXUU6Snp5dTWpH81fOrxpejOvHh0HbU8nThaFwaw2Zt5M2lF0bFqvnZzikLaA1pZ23F7PI5zkREpMoztJTNnz+fcePGMXHiRLZs2UKbNm3o06cPsbGx+W7\/zTffMH78eCZOnMjevXuZOXMm8+fP5\/nnny\/n5CJXMplM3Nq6Diue7sWobrYrLT+JOMzqgxdGzNx9bVdh1mkP5+NhzgA4tc24wCIiYlcMLWXvvPMOY8aMYeTIkTRv3pzp06fj7u7OrFmz8t3+r7\/+olu3bgwdOpR69epx8803M2TIkGuOromUJ09XJ14e0JxhXUIAeG7hDpLSs2xPulWHYT9AYEc4fw6+vA1ObjYurIiI2A3DSllmZiabN28mPDz8UhizmfDwcNatW5fva7p27crmzZtzS9iRI0f45Zdf6NevX4Gfk5GRQVJSUp6bSHkYf0tTQmq4czoxndd+uuwcMldvuH8RBHWG9ET4ciAc118sRESqOsNK2dmzZ8nJycHf3z\/P4\/7+\/kRHR+f7mqFDh\/Laa6\/RvXt3nJycaNCgAb17977q4ctJkybh7e2dewsKCirV\/RApiLuzI1PvboPJBAs3n2D5nsuWYXL1gvu\/g5DukJEEX90Bx\/L\/y4iIiFQNhp\/oXxQRERG88cYbfPzxx2zZsoVFixbx888\/8\/rrrxf4mgkTJpCYmJh7O378eDkmlqruunq+PNSjPgATFu0k\/sLi5gC4eMB930JoT8hMga8HwdE1BiUVERGjGVbK\/Pz8cHBwICYmJs\/jMTExBAQE5Pual156iQceeIAHH3yQVq1acccdd\/DGG28wadIkLBZLvq9xcXHBy8srz02kPD11U2Ma1fLgbEoGL\/24K++TztVg6LfQ4AbISoWv74IjEYbkFBERYxlWypydnenQoQMrVqzIfcxisbBixQq6dOmS72vS0tIwm\/NGdnBwAKCKrRYlFYirkwPv3NMWB7OJn3ec5qftp\/Ju4OQG986FRjfbFjL\/ZjAc+t2YsCIiYhhDD1+OGzeOGTNmMGfOHPbu3cujjz5KamoqI0eOBGDYsGFMmDAhd\/sBAwbwySefMG\/ePCIjI1m+fDkvvfQSAwYMyC1nIvaoVaA3j1\/fEICXftxFbNI\/5tZzcoXBX0OTfpCdDnOHwIHfDEgqIiJGcTTywwcPHsyZM2d4+eWXiY6Opm3btixdujT35P+oqKg8I2MvvvgiJpOJF198kZMnT1KzZk0GDBjAf\/\/7X6N2QaTQHr+hIb\/vjWH3qSQmLNrJ58Ovy7uAuaML3D0HvhsFe3+CeUPhni+hacFXF4uISOVhslax436FXaldpCzsj05mwAdryMyx8NZdrbnnunyuBs7Jgu8ehD0\/gNkR7voCmt9W7llFRKR0FLZ7VKirL0UquiYBnoy7uTEAr\/20hxPn0q7cyMEJBs2EVneDJRsWjIBdi8o3qIiIlDuVMpFyNqZHfdoH+5CSkc1zC3dgseQzWO3gCHd8Cm2GgDUHvhsNOxaUf1gpEavVyqHYFHLy+x2LiPyDSplIOXMwm5h6T1tcncz8dTiOrzccy39DswPc\/hG0ux+sFvj+Idg2t3zDSrFl51gYO28b4e\/8yU3v\/MnCzSfIzsl\/6h4REVApEzFEqF81JtzSDIBJv+wj8mxq\/huaHWDAB9BhpK2Y\/fAobPmqHJNKcWTlWPjXvK0svjD9yZGzqTyzYDs3TP2TeRujyMxWORORK6mUiRjkgc4hdG1Qg\/NZOTyzYHvBh7jMZrj1Xeg4BrDC4sdh06xyzSqFl5lt4fFvtvDLzmicHEy8P6Qd429pSo1qzkTFpzF+0U6unxLBV+uPkZGdY3RcEbEjuvpSxEAnzqXRd9pqUjKymXBLUx7u1aDgja1WWPY8rP\/Y9nO\/KdBpTPkElULJyM7hsf9t4fe9sTg7mvn0\/g5c37QWAGmZ2XyzIYpPVx3hTHIGAAFerjzcqz5DOgXj6qS5FkUqq8J2D5UyEYN9+\/dxnvtuB84OZpb8qzuN\/T0L3thqheUvw1\/v237uMwm6\/F\/5BJWrSs\/K4ZGvNxOx\/wwujmZmDLuOno1r5rvd\/L+P80nEYaIvTCLs5+HCwz3rc1\/nYNydDZ0+UkTKgEpZAVTKxN5YrVZGz9nEH\/tiaVnXi+\/\/rxtODlc5s8BqhT9eh9VTbT\/f9Bp0G1s+YSVf5zNzeOirTaw+eBZXJzMzh3ekW0O\/q74mIzuHhZtP8PHKw5xMOA+AbzVnHuwRyrAu9fBwUTkTqSxUygqgUib2KDYpnZveXUXi+SyeDG\/Ek+GNr\/4CqxUiJsOfk20\/3\/I2hD1U9kHlCmmZ2YyevYl1R+Jwd3Zg1oiOdK5fo9Cvz8qx8P2Wk3wUcYhjcbZ563zcnRjVLZThXevh7eZUVtFFpJyolBVApUzs1eLtp\/jX3K04mk18\/3\/daBXofe0XRbwJEW+AixeM3Q7uvmUfVHKlZGQz6ou\/2Xg0Hg8XR2aP7Mh19Yr3O8jOsbB4+yk+XHmII2dsV+N6ujoysms9RnUPxcfduTSji0g50oz+IhXMgNa16d+qNtkWK08v2EZ6ViGuzOv5LPi3gowkWPdh2YeUXMnpWQyftZGNR+PxdHHky9Gdil3IABwdzNzZPpDlT\/Xi\/SHtaFTLg+T0bN7\/4xDdJv\/Bm0v3EZeSUYp7ICL2RqVMxE6YTCZeH9gSPw8XDsSk8O7vB679IrMZrp9gu79+OqSeLduQZSwmKZ2XftjF8j0xRke5qsTzWdw\/cyObj53Dy9WR\/40Jo31w9VJ5bwezidva1GHZkz355L72NKvtRWpmDp9EHKb7myv57897iE1OL5XPEhH7osOXInZm+Z4Yxny5CZMJFj7ShQ4h1xh9sVrhs95weht0\/Rfc\/Hp5xCx1VquVB2ZuZM0hW7EMb1aLiQNaEOTrbnCyvBLSMnlg5kZ2nkzEx92Jr0eH0bJuIQ41F5PVauX3vbF88MdBdpxIBMDF0czQsGAe7tmAAG\/XMvtsESkdOqesACplUhE8s2A7CzefoF4Nd34Z2+Pa0yQc+A2+uRsc3Wznlnn6l0\/QUvTD1pM8OX8bzg5mrFjJyrHi6mTmiRsaMaZHfZwdjR\/Yj0\/N5P7PN7DndBK+1Zz5enQYzeuUz58jVquViANneH\/FQbZGJQDg7GBmcMcgHundgLo+buWSQ0SKTueUiVRgLw9oTh1vV47GpfHmr\/uu\/YJGN0FgR8g+D2unlXm+0paQlsnrS\/YAMDa8Eb\/8qwdhob6kZ1l4e9l++r2\/mnWH4wzNeDYlg6Ez1rPndBJ+Hs7MHdO53AoZ2A5vX9+kFose7crXo8PoVM+XzBwLX60\/Ru+3VzJh0Q5SM7LLLY+IlD6VMhE75OXqxFt3tQFgzrpjrD10jXPFTCa4\/nnb\/b9nQtKpMk5Yuib9so+41Ewa+3swpkd9Gvl7Mu+hzrxzTxtqVHPmUGwKQ2asZ9z8bZw14GT32OR0hny2nn3RydT0dGHeQ51pEnCVSX7LkMlkonsjP759pAvzHupM1wY1yMqxMnfjcd5cWogCLyJ2S6VMxE51b+THA51DAHhu4Q6S0rOu\/oL610NwV8jJgNXvlEPC0rHhSBzzNx0H4I07WuUepjSZTNzZPpA\/nu7NfWHBmEywaOtJbpgSwdfrjxW8Vmgpi0lK597P1nMwNoUAL1fmP9SZhrWMKWT\/1Ll+Db4Z05mPhrYHYOHmE9f+70RE7JZKmYgdG39LU0JquHMy4Tz\/uXB4r0CXj5ZtmQMJx8s+YAllZOcw4fudAAwNC853Sglvdyf+e0crFj3alRZ1vEhKz+bFH3Zx5yd\/setkYpnmO514nns\/W8+RM6nU8XZl\/sOdqV\/To0w\/szj6tQqgsb8HaZk5LNh0wug4IlJMKmUidqyaiyNT7m6DyQTfbjrBir3XmCoitAeE9oScTFg9pXxClsD0iCMcOZOKn4cL\/+7b9Krbtguuzo+PdWPigOZ4uDiy\/XgCt324hlcW7y6T0aET59IY\/Ol6Is+mEljdjfkPdyGkRrVS\/5zSYDKZGNE1FIA5fx0tt1FEESldKmUidq5jPV\/G9KgPwPhFOzmXmnn1F1z\/gu2fW7+G+MgyTld8h8+k8NHKQwBMHNC8UMsJOTqYGdktlBVP9+LW1rWxWGH2X0cJn\/oni7eforQuJj8ebytkUfFphNRwZ\/7DXexuao5\/GtiuDt5uTkTFpxGxP9boOCJSDCplIhXAuJsa07CWB2eSM3h58e6rbxzcGRrcCJZsWPV2+QQsIqvVygvf7yQzx0LvJjW5tXXtIr3e38uVD4e256vRnQj1q0Zscgb\/mruVB2Zu5MiZlBJlO3o2lcGfruNkwnlC\/aox\/6EuFWK6CXdnR+7tGATYiqqIVDwqZSIVgKuTA+\/c0wYHs4mftp9iyY5rXF15cbRs+1yIO1z2AYto4eYTrD8Sj6uTmddvb4nJZCrW+\/RoVJNfx\/bgqfDGODuaWXPoLH2nread3\/YXbpmqfzhyJoXBn63jVGI6DWpWY\/5DnSvU5Kz3dw7BbILVB89yMCbZ6DgiUkQqZSIVROtAHx67viEAL\/2w6+pL7QR2gMZ9wWqBiMnllLBw4lIy+O8vewF4KrxxiQ8Lujo5MDa8Eb892ZOejWuSmWPh\/T8O0WfaqiIdxjsUm8zgz9YTk5RBY38P5j3UhVpeFaeQAQT5uhPezDZx8Jx1R40NIyJFplImUoE8fn1DWtTx4lxaFs8v2nX1c6h6X1gTc+cCOLO\/fAIWwn9\/3ktCWhbNansxqntoqb1vPb9qzBnZkY+Gtsffy4VjcWmM+OJv\/u9\/m4lOvPpakfujk7n3s\/WcSc6gaYAnc8d0pqanS6llK08jutUD4LvNJ0k8r+kxRCoSlTKRCsTZ0czUe9rg7GDm970xfLflZMEb12kLTW8FrBAxqbwiXtXaQ2dZtPUkJhNMurMVTg6l+0eQyWSif+va\/D6uF6O6hWI2wS87o7lxagSfrz5Cdo7litfsOZXEvZ+t42xKJi3qeDF3TGdqeFTMQgbQpX4Nmvh7cj4rhwWb7H9aFBG5RKVMpIJpGuDFUzc1BuDVxbs5lXC+4I0vjpbt\/h5irnGBQBlLz8rhhQtzkg3rHELbIJ8y+yxPVydeHtCcn57oTrtgH1Izc\/jPz3sZ8OFaNh87l7vdrpOJDP18PefSsmgd6M03D3amejXnMstVHkwmU+5o2Zfrym+SXREpOZUykQrooZ71aRfsQ3JGNs8t3FHwYcyAltDiDtv9lW+UX8B8fPjHIY7GpeHv5cIzfZqUy2e2qOPNd4905Y07WuHt5sTe00kM+uQvJizawaoDZxg6Yz0JaVm0DfLhq9FheLtfe1qOimBg27q502Os3KfpMUQqCpUykQrIwWxi6t1tcHWyXXE4c81V5iPrNR4wwb4lcGpbeUXM40BMMp+usl0F+uptLfB0Lb\/yYzabGBoWzB9P9+KuDoEAzN14nGGzNpKUns11IdX5anSnQs2TVlG4OTtwbydNjyFS0aiUiVRQ9Wt6MP7CLPj\/+XkvX60\/lv+GtZpCq7tt9w04t8xisfL8op1k5VgJb+ZPnxYB5Z4BoIaHC1PubsO3D3ehsb9tqaROob7MGdWpXEtieXngwvQYaw5pegyRikKlTKQCG961Hg9euILxpR92MXttASNmvf4NJjMcWAonNpdjQpi\/6Tibjp3D3dmBV29vUew5yUpLp1Bffv5XD757tAtfjw6jmoujoXnKSmB1d25ubivAGi0TqRhUykQqMJPJxAv9m\/FIrwYAvPLTHj5ffeTKDf0aQpshtvsr\/1tu+WKT05l0YU6yp29uYjcz4zs5mOkQ4ouzY+X+I\/DiCf+LtpwkMU3TY4jYu8r9J5JIFWAymfh33yY8cYNtYtn\/\/LyXTyLymcW\/57NgdoTDKyBqfblke33JXpLSs2lV15sRXeuVy2fKJWGhvjQNsE2P8a2mxxCxeyplIpWAyWTi6Zub8FS4baqMN5fu44MVB\/Nu5BsKbe+z3S+H0bKI\/bH8tP0U5gtzkjmYjT1sWRWZTCZGXhgtm7PuqKbHELFzKmUilcjY8EY8e2G6ianLD\/Du8gN5p8vo+SyYnSByFUSuLrMc5zNzeOnHXQCM7BZKy7reZfZZcnW3t62Lj7sTJ86dZ8XeGKPjiMhVqJSJVDKPXd+QCbfYrsp8b8VBpvy2\/1Ix8wmCDsNt91e+AVdbpqkEpq04wPH489TxdmXchYluxRiuTg7c2zEY0An\/IvZOpUykEnq4VwNe7N8MgI9WHmbyr\/suFbMeT4ODC0T9BUciSv2z955O4vPVtqtAX7u9ZaW9urEieaCLbXqMvw7HsT9a02OI2CuVMpFK6sEe9Xn1thYAfLrqCK8v2WsrZl514LpRto1W\/rdUR8tyLFYmLNpJjsXKLS0DCG\/uX2rvLcVX18ctd344jZaJ2C+VMpFKbHjXevz3jpYAzFobySuLd9uKWfenwNENTvwNh34vtc\/734ZjbDuegIeLIxMHtCi195WSu3j16\/dbT2h6DBE7pVImUsndFxbCm4NaYTLBnHXHeOGHXViq1YJOD9o2KKXRspikdN5auh+A5\/o2IcDbtcTvKaWnU6gvzWp7kZ5lYf6mKKPjiEg+VMpEqoDBHYN5+642mEzwzYYoJizaiaXLWHCqBqe2wv5fS\/wZryzeTUpGNm2DfLgvLKQUUktpMplMjLwwWjbnr2OaHkPEDqmUiVQRd3UIZNrgtphNtqWPnvn1JJZOD9ueXPkGWCzFfu\/f98Tw665oHMwmzUlmx25rW4fq7k6cTDjP75oeQ8TuqJSJVCG3t63L+0Pa4WA2sWjLSV6I7Y3V2RNidsK+n4r1nqkZ2bx8YU6yB3uE0qy2V2lGllLk6uTAkE4XpsdYe9TYMCJyBZUykSrm1tZ1+HBIOxzNJubuTOFXjztsT6ycBJacIr\/fO8sPcCoxncDqboy9sVEpp5XSdn\/nEBzMJtYdiWNfdJLRcUTkMiplIlXQLa1q8\/F97XFyMDH+VA9SzR5wZi\/s\/r5I77PrZCJfrLXNSfafgS1xd9acZPaujo8bfS9MjzFH02OI2BWVMpEq6uYWAXz2wHWkO3ryScYtAFhWToKc7EK9PjvHYrtgwAoD2tShd5NaZRlXStGIC+thfr\/1JOdSM40NIyK5VMpEqrDrm9bi82HX8Y2pH+esHpjjD5G5bX6hXjtn3TF2nkzEy9WRl25tVsZJpTRdF1Kd5rnTYxw3Oo6IXKBSJlLF9Wxckw9G9GSmdQAA5379D+np6Vd9zamE80z9zTYn2fhbmlHLU3OSVSQmkyl3tOyrdcfIzin+lbciUnpUykSEbg396HnfC8RZvfDPPsWX0yeTlpn\/YUyr1crLP+4mLTOH60Kqc2\/HoHJOK6XhtjZ18K3mrOkxROyISpmIANCpSRCpnZ4AoN+5rxg96y9SM64sZst2R\/P73hicHEy8cWcrzJqTrEKyTY9hK9RfaHoMEbugUiYiuYJvfoIst5oEms5S\/\/j3DJ+1keT0S+skJqdnMXHxbgAe7tmAxv6eRkWVUnBxeowNkfHsPa3pMUSMplImIpc4ueHU+1kAnnD6kZ3HYhg2ayNJF4rZlGX7iUnKoF4Ndx6\/oaGRSaUU1PZ2o29LTY8hYi9UykQkr\/bDwasuAcQx0m0VW6MSuP\/zDfx54Axfrj8GwH\/vaIWrk4PBQaU0XFwPU9NjiBhPpUxE8nJyhR5PA\/C06xJqu1vZcSKR4bM2YrXCne3q0q2hn8EhpbR0CKlOy7peZGRbmPe3pscQMZLhpeyjjz6iXr16uLq6EhYWxsaNG6+6fUJCAo899hi1a9fGxcWFxo0b88svv5RTWpEqot0D4B2M0\/lYfgzbj5+HMwA+7k680F9zklUmJpOJEV1DAfhq3VFNjyFiIENL2fz58xk3bhwTJ05ky5YttGnThj59+hAbG5vv9pmZmdx0000cPXqUhQsXsn\/\/fmbMmEHdunXLOblIJefoDL1s55bV2v4x80e2YWDbOnx8X3tqeLgYHE5K262ta1OjmjOnEtNZvkfTY4gYxWS1Wq1GfXhYWBgdO3bkww8\/BMBisRAUFMQTTzzB+PHjr9h++vTpvP322+zbtw8nJ6difWZSUhLe3t4kJibi5eVVovwilVpOFnzYEc5FQvgr0P0poxNJGZr6234++OMQnUJ9+fbhLkbHEalUCts9DBspy8zMZPPmzYSHh18KYzYTHh7OunXr8n3N4sWL6dKlC4899hj+\/v60bNmSN954g5ycnAI\/JyMjg6SkpDw3ESkEByfofeEvR2vfg3R9dyqz+8JCcDSb2BgZz+5TiUbHEamSDCtlZ8+eJScnB39\/\/zyP+\/v7Ex0dne9rjhw5wsKFC8nJyeGXX37hpZdeYurUqfznP\/8p8HMmTZqEt7d37i0oSLOPixRaq7uhRiM4fw42fGp0GilDAd6umh5DxGCGn+hfFBaLhVq1avHZZ5\/RoUMHBg8ezAsvvMD06dMLfM2ECRNITEzMvR0\/rquLRArN7HBptGzdB3A+wdA4UrZGXlgP84dtp4jX9Bgi5c6xOC9KSEhg5syZ7N27F4AWLVowatQovL29C\/0efn5+ODg4EBOT96TSmJgYAgIC8n1N7dq1cXJywsHh0vxIzZo1Izo6mszMTJydna94jYuLCy4uOjFZpNha3AmrpsCZvfDHf6Df22DS0kqVUfvg6rSq683Ok4nM3RjFY9drgmCR8lTkkbJNmzbRoEED3n33XeLj44mPj+edd96hQYMGbNmypdDv4+zsTIcOHVixYkXuYxaLhRUrVtClS\/4nmXbr1o1Dhw5hsVy6ZPvAgQPUrl0730ImIqXAbIbwibb7f8+A5S+BcdcHSRmyTY9RD4Cv1x\/T9Bgi5azIpeypp57itttu4+jRoyxatIhFixYRGRnJrbfeypNPPlmk9xo3bhwzZsxgzpw57N27l0cffZTU1FRGjhwJwLBhw5gwYULu9o8++ijx8fGMHTuWAwcO8PPPP\/PGG2\/w2GOPFXU3RKQomtwC\/abY7v\/1ASydoGJWSd3apjZ+Hs6cTkznN02PIVKuinz4ctOmTcyYMQNHx0svdXR05LnnnuO6664r0nsNHjyYM2fO8PLLLxMdHU3btm1ZunRp7sn\/UVFRmM2XemNQUBDLli3jqaeeonXr1tStW5exY8fy73\/\/u6i7ISJF1WkMmB1hyZOw4ROwZMMtb9lG0qTScHF0YGinYN7\/4xCz1x6lX6vaRkcSqTKKPE+Zv78\/X331FTfffHOex5ctW8awYcOuOEfM3mieMpES2vIVLH4CsEKHEdD\/XRWzSiYmKZ1uk\/8g22JlyRPdaVm38OcLi8iVymyessGDBzN69Gjmz5\/P8ePHOX78OPPmzePBBx9kyJAhJQotIhVA+wdg4CdgMsPm2fDTE2ApeK5AqXj8vVxzR8g0PYZI+Sny4cspU6ZgMpkYNmwY2dnZADg5OfHoo48yefLkUg8oInao7RDboczvH4KtX0NONgz82DaFhlQKI7rVY\/H2U\/y4\/RTjb2mq5bVEykGxl1lKS0vj8OHDADRo0AB3d\/dSDVZWdPhSpBTt\/h4WjgZrDrQcBHd8Bg7FmmlH7IzVamXgR2vZfiKRZ\/s00fQYIiVQ5sssubu706pVK1q1alVhCpmIlLIWd8Dds22jZru+g+9G2dbMlArPZDIx4sJksl+tO0aWpscQKXOF+ivtnXfeyezZs\/Hy8uLOO++86raLFi0qlWAiUkE0vw3u+Qq+HQZ7frSdX3bXF+CouQMrun6tavPfn\/cSnZTOst3R3Nq6jtGRRCq1Qo2UeXt7Y7owg7eXl1eetST\/eRORKqhpP7j3G3BwgX1LbAUtO8PoVFJCLo4ODA0LAWD22qPGhhGpAop9TllFpXPKRMrQoRUwbyhkp0PDm2Dw1+DkanQqKYHYpHS6Xpge46fHu9MqUH\/5FimqMjun7IYbbiAhISHfD7zhhhuK+nYiUpk0vBGGzgdHNzi0HObeC5lpRqeSEqjl5Ur\/1rbpMWZregyRMlXkUhYREUFmZuYVj6enp7N69epSCSUiFVj93nD\/QnCqBkdWwjf3QGaq0amkBC6uh\/nT9lOcTdFhaZGyUuhr13fs2JF7f8+ePURHR+f+nJOTw9KlS6lbt27pphORiqled7j\/O\/jfXXB0NfzvbtsImoun0cmkGNoFV6dNkA\/bjycwb2MUj9\/QyOhIIpVSoc8pM5vNuSf75\/cSNzc3PvjgA0aNGlW6CUuZzikTKUfH\/4av74SMJAgKg\/sWgqu+dxXRD1tP8uT8bfh7ubDm3zfg5KCltUQKq9TPKYuMjOTw4cNYrVY2btxIZGRk7u3kyZMkJSXZfSETkXIW1BGG\/QCu3nB8A3x1B5xPMDqVFEO\/VrWp6elCTFIGP+84bXQckUpJV1+KSNk7tQ2+Ggjnz0GddnD\/InD3NTqVFNGHfxxkym8HCPZ15\/dxvXB21GiZSGEUtnsUu5Tt2bOHqKioK076v+2224rzduVGpUzEINE74cvbIS0OAlrBsMUqZhVMakY2vd6O4GxKBq8MaM6IbqFGRxKpEMqslB05coQ77riDnTt3YjKZcs8vu3i+WU5OTglilz2VMhEDxeyBL2+D1DNQqwUMXwzV\/IxOJUXw9fpjvPjDLnyrOfPns73xdHUyOpKI3SuzecrGjh1LaGgosbGxuLu7s3v3blatWsV1111HRERESTKLSGXn3xxG\/Awe\/hC7G2bfCimxRqeSIhjcMYj6ftWIT83ks1VHjI4jUqkUuZStW7eO1157DT8\/P8xmM2azme7duzNp0iT+9a9\/lUVGEalMajaxFTPP2nBmL8zuD8nR136d2AUnBzPP9W0CwIzVR4hJSjc4kUjlUeRSlpOTg6enba4hPz8\/Tp06BUBISAj79+8v3XQiUjn5NbIVM69AOHsAvugHiSeNTiWF1KdFAO2DfUjPsjDt9wNGxxGpNIpcylq2bMn27dsBCAsL46233mLt2rW89tpr1K9fv9QDikglVaMBjPwZvIMh\/jDM7gcJx41OJYVgMpmY0K8ZAPP\/Ps6h2GSDE4lUDkUuZS+++CIWiwWA1157jcjISHr06MEvv\/zC+++\/X+oBRaQSq17PVsyq14NzR23F7Nwxg0NJYXSs58tNzf2xWOHNpTpKIlIaSmWesvj4eKpXr557BaY909WXInYo8STMuRXij9gOaY5YAr6absHeHYpN5uZ3V2GxwoJHutCxnqY4EclPmVx9mZWVhaOjI7t27crzuK+vb4UoZCJip7zrwohfoEYjSDoBC0eBxb6n1xFoWMuTwR2DAHjjl735LsEnIoVXpFLm5OREcHCw3c9FJiIVkFdtGPYjuHjBqS3w9+dGJ5JCeDK8MW5ODmyNSmDZbl1FK1ISRT6n7IUXXuD5558nPj6+LPKISFXmXRdufNl2f8XruiKzAvD3cuXBHrZDzW8t3U9WjsXgRCIVV5HPKWvXrh2HDh0iKyuLkJAQqlWrluf5LVu2lGrA0qZzykTsnMUCs26GE39D01vh3v8ZnUiuITk9i15vRxCfmsl\/Brbk\/s4hRkcSsSuF7R6ORX3jgQMHliSXiMjVmc0w4D34tCfsWwL7foam\/Y1OJVfh6erEv25oyCs\/7WHa7we5o11dqrkU+X8vIlVeqVx9WZFopEykglg+EdZOA6+68NgGcPE0OpFcRWa2hZve\/ZNjcWk8Gd6IJ8MbGx1JxG6U2dqXIiLlote\/wScEkk7CH\/81Oo1cg7OjmWf72JZf+mzVEc4kZxicSKTiUSkTEfvk7A63vmO7v\/FTOGnf56sK9G9VmzaB3qRl5vD+ioNGxxGpcFTKRMR+NQyHlneB1QI\/jYWcbKMTyVWYTCbG32Jbfmnuxigiz6YanEikYlEpExH71ncSuHpD9A7YMN3oNHINXRrU4PomNcm2WHl72T6j44hUKIUuZfXr1ycuLq4ss4iIXMmjFtz0uu3+yv9CQpSxeeSaxt\/SDLMJftkZzZaoc0bHEakwCl3Kjh49qpn8RcQY7R6A4C6QlQa\/PAtV66LxCqdJgCeD2gcCMPmXfVp+SaSQdPhSROzfxbnLzE5wYCns+dHoRHIN425ujIujmY1H41mxN9boOCIVQpFm91u2bBne3t5X3ea2224rUSARkXzVbALdn4JVb8Gv\/4YG19vONRO7VNvbjZHdQpn+52HeXLqP3k1q4uigcQCRqyn05LFm87W\/TCaTye4PcWryWJEKLCsdPukK8Yeh44PQf6rRieQqEs9n0evtlSSkZfHmoFYM7hhsdCQRQ5TJ5LHR0dFYLJYCb\/ZeyESkgnNyhVvftd3\/eyYc\/9vYPHJV3m5OPH59QwDeWX6A85n6f4TI1RS6lJlMprLMISJSOPV7QZuhgPXC3GVZRieSq3igSwiB1d2IScpg1tpIo+OI2LVCl7LCHOXctWtXicKIiBTKzf8BN1+I3Q3rPjQ6jVyFi6MDz9xsW35pesRh4lMzDU4kYr8KXcqGDx+Om5vbFY8nJyfz2Wef0alTJ9q0aVOq4URE8lWtBvS5sB5mxJsQrxEYe3Zbmzq0qONFckY2H\/yh5ZdEClLoUvbFF1\/g6emZ+\/OqVasYPnw4tWvXZsqUKdxwww2sX7++TEKKiFyhzRCo1wOyz8PPT2vuMjtmNpuYcGH5pa\/XHyMqLs3gRCL2qcgn+k+ePJlGjRpx99134+XlRUZGBj\/88AOTJ0+mY8eOZZVTRCQvkwlunQYOLnB4Bez6zuhEchXdG\/nRo5EfWTlW3v5tv9FxROxSoUvZgAEDaNKkCTt27GDatGmcOnWKDz74oCyziYhcnV9D6PmM7f7S8XBeS\/rYs\/G3NMVkgp+2n2LHiQSj44jYnUKXsl9\/\/ZXRo0fz6quv0r9\/fxwcHMoyl4hI4XQbC35NIPUMLJ9odBq5ihZ1vBnYti4Ak3\/V8ksi\/1ToUrZmzRqSk5Pp0KEDYWFhfPjhh5w9e7Yss4mIXJujCwyYZru\/ZQ4cW2doHLm6p29ujLODmb8Ox\/HngTNGxxGxK4UuZZ07d2bGjBmcPn2ahx9+mHnz5lGnTh0sFgvLly8nOTm5LHOKiBQspCu0H2a7v+RJyNa0C\/YqsLo7w7uGALbRshyLRstELiryQmTVqlVj1KhRrFmzhp07d\/L0008zefJkatWqpXUvRcQ44a9CtZpwZh+sfc\/oNHIVj13fEC9XR\/ZFJ\/P91pNGxxGxGyVaHbZJkya89dZbnDhxgrlz55ZWJhGRonP3hT6TbPdXvQ1xh43NIwXycXfm\/y4uv\/TbftKztPySCJSwlF3k4ODAwIEDWbx4cWm8nYhI8bS6CxrcADkZtsOYOpHcbo3oWo863q6cSkxnzl9HjY4jYhcKXcrWrVvHkiVL8jz25ZdfEhoaSq1atXjooYfIyMgo9YAiIoVmMkH\/d8DRFSJXwfZ5RieSArg6OTDuwvJLH608REKazgMUKXQpe+2119i9e3fuzzt37mT06NGEh4czfvx4fvrpJyZNmlQmIUVECs03FHr923Z\/2fOQGmdsHinQHe3q0jTAk6T0bD5aecjoOCKGK3Qp27ZtGzfeeGPuz\/PmzSMsLIwZM2Ywbtw43n\/\/fb799tsyCSkiUiRdn4BaLeB8PCx\/yeg0UgAHs4l\/39IUgDl\/HePEOS2\/JFVboUvZuXPn8Pf3z\/35zz\/\/5JZbbsn9uWPHjhw\/frxYIT766CPq1auHq6srYWFhbNy4sVCvmzdvHiaTiYEDBxbrc0WkknJwujB3mQm2\/Q8iVxudSArQu3FNutSvQWaOhXd+O2B0HBFDFbqU+fv7ExkZCUBmZiZbtmyhc+fOuc8nJyfj5ORU5ADz589n3LhxTJw4kS1bttCmTRv69OlDbGzsVV939OhRnnnmGXr06FHkzxSRKiCoE1w3ynZ\/yZOQlW5oHMmfyWRiQj\/baNn3206y51SSwYlEjFPoUtavXz\/Gjx\/P6tWrmTBhAu7u7nkK0Y4dO2jQoEGRA7zzzjuMGTOGkSNH0rx5c6ZPn467uzuzZs0q8DU5OTncd999vPrqq9SvX7\/InykiVUT4RPAIgLhDsOYdo9NIAVoH+jCgTR2sVpi8dJ\/RcUQMU+hS9vrrr+Po6EivXr2YMWMGM2bMwNnZOff5WbNmcfPNNxfpwzMzM9m8eTPh4eGXApnNhIeHs25dwUulvPbaa9SqVYvRo0cX6fNEpIpx9YZb3rTdX\/0OnNHhMXv17M1NcHIwserAGdYc1BJ+UjU5FnZDPz8\/Vq1aRWJiIh4eHlcsSL5gwQI8PDyK9OFnz54lJycnz7lqYDtUum9f\/n9bWrNmDTNnzmTbtm2F+oyMjIw8U3UkJWloXKRKaX47NOoDB5fZDmMOXwLmUpmiUUpRcA137gsLYfZfR5n0615+atAds9lkdCyRclXkP5m8vb2vKGQAvr6+eUbOykJycjIPPPAAM2bMwM\/Pr1CvmTRpEt7e3rm3oKCgMs0oInbGZIL+U8DJHY6thW1fG51ICvDEDQ3xdHFk96kkftpxyug4IuXO0L8u+vn54eDgQExMTJ7HY2JiCAgIuGL7w4cPc\/ToUQYMGICjoyOOjo58+eWXLF68GEdHRw4fvnJZlQkTJpCYmJh7K+4VoiJSgfkEw\/Uv2O7\/9hKknDE2j+SrhocLj\/S2nZv89rL9ZGRr+SWpWgwtZc7OznTo0IEVK1bkPmaxWFixYgVdunS5YvumTZuyc+dOtm3blnu77bbbuP7669m2bVu+o2AuLi54eXnluYlIFRT2CAS0hvQE26SyYpdGdQvF38uFE+fO89mfR4yOI1KuDD+xYty4ccyYMYM5c+awd+9eHn30UVJTUxk5ciQAw4YNY8KECQC4urrSsmXLPDcfHx88PT1p2bJlmR8+FZEKzMERBrwHJjPs\/BYO\/2F0IsmHm7MDz\/drBsD7fxxk96lEgxOJlB\/DS9ngwYOZMmUKL7\/8Mm3btmXbtm0sXbo09+T\/qKgoTp8+bXBKEakU6raHTg\/b7i8ZB1nnjc0j+bqtTR36tgggK8fK099u12FMqTJMVqvVanSI8pSUlIS3tzeJiYk6lClSFWUkw0dhkHQSeo2H6ycYnUjycTYlgz7vriIuNZPHrm\/As32aGh1JpNgK2z0MHykTESlXLp5w839s99d\/Auk6PGaP\/Dxc+O8dLQH4JOIwW6POGZxIpOyplIlI1dN8IPg1gYxE+Hum0WmkAH1b1uaOdnWxWOHpb7dzPlOHMaVyUykTkarHbIYe42z3130EmWnG5pECvTKgBf5eLhw5m8pby7QEk1RuKmUiUjW1vAt8QiDtLGz50ug0UgBvdyfeHNQagC\/WHuWvw1qCSSovlTIRqZocHKH7k7b7f70P2ZmGxpGC9W5SiyGdggF4dsEOUjKyDU4kUjZUykSk6mp7H3jWtl2JuX2u0WnkKl7o34zA6m6cTDjPf3\/eY3QckTKhUiYiVZejC3R9wnZ\/zbuQoxEYe+Xh4siUu9sAMHfjcVbujzU4kUjpUykTkaqtwwhw84VzkbDnB6PTyFV0rl+DUd1CAfj3wh0kpOmQs1QuKmUiUrU5V4PO\/2e7v3oqWCzG5pGreq5vE+rXrEZscgavLN5tdByRUqVSJiLSaQy4eEHsHjjwq9Fp5CpcnRyYencbzCb4Ydspft2pZfik8lApExFx84GOD9rur5oCVWv1uQqnXXB1Hu3dAIAXftjF2ZQMgxOJlA6VMhERgC6PgaMbnNoCR1YanUau4V83NqJpgCfxqZk8v2gnVWwZZ6mkVMpERACq+dlO+gdYNdXQKHJtLo4OvHNPW5wcTPy2J4Yftp00OpJIiamUiYhc1PUJMDvBsTUQtd7oNHINzet4MfbGRgC8\/ONuTieeNziRSMmolImIXORdF9oOsd1frdGyiuCRXg1oE+hNcno2\/\/5OhzGlYlMpExG5XLcnwWSGg7\/B6e1Gp5FrcHQwM\/Wetrg4mll14AxzNx43OpJIsamUiYhcrkYDaDnIdl+jZRVCw1oePNe3KQD\/+XkPUXFpBicSKR6VMhGRf+o+zvbPPYvhzH5js0ihjOxaj7BQX9Iyc3hm4XYsFh3GlIpHpUxE5J\/8m0PTWwGrbU1MsXtms4kpd7fB3dmBjZHxfPHXUaMjiRSZSpmISH56XBgt2\/EtnDtqaBQpnCBfd17s3xyAt5bu41BsisGJRIpGpUxEJD91O0D968GaA2vfNzqNFNKQTkH0bFyTjGwLTy\/YTnaO1jKVikOlTESkID2fsf1z69eQHG1sFikUk8nEW4Na4+XqyPbjCXy66ojRkUQKTaVMRKQgId0gqDPkZMBfHxidRgopwNuVV29vAcC03w+w51SSwYlECkelTESkICbTpdGyTV9AWryxeaTQBratS58W\/mTlWBn37TYysnOMjiRyTSplIiJX0zAcareBrFRY\/4nRaaSQTCYT\/72jFb7VnNkXncz7Kw4aHUnkmlTKRESuxmSCHk\/b7m\/8FNJ1KKyi8PNw4Y07WgLwScRhtkadMziRyNWplImIXEvTAeDXGNITYdNMo9NIEfRtWZuBbetgscLT327nfKYOY4r9UikTEbkWs\/nSLP\/rPoKs88bmkSJ59baW+Hu5cORsKm8v0woNYr9UykRECqPVXeATDKlnYMuXRqeRIvB2d2LyoNYAzFobybrDcQYnEsmfSpmISGE4OEG3J233174H2ZmGxpGiub5JLYZ0CgLg2YXbScnINjiRyJVUykRECqvtfeARAEknYcc8o9NIEb3QvzmB1d04ce48\/\/15r9FxRK6gUiYiUlhOrtD1Cdv9Ne9CjkZbKhIPF0fevqsNAHM3RhGxP9bgRCJ5qZSJiBRFhxHgVh3ij8CeH4xOI0XUpUENRnarB8C\/v9tBYlqWsYFELqNSJiJSFC4e0Pn\/bPdXvwMWLXhd0TzXpyn1\/aoRk5TBKz\/tNjqOSC6VMhGRouo0Bpw9IXY3HFhqdBopIjdnB6bc0wazCb7fepLf98QYHUkEUCkTESk6t+rQ6UHb\/dVTwGo1No8UWfvg6ozpUR+A13\/eo7UxxS6olImIFEfnx8DRDU5uhiMRRqeRYnjixkbU8nThWFwaM9dEGh1HRKVMRKRYPGpCh+G2+6unGptFisXDxZHxtzQF4MM\/DhGTlG5wIqnqVMpERIqr6xNgdoKjqyFqg9FppBgGtq1Lu2Af0jJzePPXfUbHkSpOpUxEpLi8A6HNvbb7Gi2rkMxmE68MaIHJBIu2nmTzsXNGR5IqTKVMRKQkuj8FJjMcXAandxidRoqhTZAPd3cIBODVn3ZjsejCDTGGSpmISEnUaAAt7rTd12hZhfVsn6Z4ujiy40QiCzefMDqOVFEqZSIiJdXjads\/9\/wIZw4Ym0WKpaanC\/+6sREAby3bR1K6ZvqX8qdSJiJSUv7NoUl\/wGpbE1MqpOFd61G\/ZjXOpmTywYqDRseRKkilTESkNFwcLdsxH84dMzaLFIuzo5mXbm0OwBdrj3IoNsXgRFLVqJSJiJSGwA5QvzdYc+Cv941OI8V0fZNa3Ni0FtkWK68v2YNVqzVIOVIpExEpLT2esf1zy1eQHG1sFim2F29tjpODiT8PnOGPfbFGx5EqRKVMRKS01OsOQWGQkwHrPjQ6jRRTqF81RnUPBeD1JVoXU8qPSpmISGkxmS6Nlv09C9Lijc0jxfbEDY2o6enC0bg0vlh71Og4UkWolImIlKZGN0FAK8hKhQ3TjU4jxeTh4si\/+9rWxfxgxUFitS6mlAOVMhGR0mQyXboSc8N0SE8yNo8U253t6tI2yIfUzBzeXLrf6DhSBaiUiYiUtma3QY1GkJ4Im2YanUaKyWw28cptLQD4bssJtkZpXUwpWyplIiKlzewAPcbZ7q\/7CLLOG5tHiq1tkA93XVgX85XFWhdTypZdlLKPPvqIevXq4erqSlhYGBs3bixw2xkzZtCjRw+qV69O9erVCQ8Pv+r2IiKGaHU3+ARD6hmYc5ttmgwdyqyQnuvbBA8XR7afSOS7LVoXU8qO4aVs\/vz5jBs3jokTJ7JlyxbatGlDnz59iI3Nf26YiIgIhgwZwsqVK1m3bh1BQUHcfPPNnDx5spyTi4hchYMT3PQ6mMxwYiMsfhymNIKFo+Hg75CTbXRCKaRanq48cUNDAN5cup9krYspZcRkNXi64rCwMDp27MiHH9rm9LFYLAQFBfHEE08wfvz4a74+JyeH6tWr8+GHHzJs2LBrbp+UlIS3tzeJiYl4eXmVOL+IyFUlnoAd38L2uXD2ssXKPQKg9d3QZgj4tzAunxRKZraFPtNWEXk2lYd71mdCv2ZGR5IKpLDdw9CRsszMTDZv3kx4eHjuY2azmfDwcNatW1eo90hLSyMrKwtfX998n8\/IyCApKSnPTUSk3HgH2s4ve2wjjFkJnR4GN19IiYa\/PoBPusL07rZzz1I0e7y9cnY08\/KFdTFnrY3kyBmtiymlz9BSdvbsWXJycvD398\/zuL+\/P9HRhVui5N\/\/\/jd16tTJU+wuN2nSJLy9vXNvQUFBJc4tIlJkJhPUbQ\/93oKn98O930CzAWB2guidsOx5mNoU\/ncP7FoEWZoXy95c37QW1zepSVaObV1MkdJm+DllJTF58mTmzZvH999\/j6ura77bTJgwgcTExNzb8ePHyzmliMg\/ODpD0\/4w+Gt45gD0nwqBHW2LmR9cBgtHwpTGsPhfcGwdaFFsu\/HShXUxV+4\/w0qtiymlzNBS5ufnh4ODAzExMXkej4mJISAg4KqvnTJlCpMnT+a3336jdevWBW7n4uKCl5dXnpuIiN1w94WOD8KDv8Pjm23LNHkHQUYibJkDX\/SF99vCykkQf8TotFVe\/ZoejOx2aV3MzGyLwYmkMjG0lDk7O9OhQwdWrFiR+5jFYmHFihV06dKlwNe99dZbvP766yxdupTrrruuPKKKiJQ9v4Zw40swdgcMXwJt7wdnDzh3FP6cDO+3g5l9YPNsOJ9gcNiq64kbGuLn4cKRs6nM\/ivS6DhSiRh+9eX8+fMZPnw4n376KZ06dWLatGl8++237Nu3D39\/f4YNG0bdunWZNGkSAG+++SYvv\/wy33zzDd26dct9Hw8PDzw8PK75ebr6UkQqlMw02PczbP8GjkSA9cLIjIMLNO1nu3qzwQ22KTik3Hy76TjPLdyBh4sjfzzTi1qe+Z9CIwKF7x6GlzKADz\/8kLfffpvo6Gjatm3L+++\/T1hYGAC9e\/emXr16zJ49G4B69epx7NixK95j4sSJvPLKK9f8LJUyEamwkk7BzgWwbS6c2Xvp8Wo1oeVd0DAcgsPAxdO4jFWExWLljo\/Xsv1EInd1CGTK3W2MjiR2rEKVsvKkUiYiFZ7VCtE7YPs82xxoaWcvPWdygNptIKQr1OsOwV3AzcewqJXZ1qhz3PHxXwD88Fg32gb5GBtI7JZKWQFUykSkUsnJgkMrYO9iOLoGEv55JMEEAS0hpNulW7UahkStjMZ9u41FW07SNsiHRY92xWw2GR1J7JBKWQFUykSkUks8Acf+shW0Y2sh7tCV29Rsaitn9bpBSHfw9L9yGymU2KR0rp8SQWpmDlPvbsOgC4uXi1xOpawAKmUiUqUkR9tK2rG1cHRt3nPRLqrR0Ha4M6S7rah5q1gUxScRh3lz6T5qerqw8pneeLg4Gh1J7IxKWQFUykSkSkuNg6i\/bAXt2BqI3gX8438DPsGXClpIN6hez7YigeQrIzuHPu+u4mhcGg\/3qs+EW7QupuSlUlYAlTIRkcucPwdRG2wF7ehaOL3dtrLA5bzqXhhJ6wahPaFGA2Oy2rEVe2MYPWcTTg4mfnuqF6F+1YyOJHZEpawAKmUiIleRkQzHN1wYSVsLJ7eAJSvvNr2fh17PafTsMlarlRFf\/M2fB85wY9NazBzR0ehIYkdUygqgUiYiUgSZaXBiY96LB8C2HNQNL6qYXeZQbAp9p60i22Jl9siO9G5Sy+hIYicK2z0q9ILkIiJSxpzdoX5vuP55GPkL3Pxf2+Orp8DvE7VY+mUa1vJgRNd6ALymdTGlGFTKRESk8Lo+Dn3ftN1f+x4se0HF7DL\/Cm+En4czR86k8uW6o0bHkQpGpUxERIqm8yPQf6rt\/vqP4Nd\/q5hd4OXqxHN9mgLw3u8HOZOcYXAiqUhUykREpOg6PggD3gdMsPFT+HkcWHS4DuCuDoG0DvQmOSObt5ftMzqOVCAqZSIiUjwdhsPAjwETbJoFS8aqmAFms4mJA1oAsGDzCXacSDA2kFQYKmUiIlJ8bYfCnZ+ByQxbvoQfHwNLzrVfV8l1CKnOHe3qYrXCK4t3U8UmOpBiUikTEZGSaX0PDPocTA6w\/Rv4\/hHIyTY6leHG39IUd2cHtkQl8MO2k0bHkQpApUxEREqu5SC4+wswO8LOb2HRGMjJuvbrKjF\/L1ceu74hAJN+2UdSetX+9yHXplImIiKlo\/ntcM+XYHaC3Ytg4SjIzjQ6laFGdw8lpIY7sckZjJi1UcVMrkqlTERESk\/T\/jD4a3Bwhr2LYcEIyK6600K4Ojnw0dD2eLs5sSUqgQc+30BimoqZ5E+lTERESleTvnDvXHBwgf0\/w\/wHICvd6FSGaVnXm7ljOlPd3YntJxK5b+Z6zqVW7RFEyZ9KmYiIlL5G4TB0Pji6wcFlMG8oZJ03OpVhmtfxYu5DnalRzZldJ5MY+vkG4lKq7gii5E+lTEREykaD6+G+BeDkDodXwDeDbQucV1FNA7yY91Bn\/Dxc2Hs6iaEzNnBWxUwuo1ImIiJlJ7QH3P8dOHtA5J\/wv7shI8XoVIZp5O\/J\/Ic74+\/lwv6YZO79bD2xSVX30K7kpVImIiJlK6Qr3L8InD3h2Br4312QkWx0KsM0qOnB\/Ie6UNvblUOxKdz72XqiE1XMRKVMRETKQ3AYDPsRXLwhah18dQekJxqdyjD1\/Kox\/6Eu1PVx48jZVAZ\/to5TCVX3nDuxUSkTEZHyEdgBhv8Irj5w4m\/4ciCcP2d0KsME13Bn\/sOdCfJ141hcGoM\/W8fx+Kp7zp2olImISHmq0w6G\/wRuvnBqC3x5O6TFG53KMIHV3Zn\/UBfq1XDnePx57v1sPVFxKmZVlUqZiIiUr9qtYcQScPeD09thzm2QetboVIap4+PGvIe6UN+vGicTzjP4s3VEnk01OpYYQKVMRETKn38LGPEzVKsFMTthzgBIOWN0KsMEeLsy7+HONKzlwenEdAZ\/uo7DZ6ruVapVlUqZiIgYo1ZTGPkLeNaG2D0wuz8kRxudyjC1PF2Z91Bnmvh7EpucweBP13MwpupepVoVqZSJiIhx\/BrZRsy86sLZ\/bZilnTK6FSG8fNwYe5DnWlW24uzKRnc+9l69kUnGR1LyolKmYiIGKtGA1sx8w6CuEPwRT9IPGF0KsP4VnNm7pgwWtb1Ii41kyGfrWf3qao7fUhVolImIiLG8w21Hcr0CYFzkfDFLbDruyq7XqaPuzP\/G92ZNoHenEvLYuiMDew8oWJW2amUiYiIffAJthUz3\/qQEAULR8GUxrD4CTj2F1itRicsV97uTnz1YBjtg31IPJ\/F0M\/Xs+14gtGxpAyZrNaq9V95UlIS3t7eJCYm4uXlZXQcERH5p9SzsP4T2DEfEo9fetwnBNrca7v51jcuXzlLychm5Bcb+fvoOTxdHJk9qhMdQqobHUuKoLDdQ6VMRETsk8UCx9bC9nmw5wfIvGyKiKDOtnLW4g5w8zEqYblJzchm9Jy\/WX8knmrODnwxshOdQn2NjiWFpFJWAJUyEZEKKDMN9v0M2+fCkZVgtdged3CBJrdAmyHQ8EZwcDI2Zxk6n5nDg1\/+zdpDcbg5OTBrREe6NKhhdCwpBJWyAqiUiYhUcEmnYee3sG0unNl76fFqNaHV3bYRtIDWYDIZl7GMpGfl8NBXm1l14AyuTmY+H9aR7o38jI4l16BSVgCVMhGRSsJqhegdtsObO76FtMuWaqrV3FbOWt0DXrWNy1gG0rNy+L\/\/beGPfbE4O5r57IEO9G5Sy+hYchUqZQVQKRMRqYRysuDwH7DtG9j\/K+Rk2B43maF+b9vhzab9wbmaoTFLS0Z2Do9\/s5Xle2JwdjDzyf3tubGZv9GxpAAqZQVQKRMRqeTOn4PdP9hG0I6vv\/S4swc0H2gbQQvpBuaKPStUZraFf83dytLd0Tg5mPhwaHv6tAgwOpbkQ6WsACplIiJVSNxh26HN7XMh4dilx72DoPVgW0Hza2RcvhLKyrHw5Pxt\/LzjNI5mE+8PaUe\/VpXrcG1loFJWAJUyEZEqyGqFqHW2crb7B8i4bD3JutdB2yHQ4k5wr3jTTGTnWHh6wXZ+3GZbMzTY152wUF86hfrSuX4NAqu7YaqEFz1UJCplBVApExGp4rLOw\/5fbFdvHv4DrDm2x81O0KTvhek1bgJHZ2NzFkGOxcori3fzvw3HsPzj\/+p1vF0Jq1+DTqG+hIX6EupXTSWtnKmUFUClTEREciXHwM4FtvPPYnZeetzNF1rdZStoddpVmOk1ktOz2HzsHBsi49lwJI4dJxLJ\/kdLq+npQtiFghZWvwaNanmopJUxlbICqJSJiEi+onfaytnOBZASc+lxvya2c89a3wPegcblK4a0zGy2RiWw4Ugc6yPj2XY8gcxsS55tfKs506meL2H1bYc8mwV4YTaXT0lLz8rhZMJ5Tp47z8mE85w4l8bJc+c5ceFnqxU61Kt+oUTaCmR5ZStNKmUFUCkTEZGrysmGIxG288\/2LYHs9AtPmCC0p230rNkAcPEwMmWxpGflsO14Ahsj49kQGcfmY+dIz8pb0rxcHS8c6rQd8mxRxwtHh+JdqZqSkX2hcF0qWycSLpSuc+c5m5JRpPer7u6UJ1uz2l44VICSplJWAJUyEREptPRE2POjbQTt2NpLjztVg+a32UbQ6vUAs4NxGUsgM9vCzpMJrD8Sz8bIeDYdjSc1MyfPNh4ujnQIqU5Yfdshz1Z1fXB2NGO1Wkk6n82JhLTcknXiYgG7ULwS0rKumcHd2YHA6m7U9XGjbnU3Aqu7597PzLZctUB6ujpeNspXg5YlKJBlSaWsACplIiJSLOeOXppeI\/7Ipce96l6aXqNmE8PilYbsHAu7TyWxITKODUfi2Xg0nuT07DzbuDk5ULe6G9GJ6aRkZBfwTpd4uTrailZ1t9zyFXhZ+fJxdyrUOW22ApmYmy2\/AlnN2YEO9Xxzz5lrHWgrkEZTKSuASpmIiJSI1Qon\/raVs13f2UbTLqrT3nZ4s+UgqFbxFwvPsVjZF53EhiO20aqNkfGc+8fol5+H85WjXD5uBPra\/unpWjaLxGfnWNhzOm+2pH8USFcnM+2DqxMWWoOw+r60DfLB1an8RzVVygqgUiYiIqUmKx0OLrNNr3FoOVgulAKzIzTqY5v\/rNHN4OhibM5SYrFYORibQkxSOnUulC83Z\/s4dJtjsbI\/OjnPKF98amaebZwdzLQN8rlwKLYG7UN8cHd2LPNsKmUFUCkTEZEykXLGNnK2fS6c3nbpcbfqtuWd6ve2Le\/kUdOggCWUkw3R2+HoWjgfD4EdIbiL3U64a7VaORSbwvoL04NsiIznTHLeCwsczSZaBXoTFlqD+8KCCfJ1L5MsKmUFUCkTEZEyF7vXdnHAjm8h+VTe5\/yaQEhXqNfdVtK87HRZpOxMOLXFdoHD0bVwfANkply5Xa0WUK+bbV\/suHRarVaOxqXlFrQNR+I4lZie+\/yvY3vQrHbZ9AKVsgKolImISLmx5EDkn7D\/V1uxid195Ta+9W0lLaS7rdz4BJd\/TrAdij25yZbz2Bo4\/jdkn8+7jas3BHeFan62knb2wJXv49fYVs7svHRarVZOnDvPhsh4th0\/x2u3tSyzOdBUygqgUiYiIoZJi7etwXl0rW0EKnoHWPNO84B38IWRp662UuNbv2xWFMhMheMbL42EndwEOXnPwcK9Rt7CWKt53uk\/UmIvvf7YX\/mXzuqhF\/bH4NJpoApVyj766CPefvttoqOjadOmDR988AGdOnUqcPsFCxbw0ksvcfToURo1asSbb75Jv379CvVZKmUiImI30hMhaoNtZOrYX3Bq66WLBS7yrH3h0OCFQ55+jYtX0tKTbKNbR9fYilR+n+Xhf2GU60KJqtmkaJ+VFm\/bj2N\/2fYpemc+pTPoss8ow9JpRypMKZs\/fz7Dhg1j+vTphIWFMW3aNBYsWMD+\/fupVavWFdv\/9ddf9OzZk0mTJnHrrbfyzTff8Oabb7JlyxZatmx5zc9TKRMREbuVkQInNl4aSTu5+crRq2o1L42ihVwcvcpnLq7z5+DYugsjWWvyH5XzCrxUjup1L\/2ClJ4IUesvjaad2nppAfiLPGvn3Z+iFsEKoMKUsrCwMDp27MiHH34IgMViISgoiCeeeILx48dfsf3gwYNJTU1lyZIluY917tyZtm3bMn369Gt+nkqZiIhUGFnn4cQmW6k5tjb\/87zcqtvO8wrpajt\/K2qDbduY3cA\/\/hdfvd6lw4gh3aB6SHntiU1Gim207thfBZdOd79Lo4L+LctvtYSA1uBs7NWXZT85x1VkZmayefNmJkyYkPuY2WwmPDycdevW5fuadevWMW7cuDyP9enThx9++CHf7TMyMsjIuHQJbFJSUsmDi4iIlAcnNwjtYbvBpSsiLx6CjNpgGxHb\/7Pt9k9+jS+dExbSFbzrlm\/+f3LxgIY32m5woXT+bStpR9fY7qedhb2Lbbfy9NhGw1dkMLSUnT17lpycHPz9\/fM87u\/vz759+\/J9TXR0dL7bR0dH57v9pEmTePXVV0snsIiIiJEcnSG4s+3GM7a5w05vt52\/dXQtpMZC3esujYR5XHkakF1xcrMt8h7a0\/Zzdgac3HJpZPDc0fLLYja0EgEGl7LyMGHChDwja0lJSQQFBRmYSEREpJQ4OEJgB9ut21ij05ScowuEdLHdeMboNOXO0FLm5+eHg4MDMTExeR6PiYkhICAg39cEBAQUaXsXFxdcXCrH8hYiIiJSeRm6dLqzszMdOnRgxYoVuY9ZLBZWrFhBly5d8n1Nly5d8mwPsHz58gK3FxEREakIDD98OW7cOIYPH851111Hp06dmDZtGqmpqYwcORKAYcOGUbduXSZNmgTA2LFj6dWrF1OnTqV\/\/\/7MmzePTZs28dlnnxm5GyIiIiIlYngpGzx4MGfOnOHll18mOjqatm3bsnTp0tyT+aOiojBfNv9K165d+eabb3jxxRd5\/vnnadSoET\/88EOh5igTERERsVeGz1NW3jRPmYiIiJSnwnYPQ88pExEREREblTIRERERO6BSJiIiImIHVMpERERE7IBKmYiIiIgdUCkTERERsQMqZSIiIiJ2QKVMRERExA4YPqN\/ebs4V25SUpLBSURERKQquNg5rjVff5UrZcnJyQAEBQUZnERERESqkuTkZLy9vQt8vsots2SxWDh16hSenp6YTKYy+YykpCSCgoI4fvx4lVrKqSrud1XcZ9B+V6X9ror7DFVzv6viPkP57LfVaiU5OZk6derkWc\/7n6rcSJnZbCYwMLBcPsvLy6tK\/Yd9UVXc76q4z6D9rkqq4j5D1dzvqrjPUPb7fbURsot0or+IiIiIHVApExEREbEDKmVlwMXFhYkTJ+Li4mJ0lHJVFfe7Ku4zaL+r0n5XxX2GqrnfVXGfwb72u8qd6C8iIiJijzRSJiIiImIHVMpERERE7IBKmYiIiIgdUCkTERERsQMqZdfwySef0Lp169xJ5bp06cKvv\/561dcsWLCApk2b4urqSqtWrfjll1\/yPG+1Wnn55ZepXbs2bm5uhIeHc\/DgwbLcjSIp6j7PmDGDHj16UL16dapXr054eDgbN27Ms82IESMwmUx5bn379i3rXSmSou737Nmzr9gnV1fXPNvY++8air7fvXv3vmK\/TSYT\/fv3z92mIvy+Lzd58mRMJhNPPvnkVber6N\/tfyrMfleW7\/dFhdnnyvLdvlxh9rsyfLdfeeWVK\/I1bdr0qq+xp++1Stk1BAYGMnnyZDZv3symTZu44YYbuP3229m9e3e+2\/\/1118MGTKE0aNHs3XrVgYOHMjAgQPZtWtX7jZvvfUW77\/\/PtOnT2fDhg1Uq1aNPn36kJ6eXl67dVVF3eeIiAiGDBnCypUrWbduHUFBQdx8882cPHkyz3Z9+\/bl9OnTube5c+eWx+4UWlH3G2wzQF++T8eOHcvzvL3\/rqHo+71o0aI8+7xr1y4cHBy4++6782