{"id":42168,"date":"2023-02-01T21:11:36","date_gmt":"2023-02-01T17:41:36","guid":{"rendered":"https:\/\/quera.org\/blog\/?p=42168"},"modified":"2023-02-02T01:58:55","modified_gmt":"2023-02-01T22:28:55","slug":"newbies-2018-solutions","status":"publish","type":"post","link":"https:\/\/quera.org\/blog\/newbies-2018-solutions\/","title":{"rendered":"\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc Newbies 2018"},"content":{"rendered":"\n<p class=\"has-medium-font-size\"><strong>\u0633\u0644\u0627\u0645!<\/strong><\/p>\n\n\n\n<p>\u0645\u0633\u0627\u0628\u0642\u0627\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc Newbies \u0632\u0645\u0633\u062a\u0648\u0646 \u0647\u0631 \u0633\u0627\u0644 \u062f\u0631 \u062f\u0627\u0646\u0634\u06af\u0627\u0647 \u0634\u0647\u06cc\u062f \u0628\u0647\u0634\u062a\u06cc \u0628\u0631\u06af\u0632\u0627\u0631 \u0645\u06cc\u0634\u0647. \u0633\u0637\u062d \u0633\u0624\u0627\u0644\u0627\u062a \u0627\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u0628\u0647 \u0646\u0633\u0628\u062a \u0645\u0633\u0627\u0628\u0642\u0627\u062a \u0631\u0633\u0645\u06cc ACM \u0622\u0633\u0648\u0646\u200c\u062a\u0631\u0647 \u0648\u0644\u06cc \u0633\u0628\u06a9 \u0633\u0624\u0627\u0644\u0627\u062a \u062d\u0641\u0638 \u0634\u062f\u0647 \u0648 \u0634\u0631\u06a9\u062a \u062a\u0648\u0634 \u0628\u0631\u0627\u06cc \u0639\u0644\u0627\u0642\u0647\u200c\u0645\u0646\u062f\u0627\u0646 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u060c \u0628\u0686\u0647\u200c\u0647\u0627\u06cc \u0627\u0644\u0645\u067e\u06cc\u0627\u062f\u06cc\u060c \u062f\u0627\u0646\u0634\u062c\u0648\u0647\u0627\u06cc \u062a\u0631\u0645 \u0627\u0648\u0644 \u0648 \u062f\u0648\u0645 \u0648 \u0647\u0645\u0647 \u06a9\u0633\u0627\u0646\u06cc \u06a9\u0647 \u0645\u06cc\u200c\u062e\u0648\u0627\u0646 \u062f\u0631 \u0645\u0633\u0627\u0628\u0642\u0627\u062a ACM-ICPC \u0634\u0631\u06a9\u062a \u06a9\u0646\u0646\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0646\u0647 \u062c\u0630\u0627\u0628 \u0648 \u0686\u0627\u0644\u0634\u06cc \u0628\u0627\u0634\u0647.<\/p>\n\n\n\n<p>\u0647\u0645\u0648\u0646 \u0637\u0648\u0631 \u06a9\u0647 \u0645\u06cc\u200c\u062f\u0648\u0646\u06cc\u062f \u062a\u0635\u0645\u06cc\u0645 \u06af\u0631\u0641\u062a\u06cc\u0645 \u0645\u0633\u0627\u0628\u0642\u0627\u062a \u0633\u0627\u0644\u200c\u0647\u0627\u06cc \u06af\u0630\u0634\u062a\u0647 Newbies \u0631\u0648 \u0628\u0647\u200c\u0635\u0648\u0631\u062a \u0622\u0646\u0644\u0627\u06cc\u0646 \u062f\u0631 \u06a9\u0648\u0626\u0631\u0627 \u0628\u0631\u06af\u0632\u0627\u0631 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0641\u0631\u0635\u062a\u06cc \u0628\u0631\u0627\u06cc \u062a\u0645\u0631\u06cc\u0646 \u0648 \u0631\u0642\u0627\u0628\u062a \u0628\u0627\u0634\u0647. \u0627\u06cc\u0646 \u0647\u0641\u062a\u0647 \u0645\u0633\u0627\u0628\u0642\u0647\u200c\u06cc \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc Newbies 2018 \u062f\u0631 \u06a9\u0648\u0626\u0631\u0627 \u0628\u0631\u06af\u0632\u0627\u0631 \u0634\u062f. \u0627\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u062f\u0631 \u0633\u0627\u0644 \u06f2\u06f0\u06f1\u06f8 \u062f\u0631 \u062f\u0627\u0646\u0634\u06af\u0627\u0647 \u0634\u0647\u06cc\u062f \u0628\u0647\u0634\u062a\u06cc \u0628\u0627 \u062a\u0644\u0627\u0634 \u00ab\u0645\u062d\u0645\u062f\u0631\u0636\u0627 \u0645\u062d\u0633\u0646\u06cc\u00bb\u060c \u00ab\u0645\u062d\u0645\u062f \u0646\u0635\u06cc\u0631\u06cc\u200c\u0641\u0631\u00bb\u060c \u00ab\u0645\u062d\u0645\u062f\u062d\u0633\u0646\u200c\u067e\u0648\u0631\u00bb\u060c \u00ab\u0639\u0631\u0641\u0627\u0646 \u0639\u0644\u06cc\u200c\u0645\u062d\u0645\u062f\u06cc\u00bb\u060c \u00ab\u0633\u0627\u0645\u0627\u0646 \u062e\u0627\u0645\u0633\u06cc\u0627\u0646\u00bb \u0648 \u00ab\u0631\u0636\u0627 \u0634\u06cc\u0631\u06cc\u00bb \u0637\u0631\u0627\u062d\u06cc \u0648 \u0628\u0631\u06af\u0632\u0627\u0631 \u0634\u062f\u0647 \u0628\u0648\u062f.<\/p>\n\n\n\n<p>\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u0627\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u062f\u0631 \u0627\u062f\u0627\u0645\u0647 \u062a\u0648\u0636\u06cc\u062d \u062f\u0627\u062f\u0647 \u0634\u062f\u0646\u062f. \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0645\u062a\u0648\u062c\u0647 \u0631\u0627\u0647\u200c\u062d\u0644\u06cc \u0646\u0634\u062f\u06cc\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0646\u06cc\u062f \u062f\u0631 \u0628\u062e\u0634 \u0646\u0638\u0631\u0627\u062a\u060c \u0633\u0624\u0627\u0644\u0627\u062a \u0648 \u0627\u0628\u0647\u0627\u0645\u200c\u0647\u0627\u06cc \u062e\u0648\u062f\u062a\u0648\u0646 \u0631\u0648 \u0645\u0637\u0631\u062d \u06a9\u0646\u06cc\u062f. \u0627\u06af\u0647 \u0631\u0627\u0647\u200c\u062d\u0644 \u062f\u06cc\u06af\u0647\u200c\u0627\u06cc \u0628\u0631\u0627\u06cc \u0633\u0624\u0627\u0644\u0627\u062a \u062f\u0627\u0631\u06cc\u062f\u060c \u062e\u0648\u0634\u062d\u0627\u0644 \u0645\u06cc\u200c\u0634\u06cc\u0645 \u06a9\u0647 \u0631\u0627\u0647\u200c\u062d\u0644\u062a\u0648\u0646 \u0631\u0648 \u062f\u0631 \u0628\u062e\u0634 \u0646\u0638\u0631\u0627\u062a \u0628\u0627 \u0645\u0627 \u0648 \u062f\u0648\u0633\u062a\u0627\u0646\u062a\u0648\u0646 \u0628\u0647 \u0627\u0634\u062a\u0631\u0627\u06a9 \u0628\u0630\u0627\u0631\u06cc\u062f.<\/p>\n\n\n\n<div style=\"height:7px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_81 counter-hierarchy ez-toc-counter-rtl ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628<\/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:\/\/quera.org\/blog\/newbies-2018-solutions\/#A_%E2%80%93_AbulHassans_Quest\" >A \u2013 AbulHassan\u2019s Quest<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#B_%E2%80%93_Farshads_Research\" >B \u2013 Farshad\u2019s Research<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#C_%E2%80%93_Shortest_but_Hardest\" >C \u2013 Shortest but Hardest<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#D_%E2%80%93_Divisible_Strings\" >D \u2013 Divisible Strings<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#E_%E2%80%93_Tennis\" >E \u2013 Tennis<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#F_%E2%80%93_Profiling\" >F \u2013 Profiling<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#G_%E2%80%93_IMEI\" >G \u2013 IMEI<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#H_%E2%80%93_Fall_in_Love\" >H \u2013 Fall in Love<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#I_%E2%80%93_Lightning_Strike\" >I \u2013 Lightning Strike<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#J_%E2%80%93_Jitter_Minimization\" >J \u2013 Jitter Minimization<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#K_%E2%80%93_Traffic_Lights\" >K \u2013 Traffic Lights<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#L_%E2%80%93_Your_House_Have_Ant\" >L \u2013 Your House Have Ant<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/quera.org\/blog\/newbies-2018-solutions\/#M_%E2%80%93_Concert\" >M \u2013 Concert<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-a-abulhassan-s-quest\"><span class=\"ez-toc-section\" id=\"A_%E2%80%93_AbulHassans_Quest\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169373\/\" target=\"_blank\" rel=\"noreferrer noopener\">A \u2013 AbulHassan\u2019s Quest<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">b \\neq 0<\/span> \u0622\u0646\u06af\u0627\u0647:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>q = \\frac{a-r}{b}<\/pre><\/div>\n\n\n\n<p>\u067e\u0633 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0686\u06a9 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">a-r<\/span> \u0645\u0636\u0631\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0647\u0633\u062a \u06cc\u0627 \u0646\u0647 \u0648 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">b = 0<\/span> \u0622\u0646\u06af\u0627\u0647 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0686\u06a9 \u06a9\u0646\u06cc\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T)<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint main()\n{\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tint a, b, r;\n\t\tcin &gt;&gt; a &gt;&gt; b &gt;&gt; r;\n\t\tif(b == 0)\n\t\t\tcout &lt;&lt; (a == r?\"Yes\\n\":\"No\\n\");\n\t\telse\n\t\t\tcout &lt;&lt; ((a-r)%b == 0?