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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/192\">Codeforces Round 121 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='093fda6e44d6257eb08f18c8d810f266'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/192/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Binary search\">\r\n binary search\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Brute force\">\r\n brute force\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, simulation\">\r\n implementation\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1300\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='093fda6e44d6257eb08f18c8d810f266'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1355\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='093fda6e44d6257eb08f18c8d810f266'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1355\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script type=\"text/javascript\">\r\n $(\".tag-box img\").click(function () {\r\n var tagName = $(this).attr(\"value\");\r\n Codeforces.confirm(\"Are you sure you want to remove this tag?\", function () {\r\n $(\"#removeTagForm input[name=tagName]\").val(tagName);\r\n $(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4635\" title=\"announcement\" target=\"_blank\">announcement <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"13218\" resourceName=\"announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4634\" title=\"tutorial\" target=\"_blank\">tutorial <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"13219\" resourceName=\"tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/192\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/192/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/192/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/192/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/192/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/192/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/192/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/192/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n }\r\n\r\n .testCaseMarker {\r\n position: absolute;\r\n font-weight: bold;\r\n font-size: 1rem;\r\n }\r\n\r\n .diff-popup {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n display: none;\r\n overflow: auto;\r\n }\r\n\r\n .input-output-copier {\r\n font-size: 1.2rem;\r\n float: right;\r\n color: #888 !important;\r\n cursor: pointer;\r\n border: 1px solid rgb(185, 185, 185);\r\n padding: 3px;\r\n margin: 1px;\r\n line-height: 1.1rem;\r\n text-transform: none;\r\n }\r\n\r\n .input-output-copier:hover {\r\n background-color: #def;\r\n }\r\n\r\n .test-explanation textarea {\r\n width: 100%;\r\n height: 1.5em;\r\n }\r\n\r\n .pending-submission-message {\r\n color: darkorange !important;\r\n }\r\n </style>\r\n <script>\r\n const OPENING_SPACE = String.fromCharCode(1001);\r\n const CLOSING_SPACE = String.fromCharCode(1002);\r\n\r\n const nodeToText = function (node, pre) {\r\n let result = [];\r\n\r\n if (node.tagName === \"SCRIPT\" || node.tagName === \"math\"\r\n || (node.classList && node.classList.contains(\"input-output-copier\")))\r\n return [];\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(OPENING_SPACE);\r\n }\r\n\r\n if (node.nodeType === Node.TEXT_NODE) {\r\n let s = node.textContent;\r\n if (!pre) {\r\n s = s.replace(/\\s+/g, \" \");\r\n }\r\n if (s.length > 0) {\r\n result.push(s);\r\n }\r\n }\r\n\r\n if (pre && node.tagName === \"BR\") {\r\n result.push(\"\\n\");\r\n }\r\n\r\n node.childNodes.forEach(function (child) {\r\n result.push(nodeToText(child, node.tagName === \"PRE\").join(\"\"));\r\n });\r\n\r\n 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}\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"A\" data-uuid=\"ps_4ad96d6175b4ec067a425153bbf5b552d98a0ae4\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Funky Numbers</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/48cf4d33526da5209922c993ddf2320013993147.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, where <span class=\"tex-span\"><i>k</i></span> is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.</p><p>A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number <span class=\"tex-span\"><i>n</i></span>, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains an integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">9</sup>)</span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print "YES" (without the quotes), if <span class=\"tex-span\"><i>n</i></span> can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>256<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>512<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/92095692c6ea93e9e3b837a0408ba7543549d5b2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>In the second sample number <span class=\"tex-span\">512</span> can not be represented as a sum of two triangular numbers.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=A]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n 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class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div>\r\n\r\n\n <div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='0e36e4ae41db037922b04beb941e4855'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" 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href=\"/profile/AlTimin\">AlTimin</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/AlTimin\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/AlTimin\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/AlTimin\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/AlTimin\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/AlTimin\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/AlTimin\" style=\"text-decoration:none;color:black !important;\">AlTimin's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4648\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4634\"> <p>Разбор Codeforces Round #121</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/AlTimin\" title=\"Expert AlTimin\" class=\"rated-user user-blue\">AlTimin</a>,\r\n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>,\r\n \r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/ru.png\" alt=\"In Russian\" title=\"In Russian\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Задача <a href=\"/contest/192/problem/A\" title=\"Codeforces Round 121 (Div. 2)\">192A - Funky Numbers</a></p><p>Кратко о решении: перебор</p><p>Подробно о решении: Нетрудно заметить, что это числа положительны, следовательно каждое из слагаемых меньше <span class=\"tex-span\"><i>N</i></span>. То есть всего различных возможных слагаемых порядка <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e13517ff4c4fef8f8f59a599e10028d5eebef947.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Это значит то, что мы взять и одно из слагаемых перебрать. Тогда нам нужно научиться проверять, является ли какое-то число треугольным. Заметим, что если мы заранее выпишем все слагаемые в порядке увеличения то мы сможем с помощью бинарного поиска в массиве искать наше число. Это даем там решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a921374df420d82523c37d44eb5dc0197ca8605.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Если перебирать первое слагаемое в порядке увеличения, то можно использовать два указателя, что дает нам решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4ddef016555085ab07bf6394739f007f3e4a716b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Задача <a href=\"/contest/192/problem/B\" title=\"Codeforces Round 121 (Div. 2)\">192B - Walking in the Rain</a></p><p>Кратко о решении: динамика.