xn77\/vi\/7++28+\/fRTWrdufdXtKsN3+3KF3e\/K8v2Gwu8zVI7v9kWF3e\/K8t1u0aJFnnxr1qwpcFu7+15bpciqV69u\/fzzz\/N97p577rH2798\/z2NhYWHWhx9+2Gq1Wq0Wi8UaEBBgffvtt3OfT0hIsLq4uFjnzp1bdqFL6Gr7\/E\/Z2dlWT09P65w5c3IfGz58uPX2228vo3Rl52r7\/cUXX1i9vb0LfG1F\/V1brUX7fb\/77rtWT09Pa0pKSu5jFeX3nZycbG3UqJF1+fLl1l69elnHjh1b4LaV6btdlP3+p4r6\/S7KPlem73ZJftcV8bs9ceJEa5s2bQq9vb19rzVSVgQ5OTnMmzeP1NRUunTpku8269atIzw8PM9jffr0Yd26dQBERkYSHR2dZxtvb2\/CwsJyt7Enhdnnf0pLSyMrKwtfX988j0dERFCrVi2aNGnCo48+SlxcXFlELhWF3e+UlBRCQkIICgq6YnSpov2uoXi\/75kzZ3LvvfdSrVq1PI9XhN\/3Y489Rv\/+\/a\/4zuanMn23i7Lf\/1RRv99F3efK8t0uye+6on63Dx48SJ06dahfvz733XcfUVFRBW5rb9\/rKrcgeXHs3LmTLl26kJ6ejoeHB99\/\/z3NmzfPd9vo6Gj8\/f3zPObv7090dHTu8xcfK2gbe1CUff6nf\/\/739SpUyfPf8R9+\/blzjvvJDQ0lMOHD\/P8889zyy23sG7dOhwcHMpqN4qsKPvdpEkTZs2aRevWrUlMTGTKlCl07dqV3bt3ExgYWGF+11D83\/fGjRvZtWsXM2fOzPN4Rfh9z5s3jy1btvD3338XavvK8t0u6n7\/U0X8fhd1nyvLd7skv+uK+t0OCwtj9uzZNGnShNOnT\/Pqq6\/So0cPdu3ahaen5xXb29v3WqWsEJo0acK2bdtITExk4cKFDB8+nD\/\/\/LPQJaUiKu4+T548mXnz5hEREZHnxNh77703936rVq1o3bo1DRo0ICIightvvLHM9qOoirLfXbp0yTOa1LVrV5o1a8ann37K66+\/Xp6xS6y4v++ZM2fSqlUrOnXqlOdxe\/99Hz9+nLFjx7J8+fIrTuCuzEq63xXx+12cfa4M3+2S\/q4r6nf7lltuyb3funVrwsLCCAkJ4dtvv2X06NEGJiscHb4sBGdnZxo2bEiHDh2YNGkSbdq04b333st324CAAGJiYvI8FhMTQ0BAQO7zFx8raBt7UJR9vmjKlClMnjyZ33777ZonlNavXx8\/Pz8OHTpUmrFLrDj7fZGTkxPt2rXL3aeK8ruG4u13amoq8+bNK9QfdPb2+968eTOxsbG0b98eR0dHHB0d+fPPP3n\/\/fdxdHQkJyfnitdUhu92cfb7oor6\/S7JPl9UEb\/bJdnvivzd\/icfHx8aN25cYD57+16rlBWDxWIhIyMj3+e6dOnCihUr8jy2fPny3L91hYaGEhAQkGebpKQkNmzYUOhzeIxwtX0G29Upr7\/+OkuXLuW666675vudOHGCuLg4ateuXZoxS9219vtyOTk57Ny5M3efKurvGgq33wsWLCAjI4P777\/\/mu9nb7\/vG2+8kZ07d7Jt27bc23XXXcd9993Htm3b8j0MUxm+28XZb6jY3+\/i7vPlKuJ3uyT7XZG\/2\/+UkpLC4cOHC8xnd9\/rUr90oJIZP3689c8\/\/7RGRkZad+zYYR0\/frzVZDJZf\/vtN6vVarU+8MAD1vHjx+duv3btWqujo6N1ypQp1r1791onTpxodXJysu7cuTN3m8mTJ1t9fHysP\/74o3XHjh3W22+\/3RoaGmo9f\/58ue9ffoq6z5MnT7Y6OztbFy5caD19+nTuLTk52Wq12q7+eeaZZ6zr1q2zRkZGWn\/\/\/Xdr+\/btrY0aNbKmp6cbso\/5Kep+v\/rqq9Zly5ZZDx8+bN28ebP13nvvtbq6ulp3796du429\/66t1qLv90Xdu3e3Dh48+IrHK8rv+5\/+eWVaZfxu5+da+11Zvt+Xu9Y+V5bv9j9da78vqsjf7aefftoaERFhjYyMtK5du9YaHh5u9fPzs8bGxlqtVvv\/XquUXcOoUaOsISEhVmdnZ2vNmjWtN954Y+7\/rKxW23\/kw4cPz\/Oab7\/91tq4cWOrs7OztUWLFtaff\/45z\/MWi8X60ksvWf39\/a0uLi7WG2+80bp\/\/\/7y2J1CKeo+h4SEWIErbhMnTrRarVZrWlqa9eabb7bWrFnT6uTkZA0JCbGOGTPGGh0dXc57dnVF3e8nn3zSGhwcbHV2drb6+\/tb+\/XrZ92yZUue97T337XVWrz\/xvft22cF8mx3UUX5ff\/TP\/+HVRm\/2\/m51n5Xlu\/35a61z5Xlu\/1PhflvvKJ\/twcPHmytXbu21dnZ2Vq3bl3r4MGDrYcOHcp93t6\/1yar1Wot\/fE3ERERESkKnVMmIiIiYgdUykRERETsgEqZiIiIiB1QKRMRERGxAyplIiIiInZApUxERETEDqiUiYiIiNgBlTIRqfKOHj2KyWRi27ZthX7N7Nmz8fHxKbNMIlL1qJSJiIiI2AGVMhERERE7oFImIlXC0qVL6d69Oz4+PtSoUYNbb72Vw4cP57ttREQEJpOJn3\/+mdatW+Pq6krnzp3ZtWvXFdsuW7aMZs2a4eHhQd++fTl9+nTuc3\/\/\/Tc33XQTfn5+eHt706tXL7Zs2VJm+ygiFZtKmYhUCampqYwbN45NmzaxYsUKzGYzd9xxBxaLpcDXPPvss0ydOpW\/\/\/6bmjVrMmDAALKysnKfT0tLY8qUKXz11VesWrWKqKgonnnmmdznk5OTGT58OGvWrGH9+vU0atSIfv36kZycXKb7KiIVk6PRAUREysOgQYPy\/Dxr1ixq1qzJnj178PDwyPc1EydO5KabbgJgzpw5BAYG8v3333PPPfcAkJWVxfTp02nQoAEAjz\/+OK+99lru62+44YY87\/fZZ5\/h4+PDn3\/+ya233lpq+yYilYNGykSkSjh48CBDhgyhfv36eHl5Ua9ePQCioqIKfE2XLl1y7\/v6+tKkSRP27t2b+5i7u3tuIQOoXbs2sbGxuT\/HxMQwZswYGjVqhLe3N15eXqSkpFz1M0Wk6tJImYhUCQMGDCAkJIQZM2ZQp04dLBYLLVu2JDMzs9jv6eTklOdnk8mE1WrN\/Xn48OHExcXx3nvvERISgouLC126dCnRZ4pI5aVSJiKVXlxcHPv372fGjBn06NEDgDVr1lzzdevXryc4OBiAc+fOceDAAZo1a1boz127di0ff\/wx\/fr1A+D48eOcPXu2GHsgIlWBSpmIVHrVq1enRo0afPbZZ9SuXZuoqCjGjx9\/zde99tpr1KhRA39\/f1544QX8\/PwYOHBgoT+3UaNGfPXVV1x33XUkJSXx7LPP4ubmVoI9EZHKTOeUiUilZzabmTdvHps3b6Zly5Y89dRTvP3229d83eTJkxk7diwdOnQgOjqan376CWdn50J\/7syZMzl37hzt27fngQce4F\/\/+he1atUqya6ISCVmsl5+AoSIiBAREcH111\/PuXPntJSSiJQbjZSJiIiI2AGVMhERERE7oMOXIiIiInZAI2UiIiIidkClTERERMQOqJSJiIiI2AGVMhERERE7oFImIiIiYgdUykRERETsgEqZiIiIiB1QKRMRERGxAyplIiIiInZApUxERETEDqiUiYiIiNgBlTIRERERO6BSJiIiImIHVMpERERE7IBKmYiIiIgdUCkTERERsQMqZSIiIiJ2QKVMRERExA6olImIiIjYAZUyERERETugUiYiIiJiB1TKREREROyASpmIiIiIHVApExEREbEDKmUiIiIidsDR6ADlzWKxcOrUKTw9PTGZTEbHERERkUrOarWSnJxMnTp1MJsLHg+rcqXs1KlTBAUFGR1DREREqpjjx48TGBhY4PNVrpR5enoCtn8xXl5eBqcRERGRyi4pKYmgoKDcDlKQKlfKLh6y9PLyUikTERGRcnOt06Z0or+IiIiIHVApExEREbEDKmUiIiIidkClTERERMQOqJSJiIiI2AGVMhERERE7oFImIiIiYgdUykRERETsgEqZiIiIiB1QKRMRERGxAyplIiIiInZApUxEpIykZ+WwbHc0JxPOGx1FRCqAKrcguYhIeZm5JpK3l+3HZIKuDWowqH0gfVsG4O6sP3pF5Er6k0FEpIz8fTQeAKsV1h6KY+2hOF76YRf9W9fmrg5BdKxXHZPJZHBKEbEXKmUiImVkf3QyAO\/d25ZjcWks3HyCqPg0vt10gm83nSDY151B7QO5s31dgnzdDU4rIkYzWa1Wq9EhylNSUhLe3t4kJibi5eVldBwRqaQS07Jo89pvAOx45Wa8XJ2wWq38ffQcCzcf5+cdp0nNzMndvkv9GgzqEMgtLQOo5qK\/L4tUJoXtHiplIiJlYMOROAZ\/tp66Pm6sHX\/DFc+nZWazbHc0Czef4K\/DcVz8k9jd2YF+rWpzV4dAOtXzxWzW4U2Riq6w3UN\/HRMRKQP7Lhy6bFbbM9\/n3Z0duaNdIHe0C+TEuTS+33KS77ac4OiFw5wLN58gyNeNQe0DGdQ+UIc3RaqAEpcyq9XK5s2bOXr0KCaTidDQUNq1a6eTV0WkStsXnQRAk4D8S9nlAqu788SNjXj8hoZsPnaOhZtPsGTHaY7Hn2fa7weZ9vtBwkJ9uatDIP1a1dbhTZFKqkTf7JUrVzJ69GiOHTvGxaOgF4vZrFmz6NmzZ6mEFBGpaC6OlDUNKPxpEiaTievq+XJdPV8mDmjBst3RfLflBGsOnWVDZDwbIuN5+cfd3NIqgLs6BNI5tIYOb4pUIsU+p+zQoUO0adOGsLAwxo4dS9OmTbFarezZs4f333+fTZs2sWPHDurXr1\/amUtE55SJSFmzWKy0fGUZaZk5\/D6uJw1rXXu07GpOJZzn+60nWbj5BJFnU3Mfr+vjxqAOgQxqX5eQGtVKGltEykiZn+j\/+OOPs3fvXlasWHHFc1arlfDwcJo3b84HH3xQnLcvMyplIlLWjsWl0uvtCJwdzex5tQ+ODqWzeIrVamVLVILt8Ob2UyRnZOc+Fxbqy5S72+jcMxE7VNjuUew\/KSIiInjyySfzfc5kMvHkk0+ycuXK4r69iEiFdfHQZaNaHqVWyMD2Z2uHkOpMurMVf78Yznv3tqVn45qYTLAhMp7nv99Zap8lIuWv2H9aREVF0apVqwKfb9myJceOHSvSe06aNImOHTvi6elJrVq1GDhwIPv378+zTXp6Oo899hg1atTAw8ODQYMGERMTU6x9EBEpC\/tOF\/18sqJydXLg9rZ1+XJUJ357sidODiZWHzzLX4fPltlnikjZKnYpS0lJwd294GFyd3d30tLSivSef\/75J4899hjr169n+fLlZGVlcfPNN5OaeukciqeeeoqffvqJBQsW8Oeff3Lq1CnuvPPO4u6GiEip2x9ju\/KyaSGuvCwNjfw9GdIpGIC3lu6nik0\/KVJplOjqyz179hAdHZ3vc2fPFv1va0uXLs3z8+zZs6lVqxabN2+mZ8+eJCYmMnPmTL755htuuME2GeMXX3xBs2bNWL9+PZ07dy76ToiIlLLckbIC5igrC4\/f0JAFm06w7XgCv+2JoU+LgHL7bBEpHSUqZTfeeGO+fyMzmUxYrdYSz1WWmJgIgK+vLwCbN28mKyuL8PDw3G2aNm1KcHAw69aty7eUZWRkkJGRkftzUlJSiTKJiFzN+cwcIuNso\/uFmaOstNTydGVU93p8tPIwU5btJ7yZPw6aLkOkQil2KYuMjCzNHFewWCw8+eSTdOvWjZYtWwIQHR2Ns7MzPj4+ebb19\/cvcMRu0qRJvPrqq2WaVUTkooOxyVitUKOaMzU9XMr1sx\/q2YCv10dxMDaF77ee5K4OgeX6+SJSMsUuZSEhIaWZ4wqPPfYYu3btYs2aNSV6nwkTJjBu3Ljcn5OSkggKCippPBGRfF1+6LK8VzbxdnPi\/3o3YNKv+3h3+QEGtKmNi6NDuWYQkeIrdinbsWNHobZr3bp1kd\/78ccfZ8mSJaxatYrAwEt\/0wsICCAzM5OEhIQ8o2UxMTEEBOR\/\/oSLiwsuLuX7t1URqbr2Xlxeyd+YeRCHd63HrLWRnEw4zzcbohjZLdSQHCJSdMUuZW3bts09d6wgJpOJnJycQr+n1WrliSee4PvvvyciIoLQ0Lx\/mHTo0AEnJydWrFjBoEGDANi\/fz9RUVF06dKleDsiIlKK9keX\/0n+l3N1cmDsjY15\/vudfPjHIe6+LggPrZUpUiHY1Tlljz32GN988w0\/\/vgjnp6eueeJeXt74+bmhre3N6NHj2bcuHH4+vri5eXFE088QZcuXXTlpYgYzmq15k4c26wM5yi7lruvC+SzVYc5GpfGrDWR\/OvGRoZlEZHCs6tzyj755BMAevfunefxL774ghEjRgDw7rvvYjabGTRoEBkZGfTp04ePP\/641LOIiBTVmZQM4lMzMZugkb+HYTmcHMw8fXMTnpi7lc9WHeH+ziH4VnM2LI+IFE6xJ489e\/bsFTP27969m5EjR3LPPffwzTffFPk9rVZrvreLhQzA1dWVjz76iPj4eFJTU1m0aFGB55OJiJSniyf51\/OrhquTsSfY929VmxZ1vEjJyObjlYcMzSIihVPsUvbEE0\/w\/vvv5\/4cGxtLjx49+Pvvv8nIyGDEiBF89dVXpRJSRKQi2BddvjP5X43ZbOLZPk0A+HL9MU4lnDc4kYhcS7FL2fr167nttttyf\/7yyy\/x9fVl27Zt\/Pjjj7zxxht89NFHpRJSRKQiuHg+WVmueVkUvRrXJCzUl8xsC+\/9ftDoOCJyDcUuZdHR0dSrVy\/35z\/++IM777wTR0fbaWq33XYbBw\/qDwERqTouLURu\/EgZ2K6Af65vUwAWbD7OodgUgxOJyNUUu5R5eXmRkJCQ+\/PGjRsJCwvL\/dlkMuVZ3khEpDLLyrHklh57GSkD6BBSnfBm\/lis8M7y\/UbHEZGrKHYp69y5M++\/\/z4Wi4WFCxeSnJycu0g4wIEDBzRzvohUGUfPppKZY6GaswOB1d2MjpPHs32aYDLBLzuj2XEiweg4IlKAYpey119\/ncWLF+Pm5sbgwYN57rnnqF69eu7z8+bNo1evXqUSUkTE3u29cD5ZkwBPzHa2EHiTAE\/uaFsXgLeXabRMxF4Ve56y1q1bs3fvXtauXUtAQECeQ5cA9957L82bNy9xQBGRimD\/xeWV7OjQ5eWeuqkxP+04xeqDZ\/nr0Fm6NvQzOpKI\/EOxR8oA\/Pz8uP32268oZAD9+\/e\/YpkkEZHK6uJJ\/s0MWl7pWoJ83RnaKRiAN5ftv+oSeSJijBKVMhERsbk4HUYTf\/ssZQCP39AId2cHth9PYNnuGKPjiMg\/qJSJiJRQUnoWJy9MzmpPV17+U01PF0Z1sx3BmPLbfnIsGi0TsScqZSIiJbT\/wihZHW9XvN2dDE5zdQ\/1qo+PuxOHYlNYtOWE0XFE5DIqZSIiJbTvsisv7Z2XqxP\/17sBANN+P0hGdo7BiUTkohKXsl69evHll19y\/rzWVRORqmnf6QtrXta230OXlxvWpR4BXq6cTDjP\/9ZHGR1HRC4ocSlr164dzzzzDAEBAYwZM4b169eXRi4RkQrj0pqX9j9SBuDq5MDY8EYAfLjyECkZ2QYnEhEohVI2bdo0Tp06xRdffEFsbCw9e\/akefPmTJkyhZgYXd0jIpWb1WrNPafMnk\/y\/6e7OwQS6leN+NRMPl99xOg4IkIpnVPm6OjInXfeyY8\/\/siJEycYOnQoL730EkFBQQwcOJA\/\/vijND5GRMTunDh3npSMbJwcTNSvWc3oOIXm6GDm6ZsbA\/D56kjiUrRWsYjRSvVE\/40bNzJx4kSmTp1KrVq1mDBhAn5+ftx6660888wzpflRIiJ24eKhywY1PXByqFjXTvVrWZuWdb1Iycjm44jDRscRqfJK\/CdIbGwsU6dOpWXLlvTo0YMzZ84wd+5cjh49yquvvsrnn3\/Ob7\/9xvTp00sjr4iIXbm4vFKzCnKS\/+XMZhPP9mkKwFfrj+XOtSYixij22pcXBQYG0qBBA0aNGsWIESOoWbPmFdu0bt2ajh07lvSjRETszt4KdpL\/P\/Vs5Efn+r6sPxLPe78f4K272hgdSaTKKvFI2YoVK9i7dy\/PPvtsvoUMwMvLi5UrV5b0o0RE7M7+CjRHWX5MJhPP9bWNli3cfIJDsckGJxKpukpcynr06AHYDmOuXr2a1atXExsbW+JgIiL2Lj0rhyNnUoCKefjyovbB1bmpuT8WK0z97YDRcUSqrBKXsuTkZB544AHq1q1Lr1696NWrF3Xr1uX+++8nMTGxNDKKiNilQ7EpWKzg4+5ELU8Xo+OUyLN9mmAywa+7otl+PMHoOCJVUolL2YMPPsiGDRtYsmQJCQkJJCQksGTJEjZt2sTDDz9cGhlFROzS5ZPGmkwmg9OUTGN\/T+5oVxeAt5ftNziNSNVU4lK2ZMkSZs2aRZ8+ffDy8sLLy4s+ffowY8YMfvrpp9LIKCJil3KXV6pAk8ZezVPhjXFyMLHm0FnWHDxrdByRKqfEpaxGjRp4e3tf8bi3tzfVq1cv6duLiNitira80rUE+bpzX1gIAG8v24fVajU4kUjVUuJS9uKLLzJu3Diio6NzH4uOjubZZ5\/lpZdeKunbi4jYrdxSVoFP8v+nx65