\"Yes\\n\":\"No\\n\");\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-b-farshad-s-research\"><span class=\"ez-toc-section\" id=\"B_%E2%80%93_Farshads_Research\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169374\/\" target=\"_blank\" rel=\"noreferrer noopener\">B \u2013 Farshad\u2019s Research<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0627\u0646\u062f\u0627\u0632\u0647\u200c\u06cc \u0647\u0631 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Component_%28graph_theory%29\">\u0645\u0624\u0644\u0641\u0647 \u0647\u0645\u0628\u0646\u062f\u06cc<\/a> \u0631\u0627 \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u0648\u0631\u06cc\u0645 (\u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0628\u0627 <code>dfs<\/code> \u060c<code>bfs<\/code> \u0648 \u06cc\u0627 <code>dsu<\/code> \u0642\u0627\u0628\u0644 \u0627\u0646\u062c\u0627\u0645 \u0627\u0633\u062a). \u0648 \u0633\u067e\u0633 \u0622\u0646\u200c\u0647\u0627 \u0631\u0627 \u0645\u0631\u062a\u0628 \u0634\u062f\u0647 \u062f\u0631 \u0622\u0631\u0627\u06cc\u0647\u200c\u0627\u06cc \u0645\u062b\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> \u0630\u062e\u06cc\u0631\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0631\u0627 \u062a\u0639\u062f\u0627\u062f \u0645\u0624\u0644\u0641\u0647\u200c\u0647\u0627 \u0628\u0627 \u0633\u0627\u06cc\u0632 \u06a9\u0645\u062a\u0631 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0628\u06af\u06cc\u0631\u06cc\u0645 \u0622\u0646\u06af\u0627\u0647 \u067e\u0627\u0633\u062e \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">f(r+1)-f(l)<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0627\u0632 \u0631\u0648\u0634 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Binary_search_algorithm\">\u062c\u0633\u062a\u200c\u0648\u062c\u0648\u06cc \u062f\u0648\u062f\u0648\u06cc\u06cc<\/a> \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T \\times (N + M \\log N + Q \\log N))<\/pre><\/div>\n\n\n\n<p>\u0645\u0627 \u0628\u0631\u0627\u06cc \u0633\u0627\u062f\u06af\u06cc \u067e\u06cc\u0627\u062f\u0647\u200c\u0633\u0627\u0632\u06cc \u0627\u0632 <code>dsu<\/code> \u0628\u0627 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">M \\log N<\/span> \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint main()\n{\n\tios_base::sync_with_stdio(false);\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tint n, m, q;\n\t\tcin &gt;&gt; n &gt;&gt; m &gt;&gt; q;\n\t\tint head[n], sz[n];\n\t\tfor(int i = 0; i &lt; n; i++)\n\t\t\thead[i] = i, sz[i] = 1;\n\t\tfor(int u, v, i = 0; i &lt; m; i++)\n\t\t{\n\t\t\tcin &gt;&gt; u &gt;&gt; v;\n\t\t\tu--, v--;\n\t\t\twhile(u != head[u])u = head[u];\n\t\t\twhile(v != head[v])v = head[v];\n\t\t\tif(u == v)continue;\n\t\t\tif(sz[v] &lt; sz[u])swap(u, v);\n\t\t\tsz[v] += sz[u];\n\t\t\thead[u] = v;\n\t\t}\n\t\tvector&lt;int&gt; sizes;\n\t\tfor(int i = 0; i &lt; n; i++)\n\t\t\tif(i == head[i])\n\t\t\t\tsizes.push_back(sz[i]);\n\t\tsort(sizes.begin(), sizes.end());\n\t\tfor(int l, r, i = 0; i &lt; q; i++)\n\t\t{\n\t\t\tcin &gt;&gt; l &gt;&gt; r;\n\t\t\tl = lower_bound(sizes.begin(), sizes.end(), l)-sizes.begin();\n\t\t\tr = upper_bound(sizes.begin(), sizes.end(), r)-sizes.begin();\n\t\t\tcout &lt;&lt; r-l &lt;&lt; '\\n';\n\t\t}\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-c-shortest-but-hardest\"><span class=\"ez-toc-section\" id=\"C_%E2%80%93_Shortest_but_Hardest\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169375\/\" target=\"_blank\" rel=\"noreferrer noopener\">C \u2013 Shortest but Hardest<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u062f\u0639\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u067e\u0627\u0633\u062e \u0628\u0631\u0627\u0628\u0631 \u06a9\u0648\u0686\u06a9\u200c\u062a\u0631\u06cc\u0646 \u0639\u0636\u0648 \u0622\u0631\u0627\u06cc\u0647 \u0627\u0633\u062a (\u0622\u0646 \u0631\u0627 \u0627\u0632 \u0627\u06cc\u0646 \u0628\u0647 \u0628\u0639\u062f <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f)! \u0645\u0634\u062e\u0635\u0627\u064b \u0632\u06cc\u0631\u062f\u0646\u0628\u0627\u0644\u0647\u200c\u0627\u06cc \u06a9\u0647 \u062a\u0646\u0647\u0627 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0633\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u06cc\u0646 \u062e\u0627\u0635\u06cc\u062a \u0631\u0627 \u062f\u0627\u0631\u062f. \u062d\u0627\u0644 \u062b\u0627\u0628\u062a \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0647\u0631 \u0632\u06cc\u0631\u062f\u0646\u0628\u0627\u0644\u0647\u200c\u0627\u06cc \u0645\u0627\u0646\u0646\u062f:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>A_l, A_{l+1}, \\dots , A_r<\/pre><\/div>\n\n\n\n<p>\u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0647\u0646\u062f\u0633\u06cc \u0628\u06cc\u0634\u062a\u0631 \u0645\u0633\u0627\u0648\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u062f\u0627\u0631\u062f.<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\sqrt[r-l+1]{A_l . A_{l+1} . \\cdots . A_r} \\ge \\sqrt[r-l+1]{m . m . \\cdots . m} = m<\/pre><\/div>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T \\times n)<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint main()\n{\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tint n;\n\t\tcin &gt;&gt; n;\n\t\tint A[n];\n\t\tfor(int i = 0; i &lt; n; i++)\n\t\t\tcin &gt;&gt; A[i];\n\t\tcout &lt;&lt; *min_element(A, A+n) &lt;&lt; \".00\" &lt;&lt; '\\n';\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-d-divisible-strings\"><span class=\"ez-toc-section\" id=\"D_%E2%80%93_Divisible_Strings\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169376\/\" target=\"_blank\" rel=\"noreferrer noopener\">D \u2013 Divisible Strings<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u062d\u0644 \u0627\u06cc\u0646 \u0633\u0624\u0627\u0644 \u062d\u0631\u06cc\u0635\u0627\u0646\u0647 \u0639\u0645\u0644 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0647 \u0627\u06cc\u0646 \u0634\u06a9\u0644 \u06a9\u0647 \u0633\u0639\u06cc \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0628\u0632\u0631\u06af\u062a\u0631\u06cc\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647 \u0628\u0627 \u062d\u0630\u0641 \u0628\u0631\u062e\u06cc \u0627\u0632 \u062d\u0631\u0648\u0641 <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u062d\u0627\u0635\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">k \\times T<\/span> \u0634\u0648\u062f \u0648 \u0628\u062f\u06cc\u0646 \u0635\u0648\u0631\u062a \u067e\u0627\u0633\u062e \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">|S| - k \\times |T|<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n\n\n\n<p>\u067e\u0633 \u0628\u0627\u06cc\u062f \u0631\u0634\u062a\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">S = s_1, s_2, \\dots , s_{k*|T|}<\/span> \u062a\u0628\u062f\u06cc\u0644 \u0634\u0648\u062f \u0628\u0647 \u0637\u0648\u0631\u06cc \u06a9\u0647:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>s_1 = T_1, s_2 = T_2, \\dots , s_{|T|+1} = T_1, \\dots, s_{|T|\\times k} = T_{|T|} <\/pre><\/div>\n\n\n\n<p>\u062d\u0627\u0644 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u0634\u0631\u0648\u0639 \u06a9\u0631\u062f\u0647 \u0648 \u0622\u0646\u0642\u062f\u0631 \u062d\u0631\u0641 \u0627\u0632 \u0627\u0628\u062a\u062f\u0627 \u062d\u0630\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">s_1<\/span> \u0628\u0631\u0633\u06cc\u0645 \u0648 \u0628\u0639\u062f \u0627\u0632 \u0622\u0646 \u062f\u0648\u0628\u0627\u0631\u0647 \u0622\u0646\u0642\u062f\u0631 \u062d\u0631\u0641 \u062d\u0630\u0641 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">s_2<\/span> \u0628\u0631\u0633\u06cc\u0645 \u0648&#8230;<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T \\times (|S| + |T|))<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint main()\n{\n\tint T;\n\tcin &gt;&gt; T;\n\tgetchar();\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tstring s, t;\n\t\tgetline(cin, s);\n\t\tgetline(cin, t);\n\t\tint ps = 0, pt = 0, k = 0;\n\t\twhile(ps &lt; s.size())\n\t\t{\n\t\t\tif(s[ps] == t[pt])pt++;\n\t\t\tps++;\n\t\t\tif(pt == t.size())k++, pt = 0;\n\t\t}\n\t\tcout &lt;&lt; s.size()-k*t.size() &lt;&lt; '\\n';\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-e-tennis\"><span class=\"ez-toc-section\" id=\"E_%E2%80%93_Tennis\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169377\/\" target=\"_blank\" rel=\"noreferrer noopener\">E \u2013 Tennis<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0633\u0624\u0627\u0644 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0647\u0645\u0647 \u062d\u0627\u0644\u0627\u062a \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">?