</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — количество дней, в течении которых плитка номер <span class=\"tex-span\"><i>i</i></span> доступна. Пересчет: <span class=\"tex-span\"><i>d</i>[<i>i</i>] = <i>min</i>(<i>a</i>[<i>i</i>], <i>max</i>(<i>d</i>[<i>i</i> - 1], <i>d</i>[<i>i</i> - 2]))</span></p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/A\" title=\"Codeforces Round 121 (Div. 1)\">191A - Dynasty Puzzles</a></p><p>Кратко о решении: динамика</p><p>Подробно о решении: динамика d[i][j], <span class=\"tex-span\"><i>i</i></span> — первый символ в имени династии, <span class=\"tex-span\"><i>j</i></span> — последний текущий символ. <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>j</i>]</span> — максимальная текущая длина. Переход: для слова с первой буквой <span class=\"tex-span\"><i>l</i></span>, последней буквой <span class=\"tex-span\"><i>r</i></span> и длиной <span class=\"tex-span\"><i>s</i></span> для всех возможных первых букв <span class=\"tex-span\"><i>i</i></span> состояние <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>r</i>]</span> может быть улучшено значением <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>l</i>] + <i>s</i></span>.</p><p>Ответом будет являться максимальное значение <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>i</i>]</span> для всех <span class=\"tex-span\"><i>i</i></span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i> * <i>alpha</i>)</span>, где <span class=\"tex-span\"><i>alpha</i></span> — это размер алфавита.</p><p>Задача <a href=\"/contest/191/problem/B\" title=\"Codeforces Round 121 (Div. 1)\">191B - Demonstration</a></p><p>Кратко о решении: конструктив</p><p>Подробно о решении: заметим, что на последнюю площадь никогда не выгодно подавать заявку (денег мэрии не потратим, ничего не изменится, мы просто потеряем ход). Переберем площадь, на которой мы хотим провести митинг. У нас есть <span class=\"tex-span\"><i>k</i> - 1</span> ход на то, чтобы потратить деньги мэрии (один ход нам нужен на подачу заявки на искомую площадь). Тратить деньги выгоднее всего на самых дорогих площадях, за исключением последней. Осталось научиться быстро выбирать <span class=\"tex-span\"><i>k</i> - 1</span> максимум из всего массива, за исключением данного элемента. Для этого сначала отсортируем массив и получим <span class=\"tex-span\"><i>k</i></span> максимумов (последнюю площадь мы не должны рассматривать). Проверяем, лежит ли наше текущее значение в <span class=\"tex-span\"><i>k</i> - 1</span> максимальных (бинпоиск и не только). Если лежит, то искомые <span class=\"tex-span\"><i>k</i> - 1</span> максимумов — это максимальные <span class=\"tex-span\"><i>k</i></span> элементов без нашего. Если не лежит, то это просто максимальные <span class=\"tex-span\"><i>k</i></span> элементов. </p><p>Теперь когда мы понимаем, сколько денег мэрии мы можем потратить, то тратим их и смотрим, остаются ли еще у мэрии деньги на проведение события на нашей текущей площади</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/36f470bf769107e6d8d30da09625de1ca4144c7b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/C\" title=\"Codeforces Round 121 (Div. 1)\">191C - Fools and Roads</a></p><p>Кратко о решении: lca</p><p>Подробно о решении: Разобьем каждый путь на два, строго идущих вверх к наименьшему общему предку. Теперь у нас есть только "вертикальные пути". Для каждой вершины насчитаем такую величину: количество вертикальных путей, начинающихся в ней минус количество вертикальных путей в ней заканчивающихся. Если мы насчитали эту величину, то ответ для ребра — это сумма значений в его поддереве. Насчитать такую величину довольно просто: берем для каждой пары дураков считаем lca этой пары. В города дураков прибавляем единичку, в lca значение уменьшаем на два.</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/64f2b782eb0a0a6592ebcf518601e6532901a6b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/D\" title=\"Codeforces Round 121 (Div. 1)\">191D - Metro Scheme</a></p><p>Кратко о решении: снова динамика</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][<i>cycle</i>]</span> — количество линий, которое требуется для того, чтобы в поддереве вершины <span class=\"tex-span\"><i>v</i></span> все покрасить, в <span class=\"tex-span\"><i>v</i></span> остаются <span class=\"tex-span\"><i>rest</i></span> незамкнутым, <span class=\"tex-span\"><i>cycle</i></span> — правда ли, что нам надо обрабатывать цикл, в котором мы находимся. </p><p>Если мы находимся не в вершине цикла, то обрабатываем всех детей, говоря что мы хотим, чтобы в них было по одному незакрытому пути. Пусть у нас есть <span class=\"tex-span\"><i>s</i></span> сыновей, нам надо взять и замкнуть все лишние линии, а недостающие нагенерить. То есть ответ это <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/0d44f4574076ece0d98f5fb9eff6a121a94744f5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, если <span class=\"tex-span\"><i>s</i> > <i>rest</i></span>, и <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/baab55368eb1a5170dfd60a1ac9d71462dcb4850.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> в противном случае.</p><p>Если мы находимся в вершине цикла, то либо мы покрываем этот цикл кольцом и это стоит нам <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/db52f6781c221ae5c2bf94aeab26cdd0afc89d60.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, где <span class=\"tex-span\"><i>u</i></span> — это вершина на цикле. отличная от <span class=\"tex-span\"><i>v</i></span>. Другой вариант — покрыть все участки кольца радиальными линиями. Утверждение: это всегда можно оптимально сделать ровно двумя радиальными. Пусть это не так. Тогда рассмотрим некоторую вершину, в которой радиальные линии <<подвешиваются>> к кольцу. От неё по кольцу в разные стороны уходят два тоннеля, принадлежащие этим линиям. Так как различных линий на кольце сейчас не менее трех, то мы можем перенаправить радиальные линии следующим образом: соединить куски вне кольца друг с другом, а кольцо замкнуть. На кольце останется не менее двух кусков, следовательно все линии останутся валидными, а их число не изменится. </p><p>Теперь надо выбрать две станции, из поддерева которых будут выходить радиальные ветки, покрывшее кольцо. Стоимость такой станции это <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0]</span>, а обычной — <span class=\"tex-span\"><i>d</i>[<i>u</i>][0][0]</span> (<span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][0]</span> в случае той вершины, которую мы сейчас обрабатываем) . Соответственно, нам надо выбрать две станции с максимальным значением <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0] - <i>d</i>[<i>u</i>][0][0]</span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/E\" title=\"Codeforces Round 121 (Div. 1)\">191E - Thwarting Demonstrations</a></p><p>Кратко о решении: бинарный поиск по ответу</p><p>Подробно о решении: Сделаем бинарный поиск по ответу. Нам надо посчитать количество отрезков, на которых сумма больше нашего некоторого значения. Как мы это будем делать: будем обрабатывать все отрезки в порядке увеличения правых концов. Отрезки с одинаковыми правыми концами будем обрабатывать пачками. Более подробно: мы будем поддерживать некоторую структуру данных в которой будут храниться суммы всех отрезков c фиксированным правым концом. </p><p>Для того, чтобы быстро пересчитывать, нам нужно всего добавить в множество некоторый элемент ( <span class=\"tex-span\">0</span>, если точнее) и добавить ко всем элементам множества некоторое значение (<span class=\"tex-span\"><i>a</i>[<i>i</i>]</span>, если быть точнее). Еще нам нужно уметь отвечать на запрос <<количество элементов, больших данного на отрезке>>. Все это умеет быстро реализовывать, например, декартово дерево. Но нам придется дополнительно хранить некоторую величину <span class=\"tex-span\"><i>X</i></span>, означающую <<надо прибавить к элементу из декартова дерева <span class=\"tex-span\"><i>X</i></span>, чтобы получить реальное значение>>. Тогда при добавлении элемента <span class=\"tex-span\"><i>a</i></span> в нашу структуру надо будет положить в декартово дерево величину <span class=\"tex-span\"><i>a</i> - <i>X</i></span>, а прибавление некоторой величины ко всему множеству реализуется простым изменением <span class=\"tex-span\"><i>X</i></span>. </p><p>То есть у нас есть структура данных, которая умеет все эти операции выполнять за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. То есть одна итерация внешнего бинпоиска работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, следовательно весь алгоритм работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-2225-4648\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"2225\",\n blogEntryId: \"4634\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+13</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/AlTimin\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/AlTimin\">\n AlTimin\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4634#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4634#comments\">\n 6\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4658\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (5)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"440048\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/lukamosiashvili\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/487409/avatar/4e37df5c1d58cc25.jpg'/> </a>\n <div><a href=\"/profile/lukamosiashvili\" title=\"Master lukamosiashvili\" class=\"rated-user user-orange\">lukamosiashvili</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/24/2018 17:04\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-440048\" href=\"?