viLuzA9tPJLJsd\/S1XyAipaZY85S1a9cuz\/kTBw8eJDg4mODgYACioqJwcXHhzJkzOq9MRCqlsykZnE3JwGSCxv4eRscpNTU9XXiweyjv\/3GIt5ftJ7yZP44VbKUCkYqqWKVs4MCBpRxDRKRiuTg\/WYivO+7OJZ6H26482LM+X64\/xuEzqSzaepJ7rgsyOpJIlVCsP0kmTpxY2jlERCqUvZXsJP\/Lebk68Vjvhvz3l71MW36A29rUwdXJwehYIpWexqRFRIphXwWfyf9aHugSQoCXK6cS0\/l6\/TGj44hUCSplIiLFcPHwZbPalbOUuTo58GR4IwA+jjhMcnqWwYlEKj+VMhGRIsrOsXAg5uJ0GJXv8OVFd3UIpL5fNeJTM\/l8daTRcUQqPZUyEZEiOhqXRka2BTcnB4J93Y2OU2YcHcw8fXMTAD5ffYS4lAyDE4lUbiplIiJFdPHQZeMAT8zmir280rXc0jKAVnW9Sc3M4aOVh42OI1KpFevqy3HjxhV623feeac4HyEiYrf2RduuvGxWSU\/yv5zZbOLZPk0YNmsjX68\/xugeodT1cTM6lkilVKxStnXr1jw\/b9myhezsbJo0sQ1zHzhwAAcHBzp06FDyhCIidqayX3n5Tz0a+dGlfg3WHYlj2vIDvH13G6MjiVRKxSplK1euzL3\/zjvv4OnpyZw5c3LXujx37hwjR46kR48epZNSRMSOXBwpq8wn+V\/OZDLxbN8m3PnxX3y35QQP9axPI\/+qUUhFylOJzymbOnUqkyZNyrP4ePXq1fnPf\/7D1KlTS\/r2IiJ2JSUjm+Px54HKsxB5YbQPrs5Nzf2xWGH6n0eMjiNSKZW4lCUlJXHmzJkrHj9z5gzJycklfXsREbty8SR\/fy8XqldzNjhN+fq\/3g0A+Gn7KWKT0w1OI1L5lLiU3XHHHYwcOZJFixZx4sQJTpw4wXfffcfo0aO58847SyOjiIjdqGqHLi\/XLrg67YN9yMyx8PU6zfIvUtpKXMqmT5\/OLbfcwtChQwkJCSEkJIShQ4fSt29fPv7449LIKCJiNy6OlFWlQ5eXG929PgBfb4giPSvH4DQilUuJS5m7uzsff\/wxcXFxbN26la1btxIfH8\/HH39MtWrVSiOjiIjd2Hf6QimrpMsrXUufFv7U9XEjPjWT77eeNDqOSKVSapPHnj59mtOnT9OoUSOqVauG1WotrbcWEbELVquVvRcOXzbxr3qHL8E2y\/+IrvUAmLUmUn\/Wi5SiEpeyuLg4brzxRho3bky\/fv04ffo0AKNHj+bpp58ucUAREXtxOjGd5PRsHM0mGtSqukcCBncKopqzAwdjU1h18KzRcUQqjRKXsqeeegonJyeioqJwd7+0BtzgwYNZunRpSd9eRMRuXDzJv0FND1wcHQxOYxwvVyfu6RgEwMw1WqhcpLSUuJT99ttvvPnmmwQGBuZ5vFGjRhw7pqtzRKTy2Hu6as3kfzUju4ZiMsGqA2c4GKPpj0RKQ4lLWWpqap4Rsovi4+NxcXEp6duLiNiN3Csvq+hJ\/pcLruHOzc39AZi1VqNlIqWhxKWsR48efPnll7k\/m0wmLBYLb731Ftdff31J315ExG5cWoi8ap7k\/08Xp8f4bstJ4lIyDE4jUvEVa+3Ly7311lvceOONbNq0iczMTJ577jl2795NfHw8a9euLY2MIiKGy8jO4ciZVECHLy\/qWK86rQO92XEikf9tiOJfNzYyOpJIhVbikbKWLVty4MABunfvzu23305qaip33nknW7dupUGDBqWRUUTEcIdjU8m2WPFydaS2t6vRceyCyWRidPdQAL5cd4yMbE0mK1ISJR4pi4qKIigoiBdeeCHf54KDg0v6ESIihrt8eSWTyWRwGvvRr1VtJv2yj+ikdH7afpq7OgRe+0Uikq8Sj5SFhobmuyB5XFwcoaGhJX17ERG7oJP88+fkYGZY1xDANj2GJpMVKb4SlzKr1Zrv3xpTUlJwddUQv4hUDntz17zUSf7\/NLRTMG5ODuw9ncS6I3FGxxGpsIp9+HLcuHGA7ZyCl156Kc+0GDk5OWzYsIG2bduWOKCIiD3Yd\/rC8ko6yf8KPu7ODOpQl6\/XRzFzdSRdG\/gZHUmkQip2Kdu6dStgGynbuXMnzs7Ouc85OzvTpk0bnnnmmZInFBExWHxqJrHJtikfVMryN6pbKF+vj2LFvliOnEmhfk0PoyOJVDjFLmUrV64EYOTIkbz33nt4eWlIX0Qqp4sn+Qf7uuPhUuLroyql+jU9uLFpLVbsi+WLtUd5fWBLoyOJVDglPqfsiy++UCETkUrt4kn+GiW7uovTYyzcfIKEtEyD04hUPKXyV75Nmzbx7bffEhUVRWZm3i\/iokWLSuMjREQMs+\/CmpfNVMquqkuDGjQN8GRfdDJzNx7n0d6aq1KkKEo8UjZv3jy6du3K3r17+f7778nKymL37t388ccfeHt7\/3979x0eVbW2DfzeM5lJ7yG9AiG0JDSJQUAhIE06iCiCytHzns8jSFHhiCLKK2DhqK96sFM8ikoTLFQBARNKIITQAyEJ6X3S2+zvj5CRGEqSPZM95f5d11yQPXvWPOsadnhmrbWfpY8YiYhk1Th9GcY7L+\/o5mKy6\/64htp6rcwREZkWyUnZm2++iX\/\/+9\/YsWMH1Go13n\/\/fVy4cAEPP\/wwC8cSkcmr14q4lFMGgDXKWmJcL194OFgjW1OFX85kyR0OkUmRnJRduXIFY8aMAdBw12V5eTkEQcC8efPw6aefSg6QiEhOaYUVqKyth7WVAsHu9nKHY\/SsrZSYGc1iskRtITkpc3V1RWlpw3oLPz8\/JCUlAQCKi4tRUVEhtXkiIlk11ifr4uUIpYLbK7XEY1GBUFspkHi9BCdSi+QOh8hkSE7KBg8ejD179gAApk6dirlz5+Lpp5\/G9OnTERMTIzlAIiI5XdBV8ufUZUu5O1hjUm8\/AMAXh1JkjobIdEi++\/LDDz9EVVUVAODll1+GSqXCH3\/8gcmTJ2PJkiWSAyQikpNuI3IfLvJvjacGhmDj8XTsPpeN9MIKBLjZ3f1FRBZOclLm5uam+7tCocCiRYukNklEZDQucqSsTbp4OWJQqAcOXc7HV0eu4dWx3eUOicjoSZ6+bJSbm4ukpCQkJiY2ebTG77\/\/jrFjx8LX1xeCIGDbtm1Nnn\/iiScgCEKTx8iRI\/XVBSKiJsqr65Ba2LA2lklZ6\/1tUEcAwHfH06CpqpU5GiLjJ3mkLD4+HrNmzcL58+eb3WUjCALq6+tb3FZ5eTkiIyPx1FNPYdKkSbc8Z+TIkfjqq690P1tbW7ctcCKiu7iUUwpRBDwcrOHuwN81rTU41AOhng64nFuG74+n65I0Iro1yUnZU089hS5duuCLL76Al5cXBKHtdyeNGjUKo0aNuuM51tbW8Pb2bvN7EBG1VOPUZTfWJ2sTQRDw1MAQLN5yBl8duYYnBgTDSqm3CRoisyM5Kbt69So2b96Mzp076yOeuzpw4AA8PT3h6uqKoUOHYvny5XB3d7\/t+dXV1aiurtb9rNFo2iNMIjIDvPNSuom9\/fD2rovIKK7E7nM5GB3uI3dIREZL8leWmJgYnD59Wh+x3NXIkSOxfv167Nu3D6tWrcLBgwcxatSoO06RrlixAs7OzrpHQEBAu8RKRKaP2ytJZ6NS4rGoht1dvjjM8hhEdyKIEsst5+fnY9asWejfvz969uwJlUrV5Plx48a1LTBBwNatWzFhwoTbnnP16lV06tQJe\/fuvW1NtFuNlAUEBKCkpAROTvxFS0S3Jooier+xB8UVtfjpuYHo6ce9fNsqV1OF+1b9htp6EVv\/3wD0DnSVOySidqXRaODs7HzX3EPy9GVsbCyOHDmCX3\/9tdlzrV3o31odO3aEh4cHkpOTb5uUWVtb82YAImq1HE01iitqoVQI6OzpIHc4Js3TyQbjIv2w+eR1fHE4BR8+yqSM6FYkT18+99xzmDFjBrKysqDVaps8DJmQAcD169dRUFAAHx+uUSAi\/WqcugzxsIeNSilzNKZv9sAQAMCvSdnIKK6UORoi4yQ5KSsoKMC8efPg5eUlOZiysjIkJCQgISEBAJCSkoKEhASkpaWhrKwML7zwAuLi4nDt2jXs27cP48ePR+fOnTFixAjJ701EdDMu8tev7r5OiO7ojnqtiPV\/XJM7HCKjJDkpmzRpEvbv36+PWHDixAn07t0bvXv3BgDMnz8fvXv3xquvvgqlUonExESMGzcOXbp0wezZs9G3b18cOnSI05NEpHeNG5EzKdOfxtGyb46loby6TuZoiIyP5DVlXbp0weLFi3H48GGEh4c3W+g\/Z86cFrf1wAMPNCtAe7Ndu3a1OU4iotb4c6SMNwTpy9CungjxsEdKfjk2xV\/HrAHBcodEZFQk330ZEhJy+8YFAVevXpXSvN619A4IIrJctfVadH91J2rrRRx+aQj8XbmZtr6sj72GV388i2B3O\/y24AEoFG0vOE5kKtrt7suUFNadISLzcjWvHLX1IhytreDnYit3OGZlSl9\/vLv7Eq4VVGDfhVwM7y59PTKRueB+F0REf\/Fn0VhHSVvHUXN2aitM799QTPbzQ8Y1k0IktzaNlM2fPx9vvPEG7O3tMX\/+\/Dueu3r16jYFRkQkl\/NZDevJwrjI3yBmDQjC54eu4mhKIZIySliYl+iGNiVlp06dQm1tre7vt8NvmERkii7eGCnr6sN1p4bg42yL0eE+2H46E18eTsHqab3kDonIKLQpKbu5BIa+ymEQERmLxjsvu3GkzGBmDwzB9tOZ2JGYiUWjusLTyUbukIhkJ3lNWUlJCQoLC5sdLywshEajkdo8EVG7KqmoRVZJFQCgC5Myg4kMcME9wa6orRexPjZV7nCIjILkpOyRRx7Bxo0bmx3\/\/vvv8cgjj0htnoioXTUu8vdzsYWTjeouZ5MUjcVk\/3s0FZU1ht2Wj8gUSE7Kjh49iiFDhjQ7\/sADD+Do0aNSmyciale6qUsfjpIZ2vDu3ghws0VRRS22nLoudzhEspOclFVXV6Ourvl2GbW1tais5KazRGRaGpMy3nlpeEqFgCcGNIyWfXk4BVqtpFrmRCZPclLWv39\/fPrpp82Or1mzBn379pXaPBFRu2qcvuT2Su3j4X7+cLC2wpW8chy8nCd3OESyklzRf\/ny5Rg2bBhOnz6NmJgYAMC+fftw\/Phx7N69W3KARETtRasVcVG35yVHytqDo40K0+4JwBeHU\/Dl4RQMCfOUOyQi2UgeKbvvvvsQGxsLf39\/fP\/999ixYwc6d+6MxMREDBo0SB8xEhG1i+tFlaioqYdaqUCIh73c4ViMJwYEQyEAhy7n65JiIkskeaQMAHr16oVvvvlGH00REcnm\/I2py1AvB1gpuQtdewlws8PInt745Uw2vjycglVTIuQOiUgWevmtc+XKFSxZsgSPPvoocnNzAQC\/\/vorzp49q4\/miYjaxQVurySbxvIYWxMykF9WLXM0RPKQnJQdPHgQ4eHhOHr0KDZv3oyysjIAwOnTp7F06VLJARIRtZeLOQ0jZd24yL\/d9Ql0RWSAC2rqtPg6jsVkyTJJTsoWLVqE5cuXY8+ePVCr1brjQ4cORVxcnNTmiYjaTeNIWVfWKGt3giDoRsu+jktFVS2LyZLlkZyUnTlzBhMnTmx23NPTE\/n5+VKbJyJqF5U19bhWUA6A05dyGdXTGz7ONsgvq8H205lyh0PU7iQnZS4uLsjKymp2\/NSpU\/Dz85PaPBFRu7icWwqtCLjbq9HBwVrucCySSqnAEwOCATQUkxVFFpMly6KXvS9feuklZGdnQxAEaLVaHDlyBAsXLsTMmTP1ESMRkcHdvMhfEASZo7Fcj\/QPhJ1aiQvZpThwicVkybJITsrefPNNdO3aFQEBASgrK0P37t0xePBgDBgwAEuWLNFHjEREBndBVzSWi\/zl5GyrwvT+gQCAV7Yloay6+TZ+ROZKclKmVqvx2Wef4cqVK\/jpp5\/w9ddf48KFC9iwYQOUSqU+YiQiMjjd9kpc5C+7ecO7wM\/FFteLKrHil\/Nyh0PUbvRSPBYAAgMDERgYqK\/miIjajSiKN42UMSmTm4O1Fd6eEoFHPz+K\/x5Nw6iePhgY6iF3WEQG16akbP78+S0+d\/Xq1W15CyKidpNXVo3C8hooBCDUk0mZMRjQ2QOP3xuEDXGpeGlzInY+PwiONiq5wyIyqDYlZadOnWry88mTJ1FXV4ewsDAAwKVLl6BUKtG3b1\/pERIRGVjjIv9gd3vYqrnswlgsGtUVBy7lIr2wEm\/+ch4rJnH7JTJvbUrK9u\/fr\/v76tWr4ejoiHXr1sHV1RUAUFRUhCeffJIbkhORSWjcBJvryYyLvbUV3p4SiUc+jcO3x9IxsqcP7u\/SQe6wiAxG8kL\/d999FytWrNAlZADg6uqK5cuX491335XaPBGRwTVuRM47L43PvR3ddbXLFm1OhKaqVt6AiAxIclKm0WiQl9e8lkxeXh5KS0ulNk9EZHDciNy4vTgyDEHudsgqqcLyn87JHQ6RwUhOyiZOnIgnn3wSW7ZswfXr13H9+nVs3rwZs2fPxqRJk\/QRIxGRwdTVa5GcWwaAG5EbKzt1wzSmIADfn7iO\/Rdy5Q6JyCAkJ2Vr1qzBqFGj8OijjyIoKAhBQUF49NFHMXLkSHz88cf6iJGIyGBS8stRU6+FvVoJf1dbucOh2+gf4oan7mvYsHzRlkSUVHAak8yP5KTMzs4OH3\/8MQoKCnDq1CmcOnUKhYWF+Pjjj2Fvb6+PGImIDKaxPlkXb0coFNxeyZgtfDAMHT3skaOpxuucxiQzJDkpa2Rvb4+IiAhEREQwGSMik3GBi\/xNhq1aibenRkAQgM0nr2PvuRy5QyLSK70lZUREpqhxkT8r+ZuGvkFueHpQRwDA4q1nUFxRI3NERPrDpIyILBq3VzI984d3QacO9sgrrcZr28\/KHQ6R3jApIyKLpamqRUZxJQBOX5oSG5US70yNhEIAtiVkYtfZbLlDItILJmVEZLEaK\/n7ONvA2Y77KpqS3oGueGZwJwDAy1vPoLCc05hk+iQnZevWrcPPP\/+s+\/nFF1+Ei4sLBgwYgNTUVKnNExEZDKcuTdvzw0IR6umA\/LIaLOU0JpkByUnZm2++CVvbhto+sbGx+Oijj\/DWW2\/Bw8MD8+bNkxwgEZGhXMi6ceelD6cuTVHjNKZSIWDH6Uz8eiZL7pCIJJGclKWnp6Nz584AgG3btmHy5Ml45plnsGLFChw6dEhygEREhnKRI2UmLzLABf9zf8PdmEu2JaGgrFrmiIjaTnJS5uDggIKCAgDA7t27MXz4cACAjY0NKisrpTZPRGQQoijeNH3JkTJTNicmFGFejigor8GrP3Iak0yX5KRs+PDh+Nvf\/oa\/\/e1vuHTpEkaPHg0AOHv2LIKDg6U2T0RkENeLKlFWXQeVUkDHDix4bcqsrZR49+GGacyfz2Thp8RMuUMiahPJSdlHH32E6Oho5OXlYfPmzXB3dwcAxMfHY\/r06ZIDJCIyhMapy04dHKBS8kZ0U9fTzxnPDmlYSvPKtiTklXIak0yPldQGXFxc8OGHHzY7vmzZMqlNExEZTOP2St24yN9s\/HNIZ+w5l4PzWRos2XYGa2b0hSBwP1MyHXr5enjo0CHMmDEDAwYMQEZGBgBgw4YNOHz4sD6aJyLSu\/M3RsrCuMjfbKitFHhnagSsFAJ2nc3B9tOcxiTTIjkp27x5M0aMGAFbW1ucPHkS1dUNQ8YlJSV48803JQdIRGQIvPPSPPXwdcZzQ0MBAEu3n0VuaZXMERG1nOSkbPny5VizZg0+++wzqFR\/VsS+7777cPLkSanNExHpXVVtPVLyywFw+tIc\/b8hndDD1wnFFbV4eWsSRFGUOySiFpGclF28eBGDBw9udtzZ2RnFxcVSmyci0rvk3DLUa0W42Kng6WgtdzikZyqlAu8+HAmVUsCecznYlpAhd0hELSI5KfP29kZycnKz44cPH0bHjh2lNk9EpHc3b6\/EheDmqau3E+bG3JjG\/PEscjScxiTjJzkpe\/rppzF37lwcPXoUgiAgMzMT\/\/3vf7Fw4UL84x\/\/0EeMRER6dehyHgCgp6+zzJGQIf3P\/Z0Q7ucMTVUdFm85w2lMMnqSS2IsWrQIWq0WMTExqKiowODBg2FtbY2FCxfiueee00eMRER6U1pVi11nswEAYyN9ZY6GDMnqxjTmQx8cxm8XcrH5ZAam9PWXOyyi25I8UiYIAl5++WUUFhYiKSkJcXFxyMvLwxtvvKGP+IiI9OqXM1moqtWis6cDIvw5Umbuung54vnhDdOYy3acRVYJt\/8j46W3MtZqtRrdu3dH\/\/794eDgoK9miYj0alP8dQDAlL7+XE9mIZ4Z1BGRAS4orarDos2cxiTj1abpy0mTJrX43C1btrTlLYiI9O5afjmOXyuCQgAm9vaTOxxqJ1ZKBd6dGoHRHxzGwUt5+P5EOqbdEyh3WETNtCkpc3bmkD8RmZ4tJxtGyQaGdoCXk43M0VB76uzpiIUPdsGbv1zA8p\/OY2BoB\/i52ModFlETbUrKvvrqK33HQURkUFqtiM0nG+pVcbG3ZZo9sCN2JmXjZFoxFm1OxPqn+nMKm4yK3taU5ebm4tChQzh06BByc3P11SwRkV7EpRQgo7gSjjZWeLC7l9zhkAyUCgFvT42EtZUChy7n49tj6XKHRNSE5KRMo9Hg8ccfh5+fH+6\/\/37cf\/