<\/span> \u0631\u0627 \u0627\u0645\u062a\u062d\u0627\u0646 \u06a9\u0646\u06cc\u062f \u0648 \u062f\u0631 \u0647\u0631 \u062d\u0627\u0644\u062a \u0645\u0639\u062a\u0628\u0631 \u0628\u0631\u0646\u062f\u0647 \u0631\u0627 \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u06a9\u0646\u06cc\u062f.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: \u0645\u0646\u0638\u0648\u0631 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">MAX_{length}<\/span> \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0647\u0645\u0627\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">11<\/span> \u0627\u0633\u062a.<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T \\times MAX_{length} \\times 3^{MAX_{length}})<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">#include &lt;iostream&gt;\n#include &lt;cmath&gt;\n#include &lt;algorithm&gt;\n#include &lt;vector&gt;\n#include &lt;cassert&gt;\n\nusing namespace std;\n\nconst int NASIRIFAR = 1;\nconst int MORTEZA = 2;\nconst int INVALID = 0;\n\nint pw(int a, int b) {\n    int ret = 1;\n    for(int i = 0 ;i &lt; b;  i++) {\n        ret *= a;\n    }\n    return ret;\n}\n\nstring renderSequence(string sequence, const vector&lt;char&gt;&amp; assignments) {\n    int assignmentPtr = 0;\n    for(int i = 0;i &lt; sequence.size(); i++) {\n        if(sequence[i] == '?') {\n            sequence[i] = assignments[assignmentPtr];\n            assignmentPtr++;\n        }\n    }\n    return sequence;\n}\n\nenum State {\n    toServe,\n    ballInAirServe,\n    ballInAir,\n    groundOnce,\n};\n\nconst char RACKET = 'R';\nconst char GROUND = 'G';\nconst char NET = 'N';\n\nint otherPlayer(int player) {\n    if(player == NASIRIFAR) {\n        return MORTEZA;\n    }\n    return NASIRIFAR;\n}\n\nint getResult(const string&amp; sequence) {\n    int scores[3] = {0};\n\n    int state = toServe;\n    int lastHit = 0;\n\n    for(auto event: sequence) {\n        if(state == toServe) {\n            if(event != RACKET) {\n                return INVALID;\n            }\n            lastHit = NASIRIFAR;\n            state = ballInAirServe;\n        } else if(state == ballInAirServe) {\n            if(event == RACKET) {\n                return INVALID;\n            } else if(event == NET) {\n                scores[otherPlayer(lastHit)] ++;\n                state = toServe;\n            } else if(event == GROUND){\n                state = groundOnce;\n            }\n        } else if(state == ballInAir) {\n            if(event == RACKET) {\n                lastHit = otherPlayer(lastHit);\n            } else if(event == NET) {\n                scores[otherPlayer(lastHit)] ++;\n                state = toServe;\n            } else if(event == GROUND){\n                state = groundOnce;\n            }\n        } else if (state == groundOnce) {\n            if(event == RACKET) {\n                lastHit = otherPlayer(lastHit);\n                state = ballInAir;\n            } else if(event == NET) {\n                return INVALID;\n            } else if(event == GROUND){\n                state = toServe;\n                scores[lastHit]++;\n            }\n        }\n    }\n\n    if(state != toServe) {\n        return INVALID;\n    }\n\n    if(scores[MORTEZA] &gt;= scores[NASIRIFAR]) {\n        return MORTEZA;\n    }\n    return NASIRIFAR;\n}\n\nint main() {\n    int t;\n    cin &gt;&gt; t;\n    assert(t &lt;= 50);\n    while(t --) {\n        string soundsSequence;\n        cin &gt;&gt; soundsSequence;\n\n        assert(soundsSequence.size() &lt;= 11);\n\n        vector&lt;char&gt; choices = {RACKET, GROUND, NET};\n        \n        int numQuestionMarks = count(soundsSequence.begin(), soundsSequence.end(), '?');\n        int numAllSequences = pw(3, numQuestionMarks);\n\n        int numMorteza = 0, numNasirifar = 0;\n\n        for(int coding = 0; coding &lt; numAllSequences; coding++) {\n            vector&lt;char&gt; assignments;\n            int origCoding = coding;\n            for(int i = 0 ;i &lt; numQuestionMarks; i++) {\n                assignments.push_back(choices[coding%3]);\n                coding \/= 3;\n            }\n            coding = origCoding;\n            string renderedSequence = renderSequence(soundsSequence, assignments);\n            int result = getResult(renderedSequence);\n            if(result == NASIRIFAR) {\n                numNasirifar++;\n            } else if (result == MORTEZA) {\n                numMorteza ++;\n            }else {\n                \/\/ invalid sequence\n            }\n        }\n        assert(numMorteza + numNasirifar &gt;= 0);\n\n        if(numMorteza &gt;= numNasirifar) {\n            cout &lt;&lt; \"Morteza to doost dashtani hasti\" &lt;&lt; endl;\n        } else {\n            cout &lt;&lt; \"Nasirifar to doost dashtani hasti\" &lt;&lt; endl;\n        }\n    }\n    \n    return 0;\n}<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-f-profiling\"><span class=\"ez-toc-section\" id=\"F_%E2%80%93_Profiling\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169378\/\" target=\"_blank\" rel=\"noreferrer noopener\">F \u2013 Profiling<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u06cc\u0646 \u0633\u0624\u0627\u0644 \u0628\u0647 \u0686\u0646\u062f \u0628\u062e\u0634 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u0634\u0648\u062f (\u0627\u06af\u0631 \u0645\u0648\u0631\u062f\u06cc \u062f\u0631 \u0686\u0646\u062f \u0628\u062e\u0634 \u0628\u0648\u062f \u0628\u062e\u0634 \u0628\u0627 \u0627\u0648\u0644\u0648\u06cc\u062a \u0628\u0627\u0644\u0627\u062a\u0631 \u0645\u062f \u0646\u0638\u0631 \u0627\u0633\u062a) : <br>1. \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n &lt; k<\/span> \u0622\u0646\u06af\u0627\u0647 \u062c\u0648\u0627\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u0627\u0633\u062a. <br>2. \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n = k<\/span> \u0622\u0646\u06af\u0627\u0647 \u062c\u0648\u0627\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u0627\u0633\u062a. <br>3. \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">k = 0<\/span> \u0622\u0646\u06af\u0627\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">fib(0)<\/span> \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">fib(2)<\/span> \u0635\u062f\u0627 \u0632\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f \u067e\u0633 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">2<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645. <br>4. \u0628\u0647 \u0627\u0633\u062a\u0642\u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f \u062c\u0648\u0627\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">fib(n-k)<\/span> \u0627\u0633\u062a. \u067e\u0627\u06cc\u0647 \u0628\u0631\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">n = k<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">n = k+1<\/span> \u0645\u0634\u062e\u0635 \u0627\u0633\u062a (\u062f\u0631 \u0627\u06cc\u0646 \u062f\u0648 \u062d\u0627\u0644\u062a \u062c\u0648\u0627\u0628 \u06cc\u06a9 \u0627\u0633\u062a \u06cc\u0639\u0646\u06cc \u0647\u0645\u0627\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">(fib(0) = fib(1) = 1)<\/span> \u0648 \u06af\u0627\u0645 \u0647\u0645 \u0628\u0647 \u0622\u0633\u0627\u0646\u06cc \u0627\u062b\u0628\u0627\u062a \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(MAX_N + T)<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nconst int mod = 1'000'000'007;\nconst int N = 100'000 + 5;\nint fib[N];\n\nint main()\n{\n\tfib[0] = fib[1] = 1;\n\tfor(int i = 2; i &lt; N; i++)\n\t\tfib[i] = (fib[i-1]+fib[i-2])%mod;\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tint n, k;\n\t\tcin &gt;&gt; n &gt;&gt; k;\n\t\tif(k == n)\n\t\t\tcout &lt;&lt; 1 &lt;&lt; '\\n';\n\t\telse if(k &gt; n or n &lt; 2)\n\t\t\tcout &lt;&lt; 0 &lt;&lt; '\\n';\n\t\telse if(k == 0)\n\t\t\tcout &lt;&lt; fib[n-2] &lt;&lt; '\\n';\n\t\telse\n\t\t\tcout &lt;&lt; fib[n-k] &lt;&lt; '\\n';\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-g-imei\"><span class=\"ez-toc-section\" id=\"G_%E2%80%93_IMEI\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169379\/\" target=\"_blank\" rel=\"noreferrer noopener\">G \u2013 IMEI<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0628\u062e\u0634 \u0627\u0648\u0644 \u0633\u0624\u0627\u0644 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u06f8 \u0631\u0642\u0645 \u0627\u0648\u0644 \u0631\u0627 \u0686\u0627\u067e \u06a9\u0646\u06cc\u062f \u0648 \u0628\u0631\u0627\u06cc \u0628\u062e\u0634 \u062f\u0648\u0645 \u0627\u0628\u062a\u062f\u0627 <code>sumdigits<\/code> \u0631\u0627 \u0637\u0628\u0642 \u062f\u0633\u062a\u0648\u0631\u0627\u0644\u0639\u0645\u0644 \u062d\u0633\u0627\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u062d\u0627\u0644 \u0628\u0627\u0642\u06cc \u0645\u0627\u0646\u062f\u0647 \u0622\u0646 \u0628\u0631 \u06f1\u06f0 \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">s<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f. \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">s = 0<\/span> \u0622\u0646\u06af\u0627\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">checksum = 0<\/span> \u0648 \u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646\u0635\u0648\u0631\u062a <span class=\"katex-eq\" data-katex-display=\"false\">checksum = 10-s<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T)<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint main()\n{\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tstring n;\n\t\tcin &gt;&gt; n;\n\t\tfor(int i = 0; i &lt; 8; i++)cout &lt;&lt; n[i];\n\t\tint sum = 0;\n\t\tfor(int i = 0; i &lt; n.size(); i++)\n\t\t{\n\t\t\tif(i%2 == 0)sum += n[i]-'0';\n\t\t\telse sum += (n[i]-'0')*2\/10+(n[i]-'0')*2%10;\n\t\t}\n\t\tsum %= 10;\n\t\tcout &lt;&lt; ' ' &lt;&lt; (sum == 0?sum:10-sum) &lt;&lt; '\\n';\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-h-fall-in-love\"><span class=\"ez-toc-section\" id=\"H_%E2%80%93_Fall_in_Love\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169380\/\" target=\"_blank\" rel=\"noreferrer noopener\">H \u2013 Fall in Love<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0639\u062f\u062f \u0627\u0648\u0644 \u0628\u0627\u0634\u062f \u06a9\u0647 \u062a\u0646\u0647\u0627 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0628\u0632\u0631\u06af\u062a\u0631 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0647\u0633\u062a \u06cc\u0627 \u0646\u0647.<br>\u062d\u0627\u0644 \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0627\u0648\u0644 \u0646\u0628\u0627\u0634\u062f. \u067e\u0633:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>m = \\Pi {p_i}^{q_i} (1 \\leq p_i \\leq \\sqrt m, 0 \\leq q_i)<\/pre><\/div>\n\n\n\n<p>\u062d\u0627\u0644 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n!<\/span> \u0628\u0631 \u0647\u0631 \u06cc\u06a9 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">{p_i}^{q_i}<\/span> \u0628\u062e\u0634\u200c\u067e\u0630\u06cc\u0631 \u0628\u0627\u0634\u062f \u0622\u0646\u06af\u0627\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">n!<\/span> \u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0628\u062e\u0634\u200c\u067e\u0630\u06cc\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631\u0647\u0627\u06cc \u0639\u0627\u0645\u0644 \u0627\u0648\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">p_i<\/span> \u062f\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n!<\/span> \u0628\u0647 \u0637\u0631\u06cc\u0642 \u0632\u06cc\u0631 \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f (\u0628\u0627 \u0627\u0633\u062a\u0642\u0631\u0627 \u0631\u0648\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u062b\u0627\u0628\u062a \u06a9\u0646\u06cc\u062f.) :<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>count_{p_i} = \\sum_{k=1}^{\\infty} \\frac{n}{{p_i}^k}<\/pre><\/div>\n\n\n\n<p>\u067e\u0633 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0686\u06a9 \u06a9\u0646\u06cc\u0645 \u0622\u06cc\u0627 \u062a\u0639\u062f\u0627\u062f \u062a\u06a9\u0631\u0627\u0631\u0647\u0627\u06cc \u0639\u0648\u0627\u0645\u0644 \u0627\u0648\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0647\u0645\u06cc\u0634\u0647 \u062f\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u0628\u0632\u0631\u06af\u062a\u0631 \u0645\u0633\u0627\u0648\u06cc \u0647\u0633\u062a \u06cc\u0627 \u0646\u0647.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc: (<span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u0631\u0627 \u062d\u062f\u0627\u06a9\u062b\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f \u06a9\u0647 \u062f\u0631 \u0633\u0624\u0627\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">2^{31}<\/span> \u0627\u0633\u062a.)<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(\\sqrt N \\log\\log\\sqrt N + T \\times \\frac{\\sqrt N}{\\log\\sqrt N} \\times \\log\\log N)<\/pre><\/div>\n\n\n\n<p>\u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt N \\log\\log\\sqrt N<\/span> \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc <a href=\"https:\/\/cp-algorithms.com\/algebra\/sieve-of-eratosthenes.html\">\u063a\u0631\u0628\u0627\u0644 \u0627\u0639\u062f\u0627\u062f \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644<\/a> \u0627\u0633\u062a \u0648 \u0646\u06cc\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\sqrt N}{\\log\\sqrt N}<\/span> \u062a\u0639\u062f\u0627\u062f \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644\u06cc \u0647\u0633\u062a \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0639\u0627\u0645\u0644 \u0627\u0648\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">m<\/span> \u0627\u0648\u0644 \u0646\u0628\u0627\u0634\u062f\u060c \u0628\u0627\u0634\u0646\u062f.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nconstexpr int N = 2147483647; \/\/ 2^31-1\nconstexpr int SQN = 31622; \/\/ sqrt(N)\nbitset&lt;SQN&gt; is_prime;\nvector&lt;int&gt; primes;\n\nint main()\n{\n\tis_prime.set(), is_prime.reset(0), is_prime.reset(1);\n\tfor(int i = 0; i &lt; SQN; i++)\n\t\tif(is_prime[i])\n\t\t{\n\t\t\tprimes.push_back(i);\n\t\t\tfor(int j = i+i; j &lt; SQN; j += i)\n\t\t\t\tis_prime.reset(j);\n\t\t}\n\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tint n, m, m_copy;\n\t\tcin &gt;&gt; n &gt;&gt; m, m_copy = m;\n\t\tbool divides = true;\n\t\tfor(auto p: primes)\n\t\t{\n\t\t\tif(p*p &gt; m or !divides)break;\n\t\t\tint cnt_p = 0;\n\t\t\twhile (m%p == 0) cnt_p++, m \/= p;\n\t\t\tint cnt_n_factorial = 0, n_copy = n;\n\t\t\twhile(cnt_n_factorial &lt; cnt_p and n_copy &gt; 0)\n\t\t\t\tn_copy \/= p, cnt_n_factorial += n_copy;\n\t\t\tdivides &amp;= (cnt_n_factorial &gt;= cnt_p);\t\n\t\t}\n\t\tif(m &gt; 1 and n &lt; m)divides = false;\n\t\tcout &lt;&lt; m_copy &lt;&lt; (divides?\" divides \":\" does not divide \") &lt;&lt; n &lt;&lt; \"!\\n\";\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-i-lightning-strike\"><span class=\"ez-toc-section\" id=\"I_%E2%80%93_Lightning_Strike\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169381\/\" target=\"_blank\" rel=\"noreferrer noopener\">I \u2013 Lightning Strike<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u062d\u0644 \u0633\u0648\u0627\u0644 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u06f4 \u0628\u062e\u0634 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. (\u0628\u0627 \u0641\u0631\u0636 \u062f\u0627\u0634\u062a\u0646 \u0628\u0631\u062e\u0648\u0631\u062f) \u0628\u0631\u062e\u0648\u0631\u062f \u062f\u0648 \u062a\u0648\u067e \u067e\u0633 \u0627\u0632 \u0628\u0631\u062e\u0648\u0631\u062f \u0647\u0631 \u06a9\u062f\u0627\u0645 \u0628\u0647 \u062f\u06cc\u0648\u0627\u0631 \u0628\u0627\u0634\u062f \u06cc\u0627 \u0628\u0631\u062e\u0648\u0631\u062f \u0647\u0631 \u062f\u0648 \u0642\u0628\u0644 \u0627\u0632 \u0628\u0631\u062e\u0648\u0631\u062f \u0628\u0647 \u062f\u06cc\u0648\u0627\u0631 \u06cc\u0627 \u06cc\u06a9\u06cc \u0642\u0628\u0644 \u0627\u0632 \u0628\u0631\u062e\u0648\u0631\u062f \u0628\u0647 \u062f\u06cc\u0648\u0627\u0631 \u0648 \u062f\u06cc\u06af\u0631\u06cc \u067e\u0633 \u0627\u0632 \u0628\u0631\u062e\u0648\u0631\u062f \u0628\u0647 \u062f\u06cc\u0648\u0627\u0631(\u06f2 \u062d\u0627\u0644\u062a).