#comment-440048\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"440048\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"440048\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"487409\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-440048\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I wrote code for 191C but I got verdict: wrong answer on test 3. please, tell to me, why my code do not works correctly. link: <a href=\"https://codeforces.com/contest/191/submission/39604271\">https://codeforces.com/contest/191/submission/39604271</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-440048 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-440048 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-440048\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"639056\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SarthakBansal\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1212402/avatar/48e2e41dbb0f3d70.jpg'/> </a>\n <div><a href=\"/profile/SarthakBansal\" title=\"Expert SarthakBansal\" class=\"rated-user user-blue\">SarthakBansal</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/10/2020 11:10\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-639056\" href=\"?#comment-639056\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"639056\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1212402\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-639056\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><strong>English Editorial of 191A — Dynasty Puzzles</strong></p><p>We create dp[26][26] where dp[i][j] represents the max. length of a dynasty which starts at letter i and ends at letter j. Since in the question, the first and last letters are to be same, Our answer will be the maximum of dp[i][i] for 0<= i <=26.</p> <pre><code>for i:0...n\n Input a string. Now for this string let l=first character and r=last character.\n Thereby dp[l][r]=max(dp[l][r],s.length())\n for j:0...26 \n Now the string which starts at j and ends at r can be improved to a string which, starts at j \n then ends at l then re begins at l and finally ends at r (i.e. input string s also included \n while the starting ending letters remain same)\n i.e. dp[j][r]=max(dp[j][r],dp[j][l]+s.length())\n Also take care that this improvement is possible only if there already exists a string which \n starts at j and ends at l (i.e. dp[j][l] !=0 ).\n</code></pre><p>Finally , answer will be maximum of all dp[i][i] , where 0<=i<=26.</p><p><a href=\"https://codeforces.com/problemset/submission/191/83279171\">Code135</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-639056 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-639056 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-639056\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"759087\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Feb/08/2021 00:02\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-759087\" href=\"?#comment-759087\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"759087\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-759087\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Very well explained!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-759087 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-759087 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-759087\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1042874\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/theCPguy\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2764258/avatar/98ad595a357c6acb.jpg'/> </a>\n <div><a href=\"/profile/theCPguy\" title=\"Specialist theCPguy\" class=\"rated-user user-cyan\">theCPguy</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/04/2023 08:48\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1042874\" href=\"?#comment-1042874\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1042874\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2764258\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1042874\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Great Explanation Sir</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1042874 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1042874 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1042874\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"695887\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mooncrater\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/656776/avatar/d19b34b1e226e4ad.jpg'/> </a>\n <div><a href=\"/profile/Mooncrater\" title=\"Specialist Mooncrater\" class=\"rated-user user-cyan\">Mooncrater</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/14/2020 17:11\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-695887\" href=\"?#comment-695887\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"695887\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"656776\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-695887\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For anyone looking for a submission for the editorial for C, look at <a href=\"https://codeforces.com/contest/191/submission/1727922\">Shik's solution here.</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-695887 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-695887 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-695887\">\r\n 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Walking in the Rain"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Walking in the Rain</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>In Berland the opposition is going to arrange mass walking on the boulevard. The boulevard consists of <span class=\"tex-span\"><i>n</i></span> tiles that are lain in a row and are numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from right to left. The opposition should start walking on the tile number <span class=\"tex-span\">1</span> and the finish on the tile number <span class=\"tex-span\"><i>n</i></span>. During the walk it is allowed to move from right to left between adjacent tiles in a row, and jump over a tile. More formally, if you are standing on the tile number <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(<i>i</i> < <i>n</i> - 1)</span>, you can reach the tiles number <span class=\"tex-span\"><i>i</i> + 1</span> or the tile number <span class=\"tex-span\"><i>i</i> + 2</span> from it (if you stand on the tile number <span class=\"tex-span\"><i>n</i> - 1</span>, you can only reach tile number <span class=\"tex-span\"><i>n</i></span>). We can assume that all the opposition movements occur instantaneously.</p><p>In order to thwart an opposition rally, the Berland bloody regime organized the rain. The tiles on the boulevard are of poor quality and they are rapidly destroyed in the rain. We know that the <span class=\"tex-span\"><i>i</i></span>-th tile is destroyed after <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> days of rain (on day <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> tile isn't destroyed yet, and on day <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> + 1</span> it is already destroyed). Of course, no one is allowed to walk on the destroyed tiles! So the walk of the opposition is considered thwarted, if either the tile number <span class=\"tex-span\">1</span> is broken, or the tile number <span class=\"tex-span\"><i>n</i></span> is broken, or it is impossible to reach the tile number <span class=\"tex-span\"><i>n</i></span> from the tile number <span class=\"tex-span\">1</span> if we can walk on undestroyed tiles.