\/98PPzw4wZM1BSUqKPGImIJNsc3zBK9lCEL2xUSpmjIbl06uCAF0aEAQD+9+dzuF5UIXNERH\/SS\/HYo0eP4qeffkJxcTGKi4vx008\/4cSJE\/j73\/+ujxiJiCQpr67Dr0lZAIApfbnA39I9eV8I7gl2RXlNPV7clAitlndjknGQnJT99NNP+PLLLzFixAg4OTnByckJI0aMwGeffYYdO3boI0YiIkl+TcpGRU09Qjzs0SfQVe5wSGZKhYC3p0TCRqXAH1cK8GtSttwhEQHQQ1Lm7u5+y7sxnZ2d4erKX35EJL\/NN2qTTe7jx4XdBAAI9rDHU\/eFAAC2nrouczREDSQnZUuWLMH8+fORnf3nN43s7Gy88MILeOWVV6Q2T0QkSXphBWKvFkAQgIl9eNcl\/amxVt2Bi3koKq+RORqiNpbE6N27d5Nvm5cvX0ZgYCACAxuK8aWlpcHa2hp5eXlcV0ZEstp6qmGB\/4BO7qxLRU2Eejmiu48TzmVp8GtSNh6NYkFZklebkrIJEyboOQwiIv0TRRGbTzZOXXKUjJob38sX57I0+DEhg0kZya5NSdnSpUv1HQcRkd6dSC1CakEF7NVKjOzpLXc4ZITGRvpixa8XcOxaITKLK+HL0VSSkd6KxxIRGZvGBf6jw31gp27Td1Ayc74utugf4gZRBHaczpQ7HLJwkpOy+vp6vPPOO+jfvz+8vb3h5ubW5NEav\/\/+O8aOHQtfX18IgoBt27Y1eV4URbz66qvw8fGBra0thg0bhsuXL0vtAhGZocqaevyU2FCbbDK3VaI7GN\/LFwDwYwKTMpKX5KRs2bJlWL16NaZNm4aSkhLMnz8fkyZNgkKhwGuvvdaqtsrLyxEZGYmPPvrols+\/9dZb+OCDD7BmzRocPXoU9vb2GDFiBKqqqqR2g4jMzO5z2SirrkOAmy36B7fuCyJZltE9fWClEHAuS4PLOaVyh0MWTHJS9t\/\/\/hefffYZFixYACsrK0yfPh2ff\/45Xn31VcTFxbWqrVGjRmH58uWYOHFis+dEUcR7772HJUuWYPz48YiIiMD69euRmZnZbESNiGjTjanLSb39oVCwNhndnqu9Gvd36QAA2M4pTJKR5KQsOzsb4eHhAAAHBwfdfpcPPfQQfv75Z6nN66SkpCA7OxvDhg3THXN2dkZUVBRiY2Nv+7rq6mpoNJomDyIyb1kllTicnA+Ad11Sy4y7aQpTFLntEslDclLm7++PrKyGdRudOnXC7t27AQDHjx+HtbW11OZ1GovTenl5NTnu5eXVpHDtX61YsQLOzs66R0BAgN5iIiLjtPVUBkQR6B\/ihkB3O7nDIRMwvLsX7NRKpBVWICG9WO5wyEJJTsomTpyIffv2AQCee+45vPLKKwgNDcXMmTPx1FNPSQ5QqsWLF6OkpET3SE9PlzskIjIgURR1U5dTOEpGLWSntsKD3Ru+9HPBP8lF8j3iK1eu1P192rRpCAwMRGxsLEJDQzF27Fipzet4ezfUGMrJyYGPj4\/ueE5ODnr16nXb11lbW+t1xI6IjFtCejGu5pXDVqXE6Aifu7+A6IbxvfywLSETPyVmYcmYbrBSsmoUtS+9\/4uLjo7G\/Pnz9ZqQAUBISAi8vb11o3IAoNFocPToUURHR+v1vYjIdDVW8B\/Z0xsO1qxNRi03MNQDrnYq5JdVI\/ZqgdzhkAVq02+s7du3Y9SoUVCpVNi+ffsdzx03blyL2y0rK0NycrLu55SUFCQkJMDNzQ2BgYF4\/vnnsXz5coSGhiIkJASvvPIKfH19ue0TEQEAqmrrsf3G1NMU1iajVlIpFRgT4YOv49Kw7VQmBoV2kDsksjBt3vsyOzsbnp6ed0yIBEFAfX19i9s9ceIEhgwZovt5\/vz5AIBZs2Zh7dq1ePHFF1FeXo5nnnkGxcXFGDhwIHbu3AkbG5u2dIOIzMy+87nQVNXB19kG0R3d5Q6HTND4Xn74Oi4Nu85m439re8JGpZQ7JLIgbUrKtFrtLf8u1QMPPHDHW5EFQcDrr7+O119\/XW\/vSUTmY1N8w408E\/v4sTYZtUnfQFf4udgio7gSv13Ixehwrkuk9iNpTVltbS1iYmK41RERyS5XU4XfL7M2GUmjUAgYG9lYsyxD5mjI0khKylQqFRITE\/UVCxFRm21LyEC9VkSfQBd07OAgdzhkwhr3wtx\/IQ8llbUyR0OWRPLdlzNmzMAXX3yhj1iIiNpEFEVsjm8Y1ZjSlwWiSZqu3o7o4uWAmnotdiXdvjg5kb5Jvl+8rq4OX375Jfbu3Yu+ffvC3t6+yfOrV6+W+hZERHd0NlODizmlUFs13D1HJIUgCBjfyw9v77qIH09n4OF7mOhT+5CclCUlJaFPnz4AgEuXLjV5ThC40JaIDK+xgv+D3b3gbKuSORoyB+MiffH2rov440oBcjVV8HTiXf5keJKTsv379+sjDiKiNqmp0+oWZLM2GelLgJsd+ga5Ij61CDsSszB7YIjcIZEF4B4SRGTSfruQi6KKWng6WrPYJ+lV44L\/7bwLk9qJXvYgOXHiBL7\/\/nukpaWhpqamyXNbtmzRx1sQEd1S47ZKE\/v4QcnaZKRHo8N9sGzHOZy+XoKU\/HKEeNjf\/UVEEkgeKdu4cSMGDBiA8+fPY+vWraitrcXZs2fx22+\/wdnZWR8xEhHdUkFZNfZfyAUATGFtMtIzDwdrDOzsAYA1y6h9SE7K3nzzTfz73\/\/Gjh07oFar8f777+PChQt4+OGHERgYqI8YiYhu6ceETNRpRUT4OyPUy1HucMgM\/TmFmXnHHWeI9EFyUnblyhWMGTMGAKBWq1FeXg5BEDBv3jx8+umnkgMkIrqdxqlLLvAnQ3mwhzesrRS4ml+OpAyN3OGQmZOclLm6uqK0tBQA4Ofnh6SkJABAcXExKioqpDZPRHRL57M0OJupgUopYGyEr9zhkJlysLbCsO5eADiFSYYnOSkbPHgw9uzZAwCYOnUq5s6di6effhrTp09HTEyM5ACJiG5l843aZMO6ecHVXi1zNGTOJvTyAwDsSMxEvZZTmGQ4ku++\/PDDD1FVVQUAePnll6FSqfDHH39g8uTJWLJkieQAiYj+qrZei20JmQC4+TgZ3v1dOsDZVoUcTTWOphRgQCcPuUMiMyU5KXNzc9P9XaFQYNGiRVKbJCK6o98v5SG\/rBoeDmrcH8baZGRYaisFRod749tj6diekMmkjAxG8vTlsGHDsHbtWmg0XABJRO2jcYH\/+F5+UClZA5sMb1xkwxTmL2eyUF1XL3M0ZK4k\/zbr0aMHFi9eDG9vb0ydOhU\/\/vgjamtr9REbEVEzxRU12HuuoTYZpy6pvfQPcYO3kw00VXU4eDFP7nDITElOyt5\/\/31kZGRg27ZtsLe3x8yZM+Hl5YVnnnkGBw8e1EeMREQ6O05noqZei+4+Tuju6yR3OGQhlAoBYyN9ADTUxyMyBL2M+ysUCjz44INYu3YtcnJy8Mknn+DYsWMYOnSoPponItLZdOOuy8msTUbtbPyNuzD3ns9BaRVnhEj\/9LoYIzs7G2vWrMGqVauQmJiIe+65R5\/NE5GFS84txenrJbBSCLpK60TtpYevEzp2sEd1nRa7z+bIHQ6ZIclJmUajwVdffYXhw4cjICAA\/\/nPfzBu3DhcvnwZcXFx+oiRiAgAsCm+oXjnA2Ge8HCwljkasjSCIGD8jQX\/P57mFCbpn+SSGF5eXnB1dcW0adOwYsUK9OvXTx9xERE1Ua8VsfVU47ZKfjJHQ5ZqfC9f\/HvvJRxJzkdeaTU6OPLLAemP5KRs+\/btiImJgULB29KJyHAOJ+cjR1MNVzsVhnb1kjscslDBHvaIDHDB6fRi\/HImC7MGBMsdEpkRyZnU8OHDmZARkcE1LvAfF+kLtRV\/55B8xkc2rGfkXpikb\/zNRkRGT1NVi91nswEAU\/oGyBwNWbqHInygEICTacVIK6iQOxwyI0zKiMjo\/ZyYheo6Lbp4OaCnH2uTkbw8nWx0Wy3tSOSCf9IfJmVEZPR0tcn6+EMQBJmjIQLG3SjJsu1UBkRRlDkaMhdtSsrc3NyQn58PAHjqqadQWlqq16CIiBql5JcjPrUICgGY2Jt3XZJxGNnTG2orBS7nluF8Fv8PJP1oU1JWU1Oj24B83bp1qKqq0mtQRESNNt8YJRvcpQM8nWxkjoaogZONCkPDPAEAP57mgn\/SjzaVxIiOjsaECRPQt29fiKKIOXPmwNbW9pbnfvnll5ICJCLLpdWK2Hqq4T+8KdxWiYzM+F6+2Hk2GzsSMvHSiK5QKDi1TtK0aaTs66+\/xujRo1FWVgZBEFBSUoKioqJbPoiI2iruagEyiivhZGOFYd1Ym4yMy5CunnC0tkJmSRVOpPL\/O5KuTSNlXl5eWLlyJQAgJCQEGzZsgLu7u14DIyJqXOD\/UKQvbFRKmaMhaspGpcTInt74If46fkzIQP8QN7lDIhMn+e7LlJQUJmREpHdl1XX4NamxNhmnLsk4je\/VcPPJz2eyUFOnlTkaMnV6KYlx8OBBjB07Fp07d0bnzp0xbtw4HDp0SB9NE5GF+uVMFipr69HRwx69A1zkDofolqI7ucPDwRrFFbU4nJwndzhk4iQnZV9\/\/TWGDRsGOzs7zJkzR7foPyYmBt98840+YiQiC9R41+XkvqxNRsZLqRAwNtIHAPBjAgvJkjSCKLHqXbdu3fDMM89g3rx5TY6vXr0an332Gc6fPy8pQH3TaDRwdnZGSUkJnJxYGZzIGKUXVmDQW\/shCMAfi4bCx\/nWd3cTGYOE9GJM+OgIbFVKxL8yDHbqNi3XJjPW0txD8kjZ1atXMXbs2GbHx40bh5SUFKnNE5EF2nyyYZRsYGcPJmRk9CL9nRHkbofK2nrsOZcjdzhkwiQnZQEBAdi3b1+z43v37kVAADcOJqLW0WpFXVI2uQ8X+JPxEwQB4yMbtl3iFCZJIXmMdcGCBZgzZw4SEhIwYMAAAMCRI0ewdu1avP\/++5IDJCLLcvxaIdILK+FgbYURPbzlDoeoRcb18sUHvyXj90t5KCyvgZu9Wu6QyARJTsr+8Y9\/wNvbG++++y6+\/\/57AA3rzL777juMHz9ecoBEZFkaR8nGhPvAVs3aZGQaOns6ooevE85mavDLmSzMuDdI7pDIBOllNeLEiRMxceJEfTRFRBasoqYOPydmAWi465LIlEzo5YezmRpsT8hkUkZtopc6ZURE+rAzKRvlNfUIdLPDPcGucodD1CoPRfpAEIBj1wqRUVwpdzhkgpiUEZHRWBebCgB4uB9rk5Hp8XG2RdSNrZZ2nOaCf2o9JmVEZBQS0otxOr0YaqUCj\/QPlDscojZp3HaJd2FSWzApIyKjsO6PawAapoA8HKzlDYaojUb19IZKKeB8lgaXckrlDodMjKSkrLa2Fp06dTK6qv1EZFrySqvxU2LDyMITA4LlDYZIAhc7Ne7v4gkA2M7RMmolSUmZSqVCVVWVvmIhIgv17bE01NaL6B3oggh\/F7nDIZJkfK8bhWRPZ0DiToZkYSRPXz777LNYtWoV6urq9BEPEVmYmjotvo5rWODPUTIyB8O6ecFOrUR6YSVOphXLHQ6ZEMl1yo4fP459+\/Zh9+7dCA8Ph729fZPnt2zZIvUtiMiM7TybjdzSanRwtMaonj5yh0Mkma1aiRE9vLH1VAa2J2SgbxDLu1DLSE7KXFxcMHnyZH3EQkQWqHGB\/2NRgVBb8d4jMg\/je\/li66kM\/JSYhVce6g4rJf9t091JTsq++uorfcRBRBbozPUSxKcWQaUU8GgUy2CQ+bivswfc7dUoKK\/BkSsFuL9LB7lDIhOgl9S9rq4Oe\/fuxSeffILS0oZbgDMzM1FWVqaP5onITK29MUo2OtwHno428gZDpEcqpQJjIhqm439MyJA5GjIVkpOy1NRUhIeHY\/z48Xj22WeRl5cHAFi1ahUWLlwoOUAiMk8FZdXYcaMMxiwu8Ccz1HgX5q6kbFTV1sscDZkCyUnZ3Llz0a9fPxQVFcHW1lZ3fOLEidi3b5\/U5onITG08no6aOi0i\/Z3RO8BF7nCI9K5PoCv8XW1RXlOPfedz5Q6HTIDkpOzQoUNYsmQJ1Gp1k+PBwcHIyOCQLRE1V1f\/ZxmMWQOCuc8lmSVBEDAu8kbNMk5hUgtITsq0Wi3q65sPy16\/fh2Ojo5SmyciM7T7XA6ySqrg4aDWrbshMkeNe2EeuJiHkopamaMhYyc5KXvwwQfx3nvv6X4WBAFlZWVYunQpRo8eLbV5IjJDa49cAwBM7x8IayulvMEQGVCYtyO6ejuipl6LH09ztIzuTHJS9u677+LIkSPo3r07qqqq8Oijj+qmLletWqWPGInIjJzL1ODYtUJYKQQ8FhUkdzhEBvfIPQEAgA2xqdx2ie5Icp0yf39\/nD59Ghs3bkRiYiLKysowe\/ZsPPbYY00W\/hMRAX8Wix3Z0xveziyDQeZvUl9\/vLXrIi7nliHuaiGiO7nLHRIZKclJGQBYWVlhxowZ+miKiMxYUXkNtt1Y8Mx9LslSONmoMLG3H\/57NA3rY68xKaPb0kvx2IsXL+Kf\/\/wnYmJiEBMTg3\/+85+4cOGCPpomIjOy8Xg6quu06OHrxP0AyaLMjA4G0HiTS6W8wZDRkpyUbd68GT179kR8fDwiIyMRGRmJkydPIjw8HJs3b9ZHjERkBlgGgyxZmLcj+oe4oV4r4tujaXKHQ0ZK8vTliy++iMWLF+P1119vcnzp0qV48cUXuVk5EQEA9p7PRUZxJVztVLraTUSWZGZ0EI6lFOKbY+n459BQqK24STk1JflfRFZWFmbOnNns+IwZM5CVlSW1eSIyE40L\/Kf3D4SNimUwyPKM6OENT0dr5JdVY+fZbLnDISMkOSl74IEHcOjQoWbHDx8+jEGDBkltnojMwMXsUsReLYBSIWDGvSyDQZZJpVRgev9AAMCG2GvyBkNGqU3Tl9u3b9f9fdy4cXjppZcQHx+Pe++9FwAQFxeHH374AcuWLdNPlDd57bXXmrUbFhbGGwuIjNjaG6NkD3b3gq8LS+WQ5Xo0KhAf7U\/G8WtFOJ+lQTcfJ7lDIiMiiG2oZKdQtGyATRCEW27BJMVrr72GTZs2Ye\/evbpjVlZW8PDwaNHrNRoNnJ2dUVJSAicnXgxEhlZSUYt7V+xDZW09Nj5zL+7tyHIAZNme\/e9J\/HwmC9P7B2LFpHC5w6F20NLco03Tl1qttkUPfSdkjaysrODt7a17tDQhI6L29\/2JdFTW1qOrtyOiQtzkDodIdo9HN0zhbzuVgZJK7odJfzLJWz8uX74MX19fdOzYEY899hjS0m5\/e3F1dTU0Gk2TBxG1j3qtiPVx1wA0FItlGQwiICrEDV28HFBZW4\/N8dflDoeMiF4q+h8\/fhz79+9Hbm4utFptk+dWr16tj7fQiYqKwtq1axEWFoasrCwsW7YMgwYNQlJSEhwdHZudv2LFCoOsbSOiu\/vtQi7SCyvhbKvC+F5+codDZBQEQcDj0cF4ZVsSvo5LxRMDgqFQ8AsLtXFN2c3efPNNLFmyBGFhYfDy8mryTVgQBPz222+Sg7yT4uJiBAUFYfXq1Zg9e3az56urq1FdXa37WaPRICAggGvKiNrBjM+P4nByPv4+uCMWj+4mdzhERqO8ug73vrkPpdV12DC7PwaFdpA7JDKglq4pkzxS9v777+PLL7\/EE088IbWpNnFxcUGXLl2QnJx8y+etra1hbW3dzlERUXJuKQ4n50MhgGUwiP7C3toKk\/v6Y+0f17A+NpVJGQHQw5oyhUKB++67Tx+xtElZWRmuXLkCHx8f2WIgoubW\/dGwpVJMNy8EuNnJHA2R8Wn8srLvfA6uF1XIHA0ZA8lJ2bx58\/DRRx\/pI5YWWbhwIQ4ePIhr167hjz\/+wMSJE6FUKjF9+vR2i4GI7kxTVYvNJxsWMD85IFjeYIiMVGdPB9zX2R1aEfgv98Mk6GH6cuHChRgzZgw6deqE7t27Q6VSNXl+y5YtUt+iievXr2P69OkoKChAhw4dMHDgQMTFxaFDBw79EhmLH05cR0VNPbp4OSC6E+uSEd3O4\/cG40hyAb47no65MaHcgszCSU7K5syZg\/3792PIkCFwd3c3+C3vGzduNGj7RCSNVivqtpCZGc0yGER3MqybJ3ydbZBZUoVfzmRhUh9\/uUMiGUlOytatW4fNmzdjzJgx+oiHiEzcwUt5uFZQAUcbK0zszTIYRHdipVTg0ahAvLP7EtbHpjIps3CS15S5ubmhU6dO+oiFiMxA4z6XD\/cLgL21XkohEpm1afcEQqUUkJBejDPXS+QOh2QkOSl77bXXsHTpUlRU8M4RIkt3Na8MBy\/lQRCAmdEsg0HUEh0crTE6vKGCwPobU\/9kmSR\/jf3ggw9w5coVeHl5ITg4uNlC\/5MnT0p9CyIyEetjG8pgDA3zRJC7vczREJmOmdFB+DEhE9tPZ+Jfo7vB1V4td0gkA8lJ2YQJE\/QQBhGZurLqOmy6sY\/fLJbBIGqVPoGu6O7jhHNZGvwQn45nBnNZkCWSnJQtXbpUH3EQkYnbHH8dZdV16NjBHgM7e8gdDpFJEQQBM6ODsGjLGXwdl4a\/DezI\/TAtkOQ1ZUREWq2IdTfWwsyK5ubKRG0xvpcfnGyskFZYgYOX8uQOh2Sgl22WlErlbR9EZP4OJefjal45HG7s50dErWerVuLhfgEAuODfUkmevty6dWuTn2tra3Hq1CmsW7cOy5Ytk9o8EZmAdTfKYEzp6w8HlsEgarMZ9wbh88MpOHApD6kF5bxhxsJI\/u05fvz4ZsemTJmCHj164LvvvsPs2bOlvgURGbHUgnLsv5gLgGUwiKQK9rDH\/V064OClPHwdl4qXx3SXOyRqRwZbU3bvvfdi3759hmqeiIzE+thUiCJwf5cO6NjBQe5wiExe45eb709cR2VNvczRUHsySFJWWVmJDz74AH5+3GKFyJyVV9fh+xPpAIAn7guWNxgiM\/FAmCf8XW1RUlmLHacz5Q6H2pHk6UtXV9cmGw6LoojS0lLY2dnh66+\/lto8ERmxLacyUFpVhxAPe9wf2kHucIjMglIhYMa9QVj56wWsj7uGqf38m\/w\/S+ZLclL23nvvNflZoVCgQ4cOiIqKgqurq9TmichIiaKI9TcW+D9+bxDLYBDp0cP9ArB6zyUkZWhwKr0YfQL5\/6klkJyUzZo1Sx9xEJGJ+eNKAS7nlsFOrcSUfiyDQaRPbvZqjI3wxeaT17EhNpVJmYXQy73rxcXFOHbsGHJzc6HVaps8N3PmTH28BREZmbU3Rskm9\/GHk43qzicTUavNjA7C5pPX8XNiFl4e0w0eDtZyh0QGJjkp27FjBx577DGUlZXBycmpyby3IAhMyojMUHphBfaezwEAzBrAMhhEhhAZ4IJIf2ecvl6C746n49khneUOiQxM8t2XCxYswFNPPYWysjIUFxejqKhI9ygsLNRHjERkZDbENZTBGBTqgc6ejnKHQ2S2Ho8OBgB8czQN9VpR3mDI4CQnZRkZGZgzZw7s7Oz0EQ8RGbnKmnp8d7yhDMasG\/9hEJFhPBThA1c7FTKKK7Hvxug0mS\/JSdmIESNw4sQJfcRCRCZgW0IGSiprEeBmiyFdPeUOh8is2aiUePiehv0wN8SlyhwNGZrkNWVjxozBCy+8gHPnziE8PBwqVdMFv+PGjZP6FkRkJERR1O1zOfPeYChZBoPI4GZEBeHT36\/i0OV8XM0r484ZZkxyUvb0008DAF5\/\/fVmzwmCgPp6bhFBZC7irhbiQnYpbFVKPNwvQO5wiCxCgJsdYrp6Yu\/5XGyIS8XSsT3kDokMRPL0pVarve2DCRmReWkcJZvYxw\/OdiyDQdReGhf8bzpxHeXVdfIGQwZjsA3Jici8ZBRXYve5bABc4E\/U3gZ19kCwux1Kq+uwLSFD7nDIQJiUEVGLfB2XCq0IRHd0R5g3y2AQtSfFjf0wAWBDbCpEkeUxzBGTMiK6q6raenx7LA0AMGtAsLzBEFmoqX0DYKNS4EJ2KY5fK5I7HDIAJmVEdFdfx6WiuKIWfi62GNaNZTCI5OBsp8KEXn4AgPWx1+QNhgyCSRkR3dGVvDK8vesiAODZIZ1hpeSvDSK5PB7dMIW5MykbuZoqmaMhfdPLhuRarRbJycm33JB88ODB+ngLIpJBvVbEwh9Oo7pOi4GdPTC9P8tgEMmph68z+ga5Ij61CN8eS8fcYaFyh0R6JDkpi4uLw6OPPorU1OYLD1mnjMi0ffr7VZxKK4ajtRVWTYmAILBYLJHcZkYHIT61CN8cS8X\/G9IJKo5emw3Jn+T\/\/M\/\/oF+\/fkhKSkJhYSE3JCcyExezS\/HvPZcAAK881B1+LrYyR0READCypzc8HNTI0VRjzznuh2lOJI+UXb58GZs2bULnzp31EQ8RGYHaei0W\/JCAmnothoR1wNR+\/nKHREQ3WFsp8cg9gfhwfzLWx17D6HAfuUMiPZE8UhYVFYXk5GR9xEJERuLj\/VeQlKGBs60KKydz2pLI2DwaFQiF0LD12aWcUrnDIT2RPFL23HPPYcGCBcjOzr7lhuQRERFS34KI2lFSRgn+77fLAIDXx\/eAl5ONzBER0V\/5utjiwe7e2Hk2GxtiU\/HGhJ5yh6Q3NXVaFFfUoKiiFs62Kng7W87vIEGUWBZYoWg+2CYIAkRRNMqF\/hqNBs7OzigpKYGTk5Pc4RAZleq6eoz7vyO4mFOKkT288Z8ZfThKRmSk\/kjOx6OfH4W9Wom4f8XA0cb49qOtqq1HUUUNCstrUFxRi6KKGhSVNyRcDcdqUFhR2\/DnjXPKbtrbUyEATw\/qiHnDu8BGpZSxJ9K0NPeQPFKWkpIitQkiMhLv772MizmlcLNXY\/nEnkzIiIxYdCd3dPZ0QHJuGbaczGiX3TZEUURmSRWu5JY1SbCKboxsNfz85\/HK2rYNzCgEwMlWheKKWnzy+1XsOZeDt6dGoG+Qm557ZFwkJ2VBQUH6iIOIZHYqrQhrDl4BAPzvhJ7wcLCWOSIiuhNBEPD4vUFYuv0sNsSlYmZ0kN6\/SFXV1uNsZglOphbjZFoRTqYVIUdT3ao2lAoBrnZquNqp4Grf8KebvRoujcfs1A2Pm55zslFBoRCw73wO\/rX1DK7ml2PKmlg8OSAEL4wIg63adEfN7kQvxWMB4Ny5c0hLS0NNTU2T4+PGjdPXWxCRgVTV1mPBD6ehFYFxkb4Yxbu5iEzCpD5+eGvnBSTnliH2SgEGdPZoc1uNo2AnUxuSr1NpxTibWYLa+qarnJQKAR097OHuoNYlV252arjcSKhuTrBc7dVwtLZqc7IY080Lu4PdsPync\/gh\/jq+PJKCfRdysGpyBO7t6N7mvhoryUnZ1atXMXHiRJw5c0a3lgyA7gMwtjVlRNTcO7su4mpeOTo4WuP18T3kDoeIWsjRRoWJffzwdVwa1semtiopa+komIeDGr0DXdEn0BW9A10Q4e8MO7XexnTuytlWhbenRmJMhA8WbzmD1IIKPPJpHGZGB+GlkV1hb91+sRia5J7MnTsXISEh2LdvH0JCQnDs2DEUFBRgwYIFeOedd\/QRIxEZ0LGUQnxxpGFt6MpJ4XCxU8scERG1xszoYHwdl4Y953OQVVIJH+fmhZ7\/Ogp2Mq0Y524zCtbNxxF9biRhfQJdEeBmaxTrSx8I88TueYPx5i8X8O2xhiT0twu5WDU5AvdJGCE0JpKTstjYWPz222\/w8PCAQqGAQqHAwIEDsWLFCsyZMwenTp3SR5xEZAAVNXV4YdNpiCIwpa8\/Yrp5yR0SEbVSFy9HRIW44WhKIb45moYFD4a1aRSsT6ALIvxdjHq9lqONCismhWNMuA9e2pyI60WVeOzzo3g0KhCLR3U1yjtQW0NyUlZfXw9HR0cAgIeHBzIzMxEWFoagoCBcvHhRcoBEZDgrf72A1IIK+Drb4NWx3eUOh4jaaGZ0MI6mFGJ9bCp+v5x\/21Gw7j5O6B3oYnSjYK01MNQDu+YNxqpfL2BDXCq+OZqGAxdysWJyBO7v0kHu8NpMclLWs2dPnD59GiEhIYiKisJbb70FtVqNTz\/9FB07dtRHjERkAEeS87E+NhUAsGpKBJxM\/BsmkSV7sIcXvJyskaOpxun0YgCmNwrWWg7WVnhjQk+MvjFqllZYgVlfHsPD\/fzx8pjucLY1vd9pkovH7tq1C+Xl5Zg0aRKSk5Px0EMP4dKlS3B3d8d3332HoUOH6itWvWDxWCKgtKoWI987hIziSjwWFYj\/nRgud0hEJFF8aiF2n8tpGA0LMN1RsLaoqKnD27suYu0f1yCKgJeTNVZMCsfQrsaxJKOluYfkpOxWCgsL4erqapT\/GJiUEQGLNidi4\/F0BLjZYufcwWZ19xIRWa7j1wrx4qZEpOSXAwAm9fbDq2O7y34DU0tzD8kbkjdKTk7Grl27UFlZCTc38664S2TK9l\/Ixcbj6QCAt6dEMiEjIrNxT7Abfp07CM8M7giFAGw5lYHh\/\/4du85myx1ai0hOygoKChATE4MuXbpg9OjRyMrKAgDMnj0bCxYskBwgEelPSUUtFm1JBAA8eV+wWRZfJCLLZqNS4l+ju2HTPwagUwd75JVW4+8b4vHct6dQWF5z9wZkJDkpmzdvHlQqFdLS0mBnZ6c7Pm3aNOzcuVNq80SkR6\/tOIscTTVCPOzx4oiucodDRGQwfQJd8fOcQfjHA52gEIAdpzMxfPVB\/JyYJXdotyU5Kdu9ezdWrVoFf3\/\/JsdDQ0ORmpoqtXki0pNdZ7Ox9VQGFALwztRIs7oLi4joVmxUSrw0siu2PXsfwrwcUVBeg2e\/OYn\/99945Je1bg\/P9iA5KSsvL28yQtaosLAQ1tbc0JjIGBSW1+DlrWcAAE8P7oi+Qa4yR0RE1H4i\/F2w\/bn7MGdoZ1gpBPxyJhvDVx\/EjwkZMMD9jm0mOSkbNGgQ1q9fr\/tZEARotVq89dZbGDJkiNTmiUgPXtmWhPyyGoR6OmDesC5yh0NE1O6srZSY\/2AYtj17H7r5OKGoohZzNybgmQ3xyNVUyR0eAD2UxEhKSkJMTAz69OmD3377DePGjcPZs2dRWFiII0eOoFOnTvqKVS9YEoMszY7TmXju21NQKgRs+3\/3IdzfWe6QiIhkVVuvxcf7r+DD\/ZdRWy\/CycYKax7viwGdDLOHZruVxOjZsycuXbqEgQMHYvz48bpCsqdOnTK6hIzI0uSWVuGVH5MAAM8O6cyEjIgIgEqpwNxhodjx3ECE+zlDoRDQ2dNB7rAMUzzWmHGkjCyFKIp4en089p5vqPC97dn7oLbSW2lCIiKzUFevxZW8coR5OxrsPVqae+ilamRVVRUSExORm5sLrVbb5Llx48bp4y2IqJW2nMzA3vM5UCkFrJ4WyYSMiOgWrJQKgyZkrSE5Kdu5cydmzpyJ\/Pz8Zs8JgoD6+nqpb0FErZRVUonXdpwFADw\/rAu6enNUmIjI2En+6vzcc89h6tSpyMrKglarbfJgQkbU\/kRRxIubElFaVYfIABf8fXBHuUMiIqIWkJyU5eTkYP78+fDyMo6d2Iks3bfH0nHocj7UVgq8OzUCVkpOWxIRmQLJv62nTJmCAwcO6CEUIpIqvbAC\/\/vzOQDACw+GobOncayTICKiu5O8puzDDz\/E1KlTcejQIYSHh0OlUjV5fs6cOVLfgohaQKsV8cKm0yivqUe\/IFc8NTBE7pCIiKgVJCdl3377LXbv3g0bGxscOHAAgiDonhMEgUkZUTtZH3sNcVcLYatS4p2pkVAqhLu\/iIiIjIbkpOzll1\/GsmXLsGjRIigUXLtCJIeU\/HKs3HkBALB4dFcEe9jLHBEREbWW5CyqpqYG06ZNY0JGJJN6rYiFP5xGVa0WAzq5Y0ZUkNwhERFRG0jOpGbNmoXvvvtOH7EQURt8cfgq4lOL4GBthbemREDBaUsiIpMkefqyvr4eb731Fnbt2oWIiIhmC\/1Xr14t9S2ICEB1XT3SCyuRWlCOawUVuj\/jrhQAAJaM6QZ\/VzuZoyQioraSnJSdOXMGvXv3BgAkJSU1ee7mRf\/69tFHH+Htt99GdnY2IiMj8X\/\/93\/o37+\/wd6PqD1U1tQjtbAc1\/IrmiRfqQUVyCypxO12qh3e3QvT7glo32CJiEivJCdl+\/fv10ccrfLdd99h\/vz5WLNmDaKiovDee+9hxIgRuHjxIjw9Pds9HqLWKK2qRWpBBa7dSLZuTr5yNNV3fK29Wokgd3sEe9g1\/Oluh2B3e9wT7GbQL0FERGR4gije7ru38YqKisI999yDDz\/8EACg1WoREBCA5557DosWLbrja1u6U3tbVdfV48z1Er23S6anXisiW1N106hXQxJWUF5zx9c52VghxMNel3Q1JmGBbvbwcFAz+SIiMjEtzT0kj5S1t5qaGsTHx2Px4sW6YwqFAsOGDUNsbGyz86urq1Fd\/efog0ajMWh8ReW1mLKmeRxEN\/NwUCPI3R5BbnbNRr5c7NRyh0dERDIwuaQsPz8f9fX1zfba9PLywoULF5qdv2LFCixbtqy9woNCAQS7c7E1NfB0svlztMvdHkHudghyt4OjjeruLyYiIoticklZay1evBjz58\/X\/azRaBAQYLgF0Z6ONjjwwhCDtU9ERETmyeSSMg8PDyiVSuTk5DQ5npOTA29v72bnW1tbw9raur3CIyIiImoTkyvDr1ar0bdvX+zbt093TKvVYt++fYiOjpYxMiIiIqK2M7mRMgCYP38+Zs2ahX79+qF\/\/\/547733UF5ejieffFLu0IiIiIjaxCSTsmnTpiEvLw+vvvoqsrOz0atXL+zcubPZ4n8iIiIiU2GSdcqkMHSdMiIiIqKbtTT3MLk1ZURERETmiEkZERERkRFgUkZERERkBJiUERERERkBJmVERERERoBJGREREZERYFJGREREZASYlBEREREZAZOs6C9FY61cjUYjcyRERERkCRpzjrvV67e4pKy0tBQAEBAQIHMkREREZElKS0vh7Ox82+ctbpslrVaLzMxMODo6QhAEg7yHRqNBQEAA0tPTLWorJ0vstyX2GWC\/LanflthnwDL7bYl9Btqn36IoorS0FL6+vlAobr9yzOJGyhQKBfz9\/dvlvZycnCzqH3YjS+y3JfYZYL8tiSX2GbDMfltinwHD9\/tOI2SNuNCfiIiIyAgwKSMiIiIyAkzKDMDa2hpLly6FtbW13KG0K0vstyX2GWC\/LanflthnwDL7bYl9Boyr3xa30J+IiIjIGHGkjIiIiMgIMCkjIiIiMgJMyoiIiIiMAJMyIiIiIiPApOwu\/vOf\/yAiIkJXVC46Ohq\/\/vrrHV\/zww8\/oGvXrrCxsUF4eDh++eWXJs+LoohXX30VPj4+sLW1xbBhw3D58mVDdqNVWtvnzz77DIMGDYKrqytcXV0xbNgwHDt2rMk5TzzxBARBaPIYOXKkobvSKq3t99q1a5v1ycbGpsk5xv5ZA63v9wMPPNCs34IgYMyYMbpzTOHzvtnKlSshCAKef\/75O55n6tf2X7Wk3+ZyfTdqSZ\/N5dq+WUv6bQ7X9muvvdYsvq5du97xNcZ0XTMpuwt\/f3+sXLkS8fHxOHHiBIYOHYrx48fj7Nmztzz\/jz\/+wPTp0zF79mycOnUKEyZMwIQJE5CUlKQ756233sIHH3yANWvW4OjRo7C3t8eIESNQVVXVXt26o9b2+cCBA5g+fTr279+P2NhYBAQE4MEHH0RGRkaT80aOHImsrCzd49tvv22P7rRYa\/sNNFSAvrlPqampTZ439s8aaH2\/t2zZ0qTPSUlJUCqVmDp1apPzjP3zbnT8+HF88skniIiIuON55nBt36yl\/TaX6xtoeZ8B87i2G7W03+Zybffo0aNJfIcPH77tuUZ3XYvUaq6uruLnn39+y+cefvhhccyYMU2ORUVFiX\/\/+99FURRFrVYrent7i2+\/\/bbu+eLiYtHa2lr89ttvDRe0RHfq81\/V1dWJjo6O4rp163THZs2aJY4fP95A0RnOnfr91Vdfic7Ozrd9ral+1qLYus\/73\/\/+t+jo6CiWlZXpjpnK511aWiqGhoaKe\/bsEe+\/\/35x7ty5tz3XnK7t1vT7r0z1+m5Nn83p2pbyWZvitb106VIxMjKyxecb23XNkbJWqK+vx8aNG1FeXo7o6OhbnhMbG4thw4Y1OTZixAjExsYCAFJSUpCdnd3kHGdnZ0RFRenOMSYt6fNfVVRUoLa2Fm5ubk2OHzhwAJ6enggLC8M\/\/vEPFBQUGCJkvWhpv8vKyhAUFISAgIBmo0um9lkDbfu8v\/jiCzzyyCOwt7dvctwUPu9nn30WY8aMaXbN3oo5Xdut6fdfmer13do+m8u1LeWzNtVr+\/Lly\/D19UXHjh3x2GOPIS0t7bbnGtt1bXEbkrfFmTNnEB0djaqqKjg4OGDr1q3o3r37Lc\/Nzs6Gl5dXk2NeXl7Izs7WPd947HbnGIPW9PmvXnrpJfj6+jb5Rzxy5EhMmjQJISEhuHLlCv71r39h1KhRiI2NhVKpNFQ3Wq01\/Q4LC8OXX36JiIgIlJSU4J133sGAAQNw9uxZ+Pv7m8xnDbT98z527BiSkpLwxRdfNDluCp\/3xo0bcfLkSRw\/frxF55vLtd3afv+VKV7fre2zuVzbUj5rU722o6KisHbtWoSFhSErKwvLli3DoEGDkJSUBEdHx2bnG9t1zaSsBcLCwpCQkICSkhJs2rQJs2bNwsGDB1ucpJiitvZ55cqV2LhxIw4cONBkYewjjzyi+3t4eDgiIiLQqVMnHDhwADExMQbrR2u1pt\/R0dFNRpMGDBiAbt264ZNPPsEbb7zRnmFL1tbP+4svvkB4eDj69+\/f5Lixf97p6emYO3cu9uzZ02wBtzmT2m9TvL7b0mdzuLalftamem2PGjVK9\/eIiAhERUUhKCgI33\/\/PWbPni1jZC3D6csWUKvV6Ny5M\/r27YsVK1YgMjIS77\/\/\/i3P9fb2Rk5OTpNjOTk58Pb21j3feOx25xiD1vS50TvvvIOVK1di9+7dd11Q2rFjR3h4eCA5OVmfYUvWln43UqlU6N27t65PpvJZA23rd3l5OTZu3NiiX3TG9nnHx8cjNzcXffr0gZWVFaysrHDw4EF88MEHsLKyQn19fbPXmMO13ZZ+NzLV61tKnxuZ4rUtpd+mfG3\/lYuLC7p06XLb+IztumZS1gZarRbV1dW3fC46Ohr79u1rcmzPnj26b10hISHw9vZuco5Go8HRo0dbvIZHDnfqM9Bwd8obb7yBnTt3ol+\/fndt7\/r16ygoKICPj48+w9S7u\/X7ZvX19Thz5oyuT6b6WQMt6\/cPP\/yA6upqzJgx467tGdvnHRMTgzNnziAhIUH36NevHx577DEkJCTcchrGHK7ttvQbMO3ru619vpkpXttS+m3K1\/ZflZWV4cqVK7eNz+iua73fOmBmFi1aJB48eFBMSUkRExMTxUWLFomCIIi7d+8WRVEUH3\/8cXHRokW6848cOSJaWVmJ77zzjnj+\/Hlx6dKlokqlEs+cOaM7Z+XKlaKLi4v4448\/iomJieL48ePFkJAQsbKyst37dyut7fPKlStFtVotbtq0SczKytI9SktLRVFsuPtn4cKFYmxsrJiSkiLu3btX7NOnjxgaGipWVVXJ0sdbaW2\/ly1bJu7atUu8cuWKGB8fLz7yyCOijY2NePbsWd05xv5Zi2Lr+91o4MCB4rRp05odN5XP+6\/+emeaOV7bt3K3fpvL9X2zu\/XZXK7tv7pbvxuZ8rW9YMEC8cCBA2JKSop45MgRcdiwYaKHh4eYm5sriqLxX9dMyu7iqaeeEoOCgkS1Wi126NBBjImJ0f1nJYoN\/8hnzZrV5DXff\/+92KVLF1GtVos9evQQf\/755ybPa7Va8ZVXXhG9vLxEa2trMSYmRrx48WJ7dKdFWtvnoKAgEUCzx9KlS0VRFMWKigrxwQcfFDt06CCqVCoxKChIfPrpp8Xs7Ox27tmdtbbfzz\/\/vBgYGCiq1WrRy8tLHD16tHjy5MkmbRr7Zy2Kbfs3fuHCBRFAk\/Mamcrn\/Vd\/\/Q\/LHK\/tW7lbv83l+r7Z3fpsLtf2X7Xk37ipX9vTpk0TfXx8RLVaLfr5+YnTpk0Tk5OTdc8b+3UtiKIo6n\/8jYiIiIhag2vKiIiIiIwAkzIiIiIiI8CkjIiIiMgIMCkjIiIiMgJMyoiIiIiMAJMyIiIiIiPApIyIiIjICDApIyKLd+3aNQiCgISEhBa\/Zu3atXBxcTFYTERkeZiUERERERkBJmVERERERoBJGRFZhJ07d2LgwIFwcXGBu7s7HnroIVy5cuWW5x44cACCIODnn39GREQEbGxscO+99yIpKanZubt27UK3bt3g4OCAkSNHIisrS\/fc8ePHMXz4cHh4eMDZ2Rn3338\/Tp48abA+EpFpY1JGRBahvLwc8+fPx4kTJ7Bv3z4oFApMnDgRWq32tq954YUX8O677+L48ePo0KEDxo4di9raWt3zFRUVeOedd7Bhwwb8\/vvvSEtLw8KFC3XPl5aWYtasWTh8+DDi4uIQGhqK0aNHo7S01KB9JSLTZCV3AERE7WHy5MlNfv7yyy\/RoUMHnDt3Dg4ODrd8zdKlSzF8+HAAwLp16+Dv74+tW7fi4YcfBgDU1tZizZo16NSpEwDgn\/\/8J15\/\/XXd64cOHdqkvU8\/\/RQuLi44ePAgHnroIb31jYjMA0fKiMgiXL58GdOnT0fHjh3h5OSE4OBgAEBaWtptXxMdHa37u5ubG8LCwnD+\/HndMTs7O11CBgA+Pj7Izc3V\/ZyTk4Onn34aoaGhcHZ2hpOTE8rKyu74nkRkuThSRkQWYezYsQgKCsJnn30GX19faLVa9OzZEzU1NW1uU6VSNflZEASIoqj7edasWSgoKMD777+PoKAgWFtbIzo6WtJ7EpH5YlJGRGavoKAAFy9exGeffYZBgwYBAA4fPnzX18XFxSEwMBAAUFRUhEuXLqFbt24tft8jR47g448\/xujRowEA6enpyM\/Pb0MPiMgSMCkjIrPn6uoKd3d3fPrpp\/Dx8UFaWhoWLVp019e9\/vrrcHd3h5eXF15++WV4eHhgwoQJLX7f0NBQbNiwAf369YNGo8ELL7wAW1tbCT0hInPGNWVEZPYUCgU2btyI+Ph49OzZE\/PmzcPbb79919etXLkSc+fORd++fZGdnY0dO3ZArVa3+H2\/+OILFBUVoU+fPnj88ccxZ84ceHp6SukKEZkxQbx5AQQREeHAgQMYMmQIioqKuJUSEbUbjpQRERERGQEmZURERERGgNOXREREREaAI2VERERERoBJGREREZERYFJGREREZASYlBEREREZASZlREREREaASRkRERGREWBSRkRERGQEmJQRERERGQEmZURERERG4P8DJ83gB0IKvZYAAAAASUVORK5CYII=\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<ul>\n<li>$\\alpha &lt; 3.7$ \u7a0b\u5ea6\u3067\u306f\uff0cSID\u3068SA\u304c\u540c\u7b49\u306e\u6027\u80fd\u3092\u793a\u3057\u307e\u3057\u305f\uff0e\u3053\u306e\u9818\u57df\u306f\uff0csurvey\u304c\u3059\u3079\u3066 0 \u306b\u53ce\u675f\u3057\uff0cSA\u3060\u3051\u3067\u554f\u984c\u304c\u89e3\u3051\u308beasy-SAT\u9818\u57df\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\uff0e<\/li>\n<li>$3.7 &lt; \\alpha &lt; 4.3$ \u7a0b\u5ea6\u3067\u306f\uff0cSID\u304cSA\u3092\u4e0a\u56de\u308b\u6027\u80fd\u3092\u793a\u3057\u307e\u3057\u305f\uff0e\u3053\u306e\u9818\u57df\u306f\uff0cSA\u3060\u3051\u3067\u306f\u89e3\u3092\u767a\u898b\u3059\u308b\u306e\u304c\u96e3\u3057\u3044hard-SAT\u9818\u57df\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\uff0cSP\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u308b\u60c5\u5831\u304c\u89e3\u306e\u767a\u898b\u306b\u5927\u304d\u304f\u5f79\u7acb\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff0e<\/li>\n<li>$\\alpha &gt; 4.3$ \u7a0b\u5ea6\u3067\u306f\uff0cSID\uff0cSA\u3068\u3082\u306b (\u78ba\u7387 0.5 \u4ee5\u4e0a\u3067) \u89e3\u306e\u767a\u898b\u306b\u5931\u6557\u3057\u3066\u3044\u307e\u3059\uff0e\u3053\u306e\u9818\u57df\u306fUNSAT\u9818\u57df\u3067\u3042\u308a\uff0c\u305d\u3082\u305d\u3082\u307b\u3068\u3093\u3069\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304cUNSAT\u3067\u3042\u308b\u3068\u8003\u3048\u3089\u308c\u307e\u3059\uff0e<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E7%B5%90%E8%AB%96\"><\/span>\u7d50\u8ad6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u8a18\u4e8b\u3067\u306f\uff0c3-SAT\u306e\u30e9\u30f3\u30c0\u30e0\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u5bfe\u3057\u3066\uff0c\u3055\u307e\u3056\u307e\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u3066\u6027\u80fd\u3092\u8a55\u4fa1\u3057\u307e\u3057\u305f\uff0e\u305d\u306e\u7d50\u679c\uff0c\u4ee5\u4e0b\u306e\u70b9\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\uff0e<\/p>\n<ol>\n<li>\u30e9\u30f3\u30c0\u30e0\u306a3-SAT\u3067\u306f\u78ba\u304b\u306b $\\alpha_c\\approx 4.3$ \u306bSAT\/UNSAT\u5883\u754c\u304c\u3042\u308b\u3089\u3057\u3044<\/li>\n<li>SA\u3067\u306f$\\alpha_c$\u306b\u8fd1\u3044 $\\alpha$ \u3067\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u96e3\u3057\u304f\u306a\u308b<\/li>\n<li>SID\u3067\u306f$\\alpha_c$\u306b\u8fd1\u3044 $\\alpha$ \u3067SA\u3088\u308a\u9ad8\u3044\u78ba\u7387\u3067\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u3044\u305f<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u672c\u8a18\u4e8b\u306e\u5b9f\u88c5\u3067\u306f\uff0c\u305d\u3053\u307e\u3067\u9ad8\u901f\u5316\u306f\u884c\u3063\u3066\u3044\u307e\u305b\u3093\uff0e\u6587\u732e [1] \u3067\u306f\uff0c\u5909\u6570\u3092\u4e00\u3064\u305a\u3064\u6c7a\u5b9a\u3059\u308b\u306e\u3067\u306f\u306a\u304f\uff0c\u8907\u6570\u500b\u4e00\u6c17\u306b\u6c7a\u5b9a\u3059\u308b\u306a\u3069\u306e\u9ad8\u901f\u5316\u624b\u6cd5\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p>\u307e\u305f\uff0cSAT\/UNSAT\u5883\u754c\u3084easy-SAT\/hard-SAT\u5883\u754c\u306e\u3088\u308a\u7cbe\u5bc6\u306a\u8a08\u7b97\u306b\u3064\u3044\u3066\u306f\uff0c\u6587\u732e [2] \u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\uff0e<\/p>\n<p>\u307e\u305f\uff0c\u672c\u8a18\u4e8b\u3067\u306f\uff0cSA\u304cSID\u306b\u52a3\u308b\u3068\u3044\u3046\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3057\u305f\u304c\uff0c\u500b\u4eba\u7684\u306b\u306f\uff0cSA\u304cHC\u3084WID\u3092\u5927\u5e45\u306b\u4e0a\u56de\u308b\u6027\u80fd\u3092\u6301\u3063\u3066\u3044\u308b\u3053\u3068\u306b\u9a5a\u304d\u307e\u3057\u305f\uff0eHC\u306b\u30e9\u30f3\u30c0\u30e0\u6027\u3092\u5c0e\u5165\u3059\u308b\u3060\u3051\u3067\u6027\u80fd\u304c\u5927\u304d\u304f\u6539\u5584\u3059\u308b\u3068\u3044\u3046\u306e\u306f\u9762\u767d\u3044\u3068\u611f\u3058\u307e\u3059\uff0eSA\u3082\u5e73\u8861\u7d71\u8a08\u529b\u5b66\u306b\u7531\u6765\u3059\u308b\u624b\u6cd5\u3067\u3059\u304b\u3089\uff0c\u7d71\u8a08\u7269\u7406\u5b66\u306e\u624b\u6cd5\u304c\u975e\u5e38\u306b\u5e45\u5e83\u3044\u53ef\u80fd\u6027\u3092\u6301\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u4f3a\u3048\u307e\u3059\uff0e<\/p>\n<p>Survey propagation \u306e\u767a\u8868\u4ee5\u964d\u3082\uff0c$K$-SAT\u3092\u7d71\u8a08\u7269\u7406\u5b66\u306e\u624b\u6cd5\u3092\u7528\u3044\u3066\u89e3\u304f\u3068\u3044\u3046\u7814\u7a76\u306f\u66f4\u306a\u308b\u767a\u5c55\u3092\u898b\u305b\u3066\u3044\u307e\u3059 (\u4f8b\u3048\u3070\u6587\u732e [3], [4])\uff0e\u3088\u308a\u767a\u5c55\u7684\u306a\u624b\u6cd5\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u306b\u3082\u6311\u6226\u3057\u3066\u307f\u305f\u3044\u3068\u601d\u3044\u307e\u3059\uff0e<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE\"><\/span>\u53c2\u8003\u6587\u732e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>[1]\n<div class=\"csl-entry\">Braunstein, A., M\u00e9zard, M., &amp; Zecchina, R. (2005). Survey propagation: An algorithm for satisfiability. <i>Random Structures and Algorithms<\/i>, <i>27<\/i>(2), 201\u2013226. https:\/\/doi.org\/10.1002\/rsa.20057<\/div>\n<\/li>\n<li>[2]\n<div class=\"csl-entry\">Mezard, M., &amp; Zecchina, R. (2002). <i>The random K-satisfiability problem: from an analytic solution to an efficient algorithm<\/i>. https:\/\/doi.org\/10.1103\/PhysRevE.66.056126<\/div>\n<\/li>\n<li>[3]\n<div class=\"csl-entry\">Marino, R., Parisi, G., &amp; Ricci-Tersenghi, F. (2016). The backtracking survey propagation algorithm for solving random K-SAT problems. <i>Nature Communications<\/i>, <i>7<\/i>(1), 12996. https:\/\/doi.org\/10.1038\/ncomms12996<\/div>\n<\/li>\n<li>[4]\n<div class=\"csl-entry\">Grover, A., Achim, T., &amp; Ermon, S. (2018). <i>Streamlining Variational Inference for Constraint Satisfaction Problems<\/i>. https:\/\/doi.org\/10.1088\/1742-5468\/ab371f<\/div>\n<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"%E8%A8%98%E4%BA%8B%E3%81%AE%E6%8B%85%E5%BD%93%E8%80%85\"><\/span>\u8a18\u4e8b\u306e\u62c5\u5f53\u8005<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u897f\u5c71\u98af\u5927<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u8a18\u4e8b\u3067\u306f\uff0c\u30e9\u30f3\u30c0\u30e0\u306a 3-SAT \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3092\u89e3\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u3044\u304f\u3064\u304b\u5b9f\u88c5\u3057\u3066\u6027\u80fd\u3092\u6bd4\u8f03\u3057\u307e\u3059\uff0e\u305d\u3057\u3066\uff0c\u30b5\u30fc\u30d9\u30a4\u4f1d\u642c\u6cd5\u306b\u57fa\u3065\u3044\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u9ad8\u3044\u6027\u80fd\u3092\u6301\u3064\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\uff0e<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-6762","post","type-post","status-publish","format-standard","hentry","category-hands-on"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - 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