<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u0639\u0645\u0644\u0627 \u0645\u0633\u0627\u0644\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u062f\u0648 \u062a\u0648\u067e \u062f\u0648 \u0628\u0639\u062f\u06cc \u0628\u0627 \u0634\u0639\u0627\u0639 \u0647\u0627, \u0645\u06a9\u0627\u0646 \u0647\u0627 \u0648 \u0633\u0631\u0639\u062a \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0627\u0631\u06cc\u0645 \u0622\u06cc\u0627 \u0627\u06cc\u0646\u0647\u0627 \u0628\u0647 \u0647\u0645 \u0628\u0631\u062e\u0648\u0631\u062f \u0645\u06cc \u06a9\u0646\u0646\u062f \u06cc\u0627 \u0646\u0647(\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0628\u0627\u06cc\u062f \u0645\u0639\u062a\u0628\u0631 \u0628\u0648\u062f\u0646 \u062c\u0648\u0627\u0628 \u0647\u0645 \u0686\u06a9 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u062b\u0644\u0627 \u0627\u0632 \u062f\u06cc\u0648\u0627\u0631 \u062a\u0648\u067e \u0631\u062f \u0646\u0634\u0648\u062f.) \u061f!<\/p>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0627\u0631 \u0627\u0632 \u0642\u0636\u06cc\u0647 <a href=\"https:\/\/blog.faradars.org\/%D8%B3%D8%B1%D8%B9%D8%AA-%D9%86%D8%B3%D8%A8%DB%8C\/\">\u0633\u0631\u0639\u062a \u0646\u0633\u0628\u06cc<\/a> \u062f\u0631 \u0641\u06cc\u0632\u06cc\u06a9 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645. \u06cc\u0639\u0646\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0641\u0631\u0636 \u06a9\u0646\u06cc\u0645 \u06cc\u06a9 \u062a\u0648\u067e \u062b\u0627\u0628\u062a \u0627\u0633\u062a \u0648 \u0641\u0642\u0637 \u06cc\u06a9 \u062a\u0648\u067e \u0628\u0627 \u0633\u0631\u0639\u062a\u06cc \u062c\u062f\u06cc\u062f \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u062f. \u062d\u0627\u0644 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0686\u06a9 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0628\u0627 \u0647\u0645 \u0628\u0631\u062e\u0648\u0631\u062f \u062f\u0627\u0631\u0646\u062f \u06cc\u0627 \u062e\u06cc\u0631.<\/p>\n\n\n\n<p>\u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u0645\u0633\u06cc\u0631 \u062d\u0631\u06a9\u062a \u0645\u0631\u06a9\u0632 \u062a\u0648\u067e \u062a\u0634\u06a9\u06cc\u0644 \u06cc\u06a9 \u062e\u0637(\u0646\u06cc\u0645\u200c\u062e\u0637 \u06cc\u0627 \u067e\u0627\u0631\u0647\u200c\u062e\u0637 \u062f\u0631 \u0648\u0627\u0642\u0639) \u0648 \u0645\u0631\u06a9\u0632 \u062a\u0648\u067e \u062f\u06cc\u06af\u0631 \u0633\u0627\u06a9\u0646 \u0627\u0633\u062a. \u067e\u0633 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <a href=\"https:\/\/blog.faradars.org\/%D9%81%D8%A7%D8%B5%D9%84%D9%87-%D9%86%D9%82%D8%B7%D9%87-%D8%A7%D8%B2-%D8%AE%D8%B7\/\">\u0641\u0631\u0645\u0648\u0644 \u0641\u0627\u0635\u0644\u0647 \u0646\u0642\u0637\u0647 \u0627\u0632 \u062e\u0637<\/a> \u06a9\u0645\u06cc\u0646\u0647 \u0641\u0627\u0635\u0644\u0647 \u0645\u0631\u06a9\u0632 \u0622\u0646 \u062f\u0648 \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645(\u0627\u0632 \u0627\u06cc\u0646 \u067e\u0633 \u0622\u0646 \u0631\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">d<\/span> \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645). \u062d\u0627\u0644 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">d \\le R_1 + R_2 <\/span> \u067e\u0633 \u0622\u0646\u06af\u0627\u0647 \u0622\u0646 \u0647\u0627 \u0628\u0627 \u0647\u0645 \u062a\u0645\u0627\u0633 \u062f\u0627\u0631\u0646\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u062c\u0627\u06cc \u0641\u0631\u0645\u0648\u0644 \u0641\u0627\u0635\u0644\u0647 \u0646\u0642\u0637\u0647 \u0627\u0632 \u062e\u0637 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0632 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u200c\u0647\u0627\u06cc\u06cc \u0645\u062b\u0644 <code>search ternary<\/code> \u0647\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T)<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">#include &lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nconst double eps = 1e-6;\n\nclass Vector;\n\nclass Point {\npublic:\n    double x, y;\n\n    Point(double x, double y): x(x), y(y) {\n    }\n\n    Point() {\n    }\n\n    Point translate(const Vector&amp; v) const ;\n};\n\nclass Vector {\npublic:\n    double x, y;\n    Vector(double x, double y): x(x), y(y) {\n    }\n\n    Vector() {\n    }\n\n    Vector scale(double factor) const;\n    Vector normalize() const;\n    double cross(const Vector&amp; o) const;\n    Vector opposite() const;\n    double length() const;\n};\n\nostream&amp; operator&lt;&lt;(ostream&amp; out, const Point&amp; p) {\n    out &lt;&lt; \"(\" &lt;&lt; p.x&lt;&lt; \", \" &lt;&lt; p.y &lt;&lt; \")\";\n    return out;\n}\n\nostream&amp; operator&lt;&lt;(ostream&amp; out, const Vector&amp; v) {\n    out &lt;&lt; \"(\" &lt;&lt; v.x&lt;&lt; \", \" &lt;&lt; v.y&lt;&lt; \")\";\n    return out;\n}\n\nclass Ball {\n    public:\n    Ball(const Point&amp; pos, const Vector&amp; displacement, double r, double velocity):\n        pos(pos), displacement(displacement.normalize()), r(r), velocity(velocity) {\n    }\n    Point pos;\n    Vector displacement;\n    double r;\n    double velocity;\n    Point posAfter(double t) const;\n};\n\nclass LinearTrajectory {\npublic:\n    double minTime, maxTime;\n\n    Point start;\n    Vector displacement;\n    double v;\n\n    Point get(double) const;\n    \n    LinearTrajectory(double minTime, double maxTime, const Point&amp; start, const Vector&amp; displacement, double v): \n        minTime(minTime), maxTime(maxTime), start(start), displacement(displacement.normalize()), v(v) {\n    }\n\n    LinearTrajectory() {\n    }\n\n};\n\nvector&lt;LinearTrajectory&gt; trajectories(const Ball&amp; b, const vector&lt;Point&gt;&amp; wall);\ndouble findMin(const LinearTrajectory&amp; l1, const LinearTrajectory&amp; l2);\nbool segmentInterLine(const Point&amp; s1, const Point&amp; s2, const Point&amp; l1, const Point&amp; l2);\nint sgn(double a);\ndouble dist(const Point&amp; p1, const Point&amp; p2);\ndouble eq(double a, double b);\nVector vectorFromTo(const Point&amp; from, const Point&amp; to);\n\nint main() {\n    int n;\n    cin &gt;&gt; n;\n\n    while(n--) {\n        vector&lt;Ball&gt; balls;\n        vector&lt;Point&gt; wall;\n\n\n        for(int i = 0 ;i &lt; 2; i++) {\n            double x, y, dx, dy;\n            cin &gt;&gt; x &gt;&gt; y &gt;&gt; dx &gt;&gt; dy;\n            double velocity, r;\n            cin &gt;&gt; velocity &gt;&gt; r;\n            balls.push_back(Ball(Point(x, y), Vector(dx, dy).normalize(), r, velocity));\n        }\n\n        for(int i = 0 ;i &lt; 2 ; i++) {\n            double x, y;\n            cin &gt;&gt; x &gt;&gt; y;\n            wall.push_back(Point(x, y));\n        }\n\n        auto traj0 = trajectories(balls[0], wall);\n        auto traj1 = trajectories(balls[1], wall);\n        bool hit = false;\n\n        for(auto t0: traj0) {\n            for(auto t1: traj1) {\n                auto minDist = findMin(t0, t1);\n                hit |=  minDist &lt; balls[0].r + balls[1].r;\n            }\n        }\n\n        if(hit) {\n            cout &lt;&lt; \"Lightning strike\" &lt;&lt;endl;\n        } else {\n            cout &lt;&lt; \"Not even a spark\" &lt;&lt;endl;\n        }\n    }\n\n    return 0;\n}\n\nvector&lt;LinearTrajectory&gt; trajectories(const Ball&amp; b, const vector&lt;Point&gt;&amp; wall) {\n    double st = 0;\n    double en = 1e12;\n\n    double lo = st, hi = en;\n    for(int i = 0 ;i &lt; 1000; i++) {\n        double md = (hi + lo)\/2;\n        if(segmentInterLine(b.pos, b.posAfter(md), wall[0], wall[1])) {\n            hi = md;\n        } else {\n            lo = md;\n        }\n    }\n\n    \n    double timeOfImpact = (hi + lo)\/2;\n    Point centerOfBallOnImpact = b.posAfter(timeOfImpact);\n    Point pointFromWall = wall[0];\n    if(eq(dist(pointFromWall, centerOfBallOnImpact), 0)) {\n        pointFromWall = wall[1];\n    }\n\n    \n    Vector vWall = vectorFromTo(centerOfBallOnImpact, pointFromWall);\n    Vector vTraj = vectorFromTo(centerOfBallOnImpact, b.pos);\n    \n    double sineOfDirections = fabs(vWall.cross(vTraj))\/(vWall.length() * vTraj.length());\n    double displacementNeededInDirOfTraj = sineOfDirections * b.r;\n    Point realCenterOfBall = centerOfBallOnImpact.translate(\n            vectorFromTo(centerOfBallOnImpact, b.pos).normalize().scale(displacementNeededInDirOfTraj));\n    