</p><p>The opposition wants to gather more supporters for their walk. Therefore, the more time they have to pack, the better. Help the opposition to calculate how much time they still have and tell us for how many days the walk from the tile number <span class=\"tex-span\">1</span> to the tile number <span class=\"tex-span\"><i>n</i></span> will be possible.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">3</sup></span>) — the boulevard's length in tiles.</p><p>The second line contains <span class=\"tex-span\"><i>n</i></span> space-separated integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of days after which the <span class=\"tex-span\"><i>i</i></span>-th tile gets destroyed (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">3</sup></span>). </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the sought number of days.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/>10 3 5 10<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>10 2 8 3 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the second tile gets destroyed after day three, and the only path left is <span class=\"tex-span\">1 → 3 → 4</span>. After day five there is a two-tile gap between the first and the last tile, you can't jump over it.</p><p>In the second sample path <span class=\"tex-span\">1 → 3 → 5</span> is available up to day five, inclusive. On day six the last tile is destroyed and the walk is thwarted.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"b7fce634a6f5565c862ab132f82f624c\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"cec91400c4d392a5994a9016975da662dcd210a1\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/192\">Codeforces Round 121 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='b7fce634a6f5565c862ab132f82f624c'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/192/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Brute force\">\r\n brute force\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, simulation\">\r\n implementation\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1100\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" 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\"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4635\" title=\"announcement\" target=\"_blank\">announcement <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"13218\" resourceName=\"announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4634\" title=\"tutorial\" target=\"_blank\">tutorial <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"13219\" resourceName=\"tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/192\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/192/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/192/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/192/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/192/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/192/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/192/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/192/customtest\">Custom 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result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"B\" data-uuid=\"ps_e1351072551558bc262238f0fa8f4cd2e5f7e41e\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Walking in the Rain</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>In Berland the opposition is going to arrange mass walking on the boulevard. The boulevard consists of <span class=\"tex-span\"><i>n</i></span> tiles that are lain in a row and are numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from right to left. The opposition should start walking on the tile number <span class=\"tex-span\">1</span> and the finish on the tile number <span class=\"tex-span\"><i>n</i></span>. During the walk it is allowed to move from right to left between adjacent tiles in a row, and jump over a tile. More formally, if you are standing on the tile number <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(<i>i</i> < <i>n</i> - 1)</span>, you can reach the tiles number <span class=\"tex-span\"><i>i</i> + 1</span> or the tile number <span class=\"tex-span\"><i>i</i> + 2</span> from it (if you stand on the tile number <span class=\"tex-span\"><i>n</i> - 1</span>, you can only reach tile number <span class=\"tex-span\"><i>n</i></span>). We can assume that all the opposition movements occur instantaneously.</p><p>In order to thwart an opposition rally, the Berland bloody regime organized the rain. The tiles on the boulevard are of poor quality and they are rapidly destroyed in the rain. We know that the <span class=\"tex-span\"><i>i</i></span>-th tile is destroyed after <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> days of rain (on day <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> tile isn't destroyed yet, and on day <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> + 1</span> it is already destroyed). Of course, no one is allowed to walk on the destroyed tiles! So the walk of the opposition is considered thwarted, if either the tile number <span class=\"tex-span\">1</span> is broken, or the tile number <span class=\"tex-span\"><i>n</i></span> is broken, or it is impossible to reach the tile number <span class=\"tex-span\"><i>n</i></span> from the tile number <span class=\"tex-span\">1</span> if we can walk on undestroyed tiles.</p><p>The opposition wants to gather more supporters for their walk. Therefore, the more time they have to pack, the better. Help the opposition to calculate how much time they still have and tell us for how many days the walk from the tile number <span class=\"tex-span\">1</span> to the tile number <span class=\"tex-span\"><i>n</i></span> will be possible.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">3</sup></span>) — the boulevard's length in tiles.</p><p>The second line contains <span class=\"tex-span\"><i>n</i></span> space-separated integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> — the number of days after which the <span class=\"tex-span\"><i>i</i></span>-th tile gets destroyed (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">3</sup></span>). </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the sought number of days.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4<br />10 3 5 10<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />10 2 8 3 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the second tile gets destroyed after day three, and the only path left is <span class=\"tex-span\">1 → 3 → 4</span>. After day five there is a two-tile gap between the first and the last tile, you can't jump over it.</p><p>In the second sample path <span class=\"tex-span\">1 → 3 → 5</span> is available up to day five, inclusive. On day six the last tile is destroyed and the walk is thwarted.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=B]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n $problem.find(\".diff-notifier\").hide();\r\n });\r\n\r\n $problem.find(\"a.view-changes\").click(function() {\r\n $.post(\"/data/diff\", {action: \"getDiff\", a: previousStatementText, b: statementText}, function (result) {\r\n if (result[\"success\"] === \"true\") {\r\n 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class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div>\r\n\r\n\n <div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='0e36e4ae41db037922b04beb941e4855'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" 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href=\"/profile/AlTimin\">AlTimin</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/AlTimin\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/AlTimin\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/AlTimin\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/AlTimin\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/AlTimin\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/AlTimin\" style=\"text-decoration:none;color:black !important;\">AlTimin's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4648\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4634\"> <p>Разбор Codeforces Round #121</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/AlTimin\" title=\"Expert AlTimin\" class=\"rated-user user-blue\">AlTimin</a>,\r\n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>,\r\n \r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/ru.png\" alt=\"In Russian\" title=\"In Russian\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Задача <a href=\"/contest/192/problem/A\" title=\"Codeforces Round 121 (Div. 2)\">192A - Funky Numbers</a></p><p>Кратко о решении: перебор</p><p>Подробно о решении: Нетрудно заметить, что это числа положительны, следовательно каждое из слагаемых меньше <span class=\"tex-span\"><i>N</i></span>. То есть всего различных возможных слагаемых порядка <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e13517ff4c4fef8f8f59a599e10028d5eebef947.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Это значит то, что мы взять и одно из слагаемых перебрать. Тогда нам нужно научиться проверять, является ли какое-то число треугольным. Заметим, что если мы заранее выпишем все слагаемые в порядке увеличения то мы сможем с помощью бинарного поиска в массиве искать наше число. Это даем там решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a921374df420d82523c37d44eb5dc0197ca8605.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Если перебирать первое слагаемое в порядке увеличения, то можно использовать два указателя, что дает нам решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4ddef016555085ab07bf6394739f007f3e4a716b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Задача <a href=\"/contest/192/problem/B\" title=\"Codeforces Round 121 (Div. 2)\">192B - Walking in the Rain</a></p><p>Кратко о решении: динамика.</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — количество дней, в течении которых плитка номер <span class=\"tex-span\"><i>i</i></span> доступна. Пересчет: <span class=\"tex-span\"><i>d</i>[<i>i</i>] = <i>min</i>(<i>a</i>[<i>i</i>], <i>max</i>(<i>d</i>[<i>i</i> - 1], <i>d</i>[<i>i</i> - 2]))</span></p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/A\" title=\"Codeforces Round 121 (Div. 1)\">191A - Dynasty Puzzles</a></p><p>Кратко о решении: динамика</p><p>Подробно о решении: динамика d[i][j], <span class=\"tex-span\"><i>i</i></span> — первый символ в имени династии, <span class=\"tex-span\"><i>j</i></span> — последний текущий символ. <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>j</i>]</span> — максимальная текущая длина. Переход: для слова с первой буквой <span class=\"tex-span\"><i>l</i></span>, последней буквой <span class=\"tex-span\"><i>r</i></span> и длиной <span class=\"tex-span\"><i>s</i></span> для всех возможных первых букв <span class=\"tex-span\"><i>i</i></span> состояние <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>r</i>]</span> может быть улучшено значением <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>l</i>] + <i>s</i></span>.</p><p>Ответом будет являться максимальное значение <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>i</i>]</span> для всех <span class=\"tex-span\"><i>i</i></span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i> * <i>alpha</i>)</span>, где <span class=\"tex-span\"><i>alpha</i></span> — это размер алфавита.</p><p>Задача <a href=\"/contest/191/problem/B\" title=\"Codeforces Round 121 (Div. 1)\">191B - Demonstration</a></p><p>Кратко о решении: конструктив</p><p>Подробно о решении: заметим, что на последнюю площадь никогда не выгодно подавать заявку (денег мэрии не потратим, ничего не изменится, мы просто потеряем ход). Переберем площадь, на которой мы хотим провести митинг. У нас есть <span class=\"tex-span\"><i>k</i> - 1</span> ход на то, чтобы потратить деньги мэрии (один ход нам нужен на подачу заявки на искомую площадь). Тратить деньги выгоднее всего на самых дорогих площадях, за исключением последней. Осталось научиться быстро выбирать <span class=\"tex-span\"><i>k</i> - 1</span> максимум из всего массива, за исключением данного элемента. Для этого сначала отсортируем массив и получим <span class=\"tex-span\"><i>k</i></span> максимумов (последнюю площадь мы не должны рассматривать). Проверяем, лежит ли наше текущее значение в <span class=\"tex-span\"><i>k</i> - 1</span> максимальных (бинпоиск и не только). Если лежит, то искомые <span class=\"tex-span\"><i>k</i> - 1</span> максимумов — это максимальные <span class=\"tex-span\"><i>k</i></span> элементов без нашего. Если не лежит, то это просто максимальные <span class=\"tex-span\"><i>k</i></span> элементов. </p><p>Теперь когда мы понимаем, сколько денег мэрии мы можем потратить, то тратим их и смотрим, остаются ли еще у мэрии деньги на проведение события на нашей текущей площади</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/36f470bf769107e6d8d30da09625de1ca4144c7b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/C\" title=\"Codeforces Round 121 (Div. 1)\">191C - Fools and Roads</a></p><p>Кратко о решении: lca</p><p>Подробно о решении: Разобьем каждый путь на два, строго идущих вверх к наименьшему общему предку. Теперь у нас есть только "вертикальные пути". Для каждой вершины насчитаем такую величину: количество вертикальных путей, начинающихся в ней минус количество вертикальных путей в ней заканчивающихся. Если мы насчитали эту величину, то ответ для ребра — это сумма значений в его поддереве. Насчитать такую величину довольно просто: берем для каждой пары дураков считаем lca этой пары. В города дураков прибавляем единичку, в lca значение уменьшаем на два.</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/64f2b782eb0a0a6592ebcf518601e6532901a6b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/D\" title=\"Codeforces Round 121 (Div. 1)\">191D - Metro Scheme</a></p><p>Кратко о решении: снова динамика</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][<i>cycle</i>]</span> — количество линий, которое требуется для того, чтобы в поддереве вершины <span class=\"tex-span\"><i>v</i></span> все покрасить, в <span class=\"tex-span\"><i>v</i></span> остаются <span class=\"tex-span\"><i>rest</i></span> незамкнутым, <span class=\"tex-span\"><i>cycle</i></span> — правда ли, что нам надо обрабатывать цикл, в котором мы находимся. </p><p>Если мы находимся не в вершине цикла, то обрабатываем всех детей, говоря что мы хотим, чтобы в них было по одному незакрытому пути. Пусть у нас есть <span class=\"tex-span\"><i>s</i></span> сыновей, нам надо взять и замкнуть все лишние линии, а недостающие нагенерить. То есть ответ это <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/0d44f4574076ece0d98f5fb9eff6a121a94744f5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, если <span class=\"tex-span\"><i>s</i> > <i>rest</i></span>, и <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/baab55368eb1a5170dfd60a1ac9d71462dcb4850.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> в противном случае.</p><p>Если мы находимся в вершине цикла, то либо мы покрываем этот цикл кольцом и это стоит нам <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/db52f6781c221ae5c2bf94aeab26cdd0afc89d60.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, где <span class=\"tex-span\"><i>u</i></span> — это вершина на цикле. отличная от <span class=\"tex-span\"><i>v</i></span>. Другой вариант — покрыть все участки кольца радиальными линиями. Утверждение: это всегда можно оптимально сделать ровно двумя радиальными. Пусть это не так. Тогда рассмотрим некоторую вершину, в которой радиальные линии <<подвешиваются>> к кольцу. От неё по кольцу в разные стороны уходят два тоннеля, принадлежащие этим линиям. Так как различных линий на кольце сейчас не менее трех, то мы можем перенаправить радиальные линии следующим образом: соединить куски вне кольца друг с другом, а кольцо замкнуть. На кольце останется не менее двух кусков, следовательно все линии останутся валидными, а их число не изменится. </p><p>Теперь надо выбрать две станции, из поддерева которых будут выходить радиальные ветки, покрывшее кольцо. Стоимость такой станции это <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0]</span>, а обычной — <span class=\"tex-span\"><i>d</i>[<i>u</i>][0][0]</span> (<span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][0]</span> в случае той вершины, которую мы сейчас обрабатываем) . Соответственно, нам надо выбрать две станции с максимальным значением <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0] - <i>d</i>[<i>u</i>][0][0]</span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/E\" title=\"Codeforces Round 121 (Div. 1)\">191E - Thwarting Demonstrations</a></p><p>Кратко о решении: бинарный поиск по ответу</p><p>Подробно о решении: Сделаем бинарный поиск по ответу. Нам надо посчитать количество отрезков, на которых сумма больше нашего некоторого значения. Как мы это будем делать: будем обрабатывать все отрезки в порядке увеличения правых концов. Отрезки с одинаковыми правыми концами будем обрабатывать пачками. Более подробно: мы будем поддерживать некоторую структуру данных в которой будут храниться суммы всех отрезков c фиксированным правым концом. </p><p>Для того, чтобы быстро пересчитывать, нам нужно всего добавить в множество некоторый элемент ( <span class=\"tex-span\">0</span>, если точнее) и добавить ко всем элементам множества некоторое значение (<span class=\"tex-span\"><i>a</i>[<i>i</i>]</span>, если быть точнее). Еще нам нужно уметь отвечать на запрос <<количество элементов, больших данного на отрезке>>. Все это умеет быстро реализовывать, например, декартово дерево. Но нам придется дополнительно хранить некоторую величину <span class=\"tex-span\"><i>X</i></span>, означающую <<надо прибавить к элементу из декартова дерева <span class=\"tex-span\"><i>X</i></span>, чтобы получить реальное значение>>. Тогда при добавлении элемента <span class=\"tex-span\"><i>a</i></span> в нашу структуру надо будет положить в декартово дерево величину <span class=\"tex-span\"><i>a</i> - <i>X</i></span>, а прибавление некоторой величины ко всему множеству реализуется простым изменением <span class=\"tex-span\"><i>X</i></span>. </p><p>То есть у нас есть структура данных, которая умеет все эти операции выполнять за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. То есть одна итерация внешнего бинпоиска работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, следовательно весь алгоритм работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-2225-4648\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"2225\",\n blogEntryId: \"4634\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+13</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/AlTimin\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/AlTimin\">\n AlTimin\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4634#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4634#comments\">\n 6\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4658\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (5)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"440048\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/lukamosiashvili\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/487409/avatar/4e37df5c1d58cc25.jpg'/> </a>\n <div><a href=\"/profile/lukamosiashvili\" title=\"Master lukamosiashvili\" class=\"rated-user user-orange\">lukamosiashvili</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/24/2018 17:04\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-440048\" href=\"?#comment-440048\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"440048\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"440048\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"487409\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-440048\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I wrote code for 191C but I got verdict: wrong answer on test 3. please, tell to me, why my code do not works correctly. link: <a href=\"https://codeforces.com/contest/191/submission/39604271\">https://codeforces.com/contest/191/submission/39604271</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-440048 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-440048 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-440048\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"639056\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SarthakBansal\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1212402/avatar/48e2e41dbb0f3d70.jpg'/> </a>\n <div><a href=\"/profile/SarthakBansal\" title=\"Expert SarthakBansal\" class=\"rated-user user-blue\">SarthakBansal</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/10/2020 11:10\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-639056\" href=\"?#comment-639056\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"639056\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1212402\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-639056\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><strong>English Editorial of 191A — Dynasty Puzzles</strong></p><p>We create dp[26][26] where dp[i][j] represents the max. length of a dynasty which starts at letter i and ends at letter j. Since in the question, the first and last letters are to be same, Our answer will be the maximum of dp[i][i] for 0<= i <=26.</p> <pre><code>for i:0...n\n Input a string. Now for this string let l=first character and r=last character.\n Thereby dp[l][r]=max(dp[l][r],s.length())\n for j:0...26 \n Now the string which starts at j and ends at r can be improved to a string which, starts at j \n then ends at l then re begins at l and finally ends at r (i.e. input string s also included \n while the starting ending letters remain same)\n i.e. dp[j][r]=max(dp[j][r],dp[j][l]+s.length())\n Also take care that this improvement is possible only if there already exists a string which \n starts at j and ends at l (i.e. dp[j][l] !=0 ).\n</code></pre><p>Finally , answer will be maximum of all dp[i][i] , where 0<=i<=26.</p><p><a href=\"https://codeforces.com/problemset/submission/191/83279171\">Code135</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-639056 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-639056 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-639056\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"759087\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Feb/08/2021 00:02\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-759087\" href=\"?#comment-759087\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"759087\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-759087\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Very well explained!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-759087 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-759087 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-759087\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1042874\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/theCPguy\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2764258/avatar/98ad595a357c6acb.jpg'/> </a>\n <div><a href=\"/profile/theCPguy\" title=\"Specialist theCPguy\" class=\"rated-user user-cyan\">theCPguy</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/04/2023 08:48\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1042874\" href=\"?#comment-1042874\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1042874\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2764258\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1042874\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Great Explanation Sir</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1042874 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1042874 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1042874\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"695887\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mooncrater\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/656776/avatar/d19b34b1e226e4ad.jpg'/> </a>\n <div><a href=\"/profile/Mooncrater\" title=\"Specialist Mooncrater\" class=\"rated-user user-cyan\">Mooncrater</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/14/2020 17:11\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-695887\" href=\"?#comment-695887\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"695887\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"656776\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-695887\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For anyone looking for a submission for the editorial for C, look at <a href=\"https://codeforces.com/contest/191/submission/1727922\">Shik's solution here.</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-695887 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-695887 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-695887\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4658\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" style=\"width:99%;\"></textarea>\r\n <div class=\"error error__content\"></div>\r\n <div style=\"text-align:center;\">\r\n <input type=\"button\" name=\"preview\" style=\"padding: 0.25em 1em; margin-top: 1em; min-width: 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Dynasty Puzzles"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Dynasty Puzzles</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>The ancient Berlanders believed that the longer the name, the more important its bearer is. Thus, Berland kings were famous for their long names. But long names are somewhat inconvenient, so the Berlanders started to abbreviate the names of their kings. They called every king by the first letters of its name. Thus, the king, whose name was Victorious Vasily Pupkin, was always called by the berlanders VVP.</p><p>In Berland over its long history many dynasties of kings replaced each other, but they were all united by common traditions. Thus, according to one Berland traditions, to maintain stability in the country, the first name of the heir should be the same as the last name his predecessor (hence, the first letter of the abbreviated name of the heir coincides with the last letter of the abbreviated name of the predecessor). Berlanders appreciate stability, so this tradition has never been broken. Also Berlanders like perfection, so another tradition requires that the first name of the first king in the dynasty coincides with the last name of the last king in this dynasty (hence, the first letter of the abbreviated name of the first king coincides with the last letter of the abbreviated name of the last king). This tradition, of course, has also been always observed.</p><p>The name of a dynasty is formed by very simple rules: we take all the short names of the kings in the order in which they ruled, and write them in one line. Thus, a dynasty of kings \"ab\" and \"ba\" is called \"abba\", and the dynasty, which had only the king \"abca\", is called \"abca\".</p><p>Vasya, a historian, has recently found a list of abbreviated names of all Berland kings and their relatives. Help Vasya to find the maximally long name of the dynasty that could have existed in Berland.</p><p>Note that in his list all the names are ordered by the time, that is, if name <span class=\"tex-span\"><i>A</i></span> is earlier in the list than <span class=\"tex-span\"><i>B</i></span>, then if <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> were kings, then king <span class=\"tex-span\"><i>A</i></span> ruled before king <span class=\"tex-span\"><i>B</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">5</sup></span>) — the number of names in Vasya's list. Next <span class=\"tex-span\"><i>n</i></span> lines contain <span class=\"tex-span\"><i>n</i></span> abbreviated names, one per line. An abbreviated name is a non-empty sequence of lowercase Latin letters. Its length does not exceed <span class=\"tex-span\">10</span> characters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — length of the sought dynasty's name in letters.</p><p>If Vasya's list is wrong and no dynasty can be found there, print a single number <span class=\"tex-span\">0</span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>abc<br/>ca<br/>cba<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/>vvp<br/>vvp<br/>dam<br/>vvp<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>ab<br/>c<br/>def<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample two dynasties can exist: the one called \"abcca\" (with the first and second kings) and the one called \"abccba\" (with the first and third kings). </p><p>In the second sample there aren't acceptable dynasties.</p><p>The only dynasty in the third sample consists of one king, his name is \"c\".</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"10410fd77b33eec7c7a0081b9d118efb\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"cec91400c4d392a5994a9016975da662dcd210a1\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/192\">Codeforces Round 121 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='10410fd77b33eec7c7a0081b9d118efb'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/192/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Dynamic programming\">\r\n dp\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1500\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='10410fd77b33eec7c7a0081b9d118efb'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1357\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='10410fd77b33eec7c7a0081b9d118efb'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1357\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script type=\"text/javascript\">\r\n $(\".tag-box img\").click(function () {\r\n var tagName = $(this).attr(\"value\");\r\n Codeforces.confirm(\"Are you sure you want to remove this tag?\", function () {\r\n $(\"#removeTagForm input[name=tagName]\").val(tagName);\r\n $(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4635\" title=\"announcement\" target=\"_blank\">announcement <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"13218\" resourceName=\"announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4634\" title=\"tutorial\" target=\"_blank\">tutorial <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"13219\" resourceName=\"tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: 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class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Dynasty Puzzles</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>The ancient Berlanders believed that the longer the name, the more important its bearer is. Thus, Berland kings were famous for their long names. But long names are somewhat inconvenient, so the Berlanders started to abbreviate the names of their kings. They called every king by the first letters of its name. Thus, the king, whose name was Victorious Vasily Pupkin, was always called by the berlanders VVP.</p><p>In Berland over its long history many dynasties of kings replaced each other, but they were all united by common traditions. Thus, according to one Berland traditions, to maintain stability in the country, the first name of the heir should be the same as the last name his predecessor (hence, the first letter of the abbreviated name of the heir coincides with the last letter of the abbreviated name of the predecessor). Berlanders appreciate stability, so this tradition has never been broken. Also Berlanders like perfection, so another tradition requires that the first name of the first king in the dynasty coincides with the last name of the last king in this dynasty (hence, the first letter of the abbreviated name of the first king coincides with the last letter of the abbreviated name of the last king). This tradition, of course, has also been always observed.</p><p>The name of a dynasty is formed by very simple rules: we take all the short names of the kings in the order in which they ruled, and write them in one line. Thus, a dynasty of kings "ab" and "ba" is called "abba", and the dynasty, which had only the king "abca", is called "abca".</p><p>Vasya, a historian, has recently found a list of abbreviated names of all Berland kings and their relatives. Help Vasya to find the maximally long name of the dynasty that could have existed in Berland.