double cosineOfDirections = sqrt(1 - pow(sineOfDirections, 2));\n    double mirrorPointDissplacementFactor = dist(realCenterOfBall, centerOfBallOnImpact) * cosineOfDirections * 2;\n    \n    Vector maybeDirectionToFindMirrorPoint = vectorFromTo(wall[0], wall[1]).normalize();\n    Point maybeMirrorPoint = realCenterOfBall.translate(maybeDirectionToFindMirrorPoint.scale(mirrorPointDissplacementFactor));\n    if(!eq(dist(maybeMirrorPoint, centerOfBallOnImpact), dist(realCenterOfBall, centerOfBallOnImpact))) {\n        maybeDirectionToFindMirrorPoint = maybeDirectionToFindMirrorPoint.opposite();\n        maybeMirrorPoint = realCenterOfBall.translate(maybeDirectionToFindMirrorPoint.scale(mirrorPointDissplacementFactor));\n    }\n\n    Vector dMirror = vectorFromTo(centerOfBallOnImpact, maybeMirrorPoint).normalize();\n\n    vector&lt;LinearTrajectory&gt; ret;\n\n    double realTimeOfImpact = dist(realCenterOfBall, b.pos)\/b.velocity;\n\n    ret.push_back(LinearTrajectory(0, realTimeOfImpact, b.pos, b.displacement, b.velocity));\n    if(timeOfImpact &lt; 1e12 - 1) {\n        ret.push_back(LinearTrajectory(realTimeOfImpact, en, realCenterOfBall, dMirror, b.velocity));\n    }\n\n    return ret;\n}\n\ndouble findMin(const LinearTrajectory&amp; l1, const LinearTrajectory&amp; l2) {\n    double lo = min(l1.minTime, l2.minTime);\n    double hi = max(l1.maxTime, l2.maxTime);\n\n    for(int i = 0 ;i&lt; 1000; i++) {\n        if(lo &gt; hi) {\n            return 1231231231.0;\n        }\n        double oneThird = lo + (hi - lo)\/3;\n        double twoThirds = lo + 2*(hi - lo)\/3;\n        if(dist(l1.get(oneThird), l2.get(oneThird)) &lt; dist(l1.get(twoThirds), l2.get(twoThirds))) {\n            hi = twoThirds;\n        } else {\n            lo = oneThird;\n        }\n    }\n    return dist(l1.get((hi + lo)\/2), l2.get((hi + lo)\/2));\n}\n\nbool segmentInterLine(const Point&amp; s1, const Point&amp; s2, const Point&amp; l1, const Point&amp; l2) {\n    return sgn(vectorFromTo(s1, l1).cross(vectorFromTo(s1, l2))) != sgn(vectorFromTo(s2, l1).cross(vectorFromTo(s2, l2)));\n}\n\ndouble dist(const Point&amp; p1, const Point&amp; p2) {\n    return sqrt(pow(p1.x - p2.x, 2) + pow(p1.y - p2.y, 2));\n}\n\ndouble eq(double a, double b) {\n    return fabs(a - b) &lt; eps;\n}\n\nint sgn(double a) {\n    if(a &lt; 0) {\n        return -1;\n    } else if(a &gt; 0) {\n        return 1;\n    }\n    return 0;\n}\n\nVector vectorFromTo(const Point&amp; from, const Point&amp; to) {\n    return Vector(to.x - from.x, to.y - from .y);\n}\n\nPoint Ball::posAfter(double t) const {\n    return pos.translate(displacement.scale(t * velocity));\n}\n\nPoint Point::translate(const Vector&amp; v) const {\n    return Point(x + v.x, y + v.y);\n}\n\nVector Vector::scale(double factor) const {\n    return Vector(factor * x, factor * y);\n}\n\nPoint LinearTrajectory::get(double t) const {\n    double dt = t - minTime;\n    return start.translate(displacement.scale(dt * v));\n}\n\nVector Vector::normalize() const {\n    double len = dist(Point(0, 0), Point(x, y));\n    return Vector(x\/len, y\/len);\n}\n\nVector Vector::opposite() const {\n    return Vector(-x, -y);\n}\n\ndouble Vector::cross(const Vector&amp; o) const {\n    return x * o.y - y * o.x;\n}\n\ndouble Vector::length() const {\n    return dist(Point(x, y), Point(0, 0));\n}<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-j-jitter-minimization\"><span class=\"ez-toc-section\" id=\"J_%E2%80%93_Jitter_Minimization\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169382\/\" target=\"_blank\" rel=\"noreferrer noopener\">J \u2013 Jitter Minimization<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0627\u0648\u0644 \u0622\u0631\u0627\u06cc\u0647 \u0631\u0627 \u0645\u0631\u062a\u0628 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u067e\u0633 \u0627\u0632 \u0627\u06cc\u0646 \u0628\u0647 \u0628\u0639\u062f \u062f\u0627\u0631\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>a_1 &lt; a_2 &lt; \\dots &lt; a_{2 \\times N} <\/pre><\/div>\n\n\n\n<p>\u062d\u0627\u0644 \u0627\u06af\u0631 \u0639\u062f\u062f\u06cc \u0645\u062b\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">dis<\/span> \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f \u06a9\u0647 \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0628\u0627\u0634\u062f \u0622\u0646\u06af\u0627\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">dis<\/span> \u0628\u0631\u0627\u0628\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">a_x - a_1<\/span> \u0646\u06cc\u0632 \u0647\u0633\u062a \u06a9\u0647 \u062d\u062a\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0628\u0647 \u0622\u0633\u0627\u0646\u06cc \u0646\u0634\u0627\u0646 \u062f\u0627\u062f <span class=\"katex-eq\" data-katex-display=\"false\">2 \\leq x \\leq N+1<\/span>. \u067e\u0633 \u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0645\u0647 \u062d\u0627\u0644\u0627\u062a \u0645\u0645\u06a9\u0646 \u0628\u0631\u0627\u06cc <span class=\"katex-eq\" data-katex-display=\"false\">dis<\/span> \u0686\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u0645\u0639\u062a\u0628\u0631 \u0647\u0633\u062a \u06cc\u0627 \u0646\u0647. \u06a9\u0647 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u062d\u0631\u06cc\u0635\u0627\u0646\u0647 \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f \u0647\u0631 \u0628\u0627\u0631 \u06a9\u0648\u0686\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0636\u0648 \u062c\u0641\u062a \u0646\u0634\u062f\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a \u0648 \u0628\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">dis<\/span> \u0628\u0647 \u0639\u0644\u0627\u0648\u0647 \u0622\u0646 \u062c\u0641\u062a \u06a9\u0631\u062f. \u0627\u06af\u0631 \u0647\u0645\u0686\u06cc\u0646 \u0639\u0636\u0648\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0634\u062a \u067e\u0633 \u0622\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">dis<\/span> \u0646\u0627\u0645\u0639\u062a\u0628\u0631 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T \\times (N \\log N + N \\times N \\log N))<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint main()\n{\n\tios_base::sync_with_stdio(false);\n\tcin.tie(0);\n\twhile(true)\n\t{\n\t\tint N;\n\t\tcin &gt;&gt; N;\n\t\tif(N == 0) return 0;\n\t\tint A[2*N];\n\t\tbool paired[2*N];\t\n\t\tfor(int i = 0; i &lt; 2*N; i++)\n\t\t\tcin &gt;&gt; A[i];\n\t\tsort(A, A+2*N);\n\t\tfor(int i = 1; ; i++)\n\t\t{\n\t\t\tif(i == N+1)\n\t\t\t{\n\t\t\t\tcout &lt;&lt; \"Unreliable Network\\n\"; \n\t\t\t\tbreak;\n\t\t\t}\n\t\t\tint dis = A[i]-A[0];\n\t\t\tmemset(paired, 0, sizeof(paired));\n\t\t\tint p = 0, l = 0;\n\t\t\twhile (l &lt; 2*N)\n\t\t\t{\n\t\t\t\tpaired[l] = true;\n\t\t\t\tauto it = lower_bound(A, A+2*N, dis+A[l]);\n\t\t\t\tif(it == A+2*N or *it != dis+A[l])break;\n\t\t\t\tpaired[it-A] = true;\n\t\t\t\twhile(l &lt; 2*N and paired[l])l++;\n\t\t\t\tp++;\n\t\t\t}\n\t\t\t\n\t\t\tif(p == N)\n\t\t\t{\n\t\t\t\tcout &lt;&lt; dis &lt;&lt; '\\n';\n\t\t\t\tbreak;\n\t\t\t}\n\t\t\t\n\t\t}\n\t}\t\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-k-traffic-lights\"><span class=\"ez-toc-section\" id=\"K_%E2%80%93_Traffic_Lights\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169383\/\" target=\"_blank\" rel=\"noreferrer noopener\">K \u2013 Traffic Lights<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u062d\u0644 \u0633\u0624\u0627\u0644 \u0627\u0632 \u0631\u0648\u0634 \u0628\u0631\u0646\u0627\u0645\u0647\u200c\u0646\u0648\u06cc\u0633\u06cc \u067e\u0648\u06cc\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645.<\/p>\n\n\n\n<p>\u0645\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">dp[i][0]<\/span> \u0631\u0627 \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">(1 \\leq i \\leq n)<\/span> \u0631\u0627 \u062a\u0639\u062f\u0627\u062f \u0628\u06cc\u0634\u06cc\u0646\u0647 \u0631\u0648\u0632\u200c\u0647\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628\u06cc \u0628\u06cc\u0646 \u0631\u0648\u0632 \u06f1 \u062a\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span> \u062f\u0631 \u062d\u0627\u0644\u062a\u06cc \u06a9\u0647 \u0622\u062e\u0631\u06cc\u0646 \u0631\u0648\u0632 \u0633\u0628\u0632 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062f\u0647 \u0628\u0627\u0634\u06cc\u0645\u060c \u062f\u0631 \u0646\u0638\u0631 \u0645\u06cc\u200c\u06af\u06cc\u0631\u06cc\u0645. <span class=\"katex-eq\" data-katex-display=\"false\">dp[i][1]<\/span> \u0628\u0631\u0627\u06cc \u0632\u0631\u062f \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">dp[i][2]<\/span> \u0628\u0631\u0627\u06cc \u0642\u0631\u0645\u0632 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc\u200c\u0634\u0648\u062f. \u067e\u0627\u0633\u062e \u0645\u0633\u0626\u0644\u0647 \u0628\u0631\u0627\u0628\u0631 \u0628\u06cc\u0634\u06cc\u0646\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">dp[n][x]<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">0 \\leq x \\leq 2<\/span>.<br>\u0628\u0631\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0642\u0631\u0627\u0631 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">dp[0][0] = dp[0][1] = dp[0][2] = 0<\/span> \u0648 \u0646\u06cc\u0632 \u0628\u0631\u0627\u06cc \u0628\u0647\u200c\u0631\u0648\u0632\u200c\u0631\u0633\u0627\u0646\u06cc \u062f\u06cc\u067e\u06cc \u0627\u06af\u0631 \u0645\u062b\u0644\u0627\u064b \u0631\u0648\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span>\u0640\u0627\u0645 \u0633\u0628\u0632 \u0628\u0627\u0634\u062f \u062f\u0627\u0631\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>dp[i][0] = max(dp[i-1][0], dp[i-1][2])+1<\/pre><\/div>\n\n\n\n<p>\u0648 \u0646\u06cc\u0632 \u0627\u06af\u0631 \u0631\u0648\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span>\u0640\u0627\u0645 \u0633\u0628\u0632 \u0646\u0628\u0627\u0634\u062f \u062f\u0627\u0631\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>dp[i][0] = dp[i-1][0]\n<\/pre><\/div>\n\n\n\n<p>\u0648 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647 \u0628\u0631\u0627\u06cc \u0632\u0631\u062f \u0648\u0642\u0631\u0645\u0632 \u0646\u06cc\u0632 \u0686\u0646\u06cc\u0646 \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T \\times N)<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint main()\n{\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tint n;\n\t\tcin &gt;&gt; n;\n\t\tstring s;\n\t\tcin &gt;&gt; s;\n\t\tint dp[n+1][3];\n\t\tdp[0][0] = dp[0][1] = dp[0][2] = 0;\n\t\tfor(int i = 0; i &lt; n; i++)\n\t\t{\t\n\t\t\tdp[i+1][0] = dp[i][0];\n\t\t\tdp[i+1][1] = dp[i][1];\n\t\t\tdp[i+1][2] = dp[i][2];\n\t\t\tif(s[i] == 'G')dp[i+1][0] = max(dp[i][0],dp[i][2])+1;\n\t\t\telse if(s[i] == 'Y')dp[i+1][1] = max(dp[i][0],dp[i][1])+1;\n\t\t\telse dp[i+1][2] = max(dp[i][1],dp[i][2])+1;\n\t\t}\n\t\tcout &lt;&lt; max(dp[n][0], max(dp[n][1], dp[n][2])) &lt;&lt; '\\n';\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-l-your-house-have-ant\"><span class=\"ez-toc-section\" id=\"L_%E2%80%93_Your_House_Have_Ant\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169384\/\" target=\"_blank\" rel=\"noreferrer noopener\">L \u2013 Your House Have Ant<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0646\u06a9\u062a\u0647 \u0633\u0624\u0627\u0644 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0631\u0627\u0647\u0631\u0648 \u062a\u0646\u06af\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u0648 \u0645\u0648\u0631\u0686\u0647\u200c\u0647\u0627 \u0622\u0632\u0627\u062f\u0627\u0646\u0647 \u062f\u0631 \u062c\u0647\u062a \u062f\u0644\u062e\u0648\u0627\u0647 \u062d\u0631\u06a9\u062a \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f! \u067e\u0633 \u0635\u0631\u0641\u0627\u064b \u06a9\u0627\u0641\u06cc\u0633\u062a \u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u0645\u0648\u0631\u0686\u0647 \u0645\u0633\u0627\u0641\u062a\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0637\u06cc \u06a9\u0646\u062f \u062a\u0627 \u0627\u0632 \u062a\u0648\u0646\u0644 \u062e\u0627\u0631\u062c \u0634\u0648\u0646 \u0631\u0627 \u0628\u0627 \u0647\u0645 \u062c\u0645\u0639 \u06a9\u0646\u06cc\u062f.<\/p>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(T \\times |S|)<\/pre><\/div>\n\n\n\n<div style=\"height:15px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">#include &lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\nint t;\nstring s;\n\nint main()\n{\n\tcin &gt;&gt; t;\n\twhile (t--)\n\t{\n\t\tcin &gt;&gt; s;\n\t\tint ans = 0;\n\t\tint l = s.size();\n\t\tfor (int i = 0; i &lt; l; i++)\n\t\t\tif (s[i] == '&lt;')\n\t\t\t\tans += i;\n\t\t\telse if (s[i] == '&gt;')\n\t\t\t\tans += l - i - 1;\n\t\tcout &lt;&lt; ans &lt;&lt; endl;\n\t}\n\treturn 0;\n}<\/code><\/pre>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"has-medium-font-size wp-block-heading\" id=\"h-m-concert\"><span class=\"ez-toc-section\" id=\"M_%E2%80%93_Concert\"><\/span><strong><a href=\"https:\/\/quera.org\/problemset\/169385\/\" target=\"_blank\" rel=\"noreferrer noopener\">M \u2013 Concert<\/a><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0641\u0631\u0636 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u062c\u0648\u0627\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span> \u0646\u0628\u0627\u0634\u062f (\u062d\u0627\u0644\u062a\u06cc \u06a9\u0647 \u062c\u0648\u0627\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span> \u0627\u0633\u062a \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f).<br>\u062d\u0627\u0644 \u0645\u06cc\u200c\u062f\u0627\u0646\u06cc\u0645 \u062c\u0648\u0627\u0628 \u0645\u0633\u0626\u0644\u0647(<span class=\"katex-eq\" data-katex-display=\"false\">K<\/span>_\u0645\u06cc\u0646 \u0639\u062f\u062f \u0627\u0648\u0644\u200c\u062f\u0648\u0633\u062a) \u062f\u0631 \u0645\u0628\u0646\u0627\u06cc \u06f3 \u06a9\u0645\u062a\u0631 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">M = 30 &gt; \\frac{log(10^{13})}{log(3)}<\/span> \u0631\u0642\u0645 \u062f\u0627\u0631\u062f \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u062c\u0645\u0639 \u0627\u0631\u0642\u0627\u0645 \u0622\u0646 \u06a9\u0645\u062a\u0631 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">S \\le 2 \\times M = 30<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<br>\u062d\u0627\u0644 \u0628\u0647 \u06a9\u0645\u06a9 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0632\u06af\u0634\u062a\u06cc \u062c\u0648\u0627\u0628 \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0627\u0631 \u0628\u0647 \u062a\u0627\u0628\u0639<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre> f(K, CntDigits, Before) <\/pre><\/div>\n\n\n\n<p>\u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u062f \u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">K<\/span>_\u0645\u06cc\u0646 \u0639\u062f\u062f \u0634\u0628\u0647\u200c\u0627\u0648\u0644\u200c\u062f\u0648\u0633\u062a \u06a9\u0647 \u062d\u062f\u0627\u06a9\u062b\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">CntDigits<\/span> \u0631\u0642\u0645 \u062f\u0631 \u0645\u0628\u0646\u0627\u06cc \u06f3 \u062f\u0627\u0631\u062f\u060c \u06a9\u062f\u0627\u0645 \u0627\u0633\u062a. \u0628\u0647 \u0639\u062f\u062f\u06cc \u0634\u0628\u0647\u200c\u0627\u0648\u0644\u200c\u062f\u0648\u0633\u062a \u0645\u06cc\u200c\u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 \u062c\u0645\u0639 \u0627\u0631\u0642\u0627\u0645\u0634 \u0628\u0647\u200c\u0639\u0644\u0627\u0648\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">Before<\/span> \u0639\u062f\u062f\u06cc \u0627\u0648\u0644 \u0634\u0648\u062f. \u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">Before = 0<\/span> \u0622\u0646\u06af\u0627\u0647 \u0645\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">K<\/span>_\u0645\u06cc\u0646 \u0639\u062f\u062f \u0627\u0648\u0644\u200c\u062f\u0648\u0633\u062a \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a. \u067e\u0633 <span class=\"katex-eq\" data-katex-display=\"false\">f(K, M, 0)<\/span> \u062c\u0648\u0627\u0628 \u0645\u0633\u0626\u0644\u0647 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n\n\n\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0627 \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0633\u0626\u0644\u0647 \u0628\u0647<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>cnt[i][j] (0 \\leq i \\leq M, 0 \\leq j \\leq S) <\/pre><\/div>\n\n\n\n<p>\u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u0627\u0639\u062f\u0627\u062f \u062d\u062f\u0627\u06a9\u062b\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">i<\/span> \u0631\u0642\u0645\u06cc (\u0642\u0627\u0639\u062f\u062a\u0627\u064b \u062f\u0631 \u0645\u0628\u0646\u0627\u06cc \u06f3) \u0628\u0627 \u062c\u0645\u0639 \u0627\u0631\u0642\u0627\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">j<\/span> \u0631\u0627 \u0645\u06cc\u200c\u0634\u0645\u0627\u0631\u062f\u060c \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0647 \u0637\u0631\u06cc\u0642 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u0622\u0646 \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>cnt[0][0] = 1, cnt[i][j] = cnt[i-1][j] + cnt[i-1][j-1] + cnt[i-1][j-2]<\/pre><\/div>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">f(K, CntDigits, Before)<\/span> \u0645\u0627 \u0647\u0631 \u0628\u0627\u0631 \u062a\u0644\u0627\u0634 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0645\u0642\u062f\u0627\u0631 \u0628\u0627\u0627\u0631\u0632\u0634\u200c\u062a\u0631\u06cc\u0646 \u0631\u0642\u0645 \u062c\u0648\u0627\u0628 \u0631\u0627 \u0645\u0634\u062e\u0635 \u06a9\u0646\u06cc\u0645. \u0628\u0647 \u0637\u0648\u0631 \u062f\u0642\u06cc\u0642\u200c\u062a\u0631 \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u062a\u0639\u062f\u0627\u062f \u0627\u0639\u062f\u0627\u062f \u0634\u0628\u0647\u200c\u0627\u0648\u0644\u200c\u062f\u0648\u0633\u062a \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u067e\u0631\u0627\u0631\u0632\u0634\u200c\u062a\u0631\u06cc\u0646 \u0631\u0642\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u0627\u0633\u062a x, <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u0627\u0633\u062a <span class=\"katex-eq\" data-katex-display=\"false\">y<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">2<\/span> \u0627\u0633\u062a <span class=\"katex-eq\" data-katex-display=\"false\">z<\/span> \u0628\u0627\u0634\u062f. \u062d\u0627\u0644 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">0 \\le K \\le x<\/span> \u0622\u0646\u06af\u0627\u0647 \u067e\u0631\u0627\u0631\u0632\u0634\u200c\u062a\u0631\u06cc\u0646 \u0631\u0642\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u0648 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">x &lt; K \\le x+y<\/span> \u067e\u0631\u200c\u0627\u0631\u0632\u0634\u200c\u062a\u0631\u06cc\u0646 \u0631\u0642\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u0648 \u0627\u06af\u0631 <span class=\"katex-eq\" data-katex-display=\"false\">x+y &lt; K \\le x+y+z<\/span> \u067e\u0631\u200c\u0627\u0631\u0632\u0634\u200c\u062a\u0631\u06cc\u0646 \u0631\u0642\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">3<\/span> \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f (\u062f\u0631\u063a\u06cc\u0631 \u0627\u06cc\u0646\u200c\u0635\u0648\u0631\u062a \u062c\u0648\u0627\u0628 <span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span> \u0627\u0633\u062a).<\/p>\n\n\n\n<p>\u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0628\u062f\u0627\u0646\u06cc\u0645 \u0686\u0646\u062f \u0639\u062f\u062f \u0634\u0628\u0647\u200c\u0627\u0648\u0644\u200c\u062f\u0648\u0633\u062a \u0628\u0627 \u067e\u0631\u0627\u0631\u0632\u0634\u200c\u062a\u0631\u06cc\u0646 \u0631\u0642\u0645 <span class=\"katex-eq\" data-katex-display=\"false\">w<\/span> \u062f\u0627\u0631\u06cc\u0645 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0639\u0628\u0627\u0631\u062a \u0632\u06cc\u0631 \u0631\u0627 \u062d\u0633\u0627\u0628 \u06a9\u0646\u06cc\u0645:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre> \\sum_{p_i \\in P} cnt[CntDigits-1][p_i-w-before] <\/pre><\/div>\n\n\n\n<p>\u06a9\u0647 \u0645\u0646\u0638\u0648\u0631 \u0627\u0632 <span class=\"katex-eq\" data-katex-display=\"false\">P<\/span> \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644 \u0628\u06cc\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u062a\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">S<\/span> \u0627\u0633\u062a.<\/p>\n\n\n\n<p>\u062d\u0627\u0644 \u062c\u0648\u0627\u0628 \u0628\u062f\u06cc\u0646 \u0634\u06a9\u0644 \u0628\u062f\u0633\u062a \u0645\u06cc\u200c\u0622\u06cc\u062f:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>w=0: f(K, CntDigits, before) = f(K, CntDigits-1,before)<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>w=1: f(K, CntDigits, before) = 3^{CntDigits-1}+f(K-x, CntDigits-1,before+1)<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>w=2: f(K, CntDigits, before) = 2*3^{CntDigits-1}+f(K-x-y, CntDigits-1,before+2)<\/pre><\/div>\n\n\n\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\mathcal{O}(\\log {MAX_N}^2 + T \\times \\log MAX_N \\times \\frac{\\log {MAX_N}}{\\log \\log MAX_N})<\/pre><\/div>\n\n\n\n<p>\u06a9\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">\\log {MAX_N}^2 <\/span> \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 <span class=\"katex-eq\" data-katex-display=\"false\">cnt[i][j]<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\log {MAX_N}}{\\log \\log MAX_N})<\/span> \u0646\u0645\u0627\u06cc\u0646\u062f\u0647 \u062a\u0639\u062f\u0627\u062f \u0627\u0639\u062f\u0627\u062f \u0627\u0648\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u062a\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">\\log MAX_N<\/span> \u0627\u0633\u062a.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code lang=\"cpp\" class=\"language-cpp line-numbers\">\/\/ In the name of Allah\n#include&lt;bits\/stdc++.h&gt;\n\nusing namespace std;\n\ntypedef long long ll;\n\nconst ll N = 30; \/\/ N = MAX_DIGIT_IN_BASE_3\nvector&lt;ll&gt; primes = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59};\nll dp[N][N*2], n, k, ans;\n\nll Find(ll k, ll digit, ll before)\n{\n\tif(digit == -1)\n\t\treturn 0;\n\tll last_sum = 0, sum = 0;\n\tfor(ll d = 0; d &lt; 3; d++)\n\t{\n\t\tfor(auto p: primes)if(p &gt;= d+before)\n\t\t\tsum += dp[digit][p-d-before];\n\t\tif(sum &gt;= k)\n\t\t\treturn d*pow(3, digit)+Find(k-last_sum, digit-1, before+d);\n\t\tlast_sum = sum;\n\t}\n\treturn -1LL;\n}\n\nint main()\n{\n\tmemset(dp, 0, sizeof(dp));\n\tdp[1][0] = dp[1][1] = dp[1][2] = 1;\n\tfor(int i = 0; i &lt; N; i++)dp[i][0] = 1;\n\tfor(int i = 0; i &lt; N; i++)dp[i][1] = i;\n\tfor(int i = 2; i &lt; N; i++)\n\t\tfor(int j = 2; j &lt; 2*N; j++)\n\t\t\tdp[i][j] = dp[i-1][j]+dp[i-1][j-1]+dp[i-1][j-2];\n\t\n\tint T;\n\tcin &gt;&gt; T;\n\tfor(int test = 0; test &lt; T; test++)\n\t{\n\t\tcin &gt;&gt; n &gt;&gt; k;\n\t\tans = Find(k, N-1, 0);\n\t\tif(ans &gt; n)\n\t\t\tans = -1;\n\t\tcout &lt;&lt; ans &lt;&lt; '\\n';\n\t}\n}\n\n\/\/Thank God<\/code><\/pre>\n\n\n\n<p>\u0627\u0645\u06cc\u062f\u0648\u0631\u0627\u0645 \u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627 \u0645\u0641\u06cc\u062f \u0628\u0648\u062f\u0647 \u0628\u0627\u0634\u0647. \u0627\u06af\u0631 \u067e\u06cc\u0634\u0646\u0647\u0627\u062f \u06cc\u0627 \u0633\u0624\u0627\u0644\u06cc \u062f\u0627\u0634\u062a\u06cc\u0646\u060c \u062d\u062a\u0645\u0627\u064b \u062f\u0631 \u0646\u0638\u0631\u0627\u062a \u0645\u0637\u0631\u062d \u0628\u0641\u0631\u0645\u0627\u06cc\u06cc\u062f.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u0644\u0627\u0645! \u0645\u0633\u0627\u0628\u0642\u0627\u062a \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc Newbies \u0632\u0645\u0633\u062a\u0648\u0646 \u0647\u0631 \u0633\u0627\u0644 \u062f\u0631 \u062f\u0627\u0646\u0634\u06af\u0627\u0647 \u0634\u0647\u06cc\u062f \u0628\u0647\u0634\u062a\u06cc \u0628\u0631\u06af\u0632\u0627\u0631 \u0645\u06cc\u0634\u0647. \u0633\u0637\u062d \u0633\u0624\u0627\u0644\u0627\u062a \u0627\u06cc\u0646 \u0645\u0633\u0627\u0628\u0642\u0647 \u0628\u0647 \u0646\u0633\u0628\u062a \u0645\u0633\u0627\u0628\u0642\u0627\u062a&#8230;<\/p>\n","protected":false},"author":40,"featured_media":42206,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46,50,141],"tags":[],"class_list":["post-42168","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-developer","category-quera-developer","category-contests-and-events"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0631\u0627\u0647\u200c\u062d\u0644\u200c\u0647\u0627\u06cc \u0645\u0633\u0627\u0628\u0642\u0647 \u0627\u0644\u06af\u0648\u0631\u06cc\u062a\u0645\u06cc Newbies 2018 - \u06a9\u0648\u0626\u0631\u0627\u200c\u0628\u0644\u0627\u06af<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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