</p><p>Note that in his list all the names are ordered by the time, that is, if name <span class=\"tex-span\"><i>A</i></span> is earlier in the list than <span class=\"tex-span\"><i>B</i></span>, then if <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> were kings, then king <span class=\"tex-span\"><i>A</i></span> ruled before king <span class=\"tex-span\"><i>B</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 5·10<sup class=\"upper-index\">5</sup></span>) — the number of names in Vasya's list. Next <span class=\"tex-span\"><i>n</i></span> lines contain <span class=\"tex-span\"><i>n</i></span> abbreviated names, one per line. An abbreviated name is a non-empty sequence of lowercase Latin letters. Its length does not exceed <span class=\"tex-span\">10</span> characters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — length of the sought dynasty's name in letters.</p><p>If Vasya's list is wrong and no dynasty can be found there, print a single number <span class=\"tex-span\">0</span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />abc<br />ca<br />cba<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br />vvp<br />vvp<br />dam<br />vvp<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />ab<br />c<br />def<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample two dynasties can exist: the one called "abcca" (with the first and second kings) and the one called "abccba" (with the first and third kings). </p><p>In the second sample there aren't acceptable dynasties.</p><p>The only dynasty in the third sample consists of one king, his name is "c".</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() 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class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div>\r\n\r\n\n <div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='0e36e4ae41db037922b04beb941e4855'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" 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href=\"/profile/AlTimin\">AlTimin</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/AlTimin\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/AlTimin\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/AlTimin\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/AlTimin\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/AlTimin\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/AlTimin\" style=\"text-decoration:none;color:black !important;\">AlTimin's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4648\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4634\"> <p>Разбор Codeforces Round #121</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/AlTimin\" title=\"Expert AlTimin\" class=\"rated-user user-blue\">AlTimin</a>,\r\n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>,\r\n \r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/ru.png\" alt=\"In Russian\" title=\"In Russian\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Задача <a href=\"/contest/192/problem/A\" title=\"Codeforces Round 121 (Div. 2)\">192A - Funky Numbers</a></p><p>Кратко о решении: перебор</p><p>Подробно о решении: Нетрудно заметить, что это числа положительны, следовательно каждое из слагаемых меньше <span class=\"tex-span\"><i>N</i></span>. То есть всего различных возможных слагаемых порядка <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e13517ff4c4fef8f8f59a599e10028d5eebef947.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Это значит то, что мы взять и одно из слагаемых перебрать. Тогда нам нужно научиться проверять, является ли какое-то число треугольным. Заметим, что если мы заранее выпишем все слагаемые в порядке увеличения то мы сможем с помощью бинарного поиска в массиве искать наше число. Это даем там решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a921374df420d82523c37d44eb5dc0197ca8605.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Если перебирать первое слагаемое в порядке увеличения, то можно использовать два указателя, что дает нам решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4ddef016555085ab07bf6394739f007f3e4a716b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Задача <a href=\"/contest/192/problem/B\" title=\"Codeforces Round 121 (Div. 2)\">192B - Walking in the Rain</a></p><p>Кратко о решении: динамика.</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — количество дней, в течении которых плитка номер <span class=\"tex-span\"><i>i</i></span> доступна. Пересчет: <span class=\"tex-span\"><i>d</i>[<i>i</i>] = <i>min</i>(<i>a</i>[<i>i</i>], <i>max</i>(<i>d</i>[<i>i</i> - 1], <i>d</i>[<i>i</i> - 2]))</span></p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/A\" title=\"Codeforces Round 121 (Div. 1)\">191A - Dynasty Puzzles</a></p><p>Кратко о решении: динамика</p><p>Подробно о решении: динамика d[i][j], <span class=\"tex-span\"><i>i</i></span> — первый символ в имени династии, <span class=\"tex-span\"><i>j</i></span> — последний текущий символ. <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>j</i>]</span> — максимальная текущая длина. Переход: для слова с первой буквой <span class=\"tex-span\"><i>l</i></span>, последней буквой <span class=\"tex-span\"><i>r</i></span> и длиной <span class=\"tex-span\"><i>s</i></span> для всех возможных первых букв <span class=\"tex-span\"><i>i</i></span> состояние <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>r</i>]</span> может быть улучшено значением <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>l</i>] + <i>s</i></span>.</p><p>Ответом будет являться максимальное значение <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>i</i>]</span> для всех <span class=\"tex-span\"><i>i</i></span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i> * <i>alpha</i>)</span>, где <span class=\"tex-span\"><i>alpha</i></span> — это размер алфавита.</p><p>Задача <a href=\"/contest/191/problem/B\" title=\"Codeforces Round 121 (Div. 1)\">191B - Demonstration</a></p><p>Кратко о решении: конструктив</p><p>Подробно о решении: заметим, что на последнюю площадь никогда не выгодно подавать заявку (денег мэрии не потратим, ничего не изменится, мы просто потеряем ход). Переберем площадь, на которой мы хотим провести митинг. У нас есть <span class=\"tex-span\"><i>k</i> - 1</span> ход на то, чтобы потратить деньги мэрии (один ход нам нужен на подачу заявки на искомую площадь). Тратить деньги выгоднее всего на самых дорогих площадях, за исключением последней. Осталось научиться быстро выбирать <span class=\"tex-span\"><i>k</i> - 1</span> максимум из всего массива, за исключением данного элемента. Для этого сначала отсортируем массив и получим <span class=\"tex-span\"><i>k</i></span> максимумов (последнюю площадь мы не должны рассматривать). Проверяем, лежит ли наше текущее значение в <span class=\"tex-span\"><i>k</i> - 1</span> максимальных (бинпоиск и не только). Если лежит, то искомые <span class=\"tex-span\"><i>k</i> - 1</span> максимумов — это максимальные <span class=\"tex-span\"><i>k</i></span> элементов без нашего. Если не лежит, то это просто максимальные <span class=\"tex-span\"><i>k</i></span> элементов. </p><p>Теперь когда мы понимаем, сколько денег мэрии мы можем потратить, то тратим их и смотрим, остаются ли еще у мэрии деньги на проведение события на нашей текущей площади</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/36f470bf769107e6d8d30da09625de1ca4144c7b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/C\" title=\"Codeforces Round 121 (Div. 1)\">191C - Fools and Roads</a></p><p>Кратко о решении: lca</p><p>Подробно о решении: Разобьем каждый путь на два, строго идущих вверх к наименьшему общему предку. Теперь у нас есть только "вертикальные пути". Для каждой вершины насчитаем такую величину: количество вертикальных путей, начинающихся в ней минус количество вертикальных путей в ней заканчивающихся. Если мы насчитали эту величину, то ответ для ребра — это сумма значений в его поддереве. Насчитать такую величину довольно просто: берем для каждой пары дураков считаем lca этой пары. В города дураков прибавляем единичку, в lca значение уменьшаем на два.</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/64f2b782eb0a0a6592ebcf518601e6532901a6b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/D\" title=\"Codeforces Round 121 (Div. 1)\">191D - Metro Scheme</a></p><p>Кратко о решении: снова динамика</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][<i>cycle</i>]</span> — количество линий, которое требуется для того, чтобы в поддереве вершины <span class=\"tex-span\"><i>v</i></span> все покрасить, в <span class=\"tex-span\"><i>v</i></span> остаются <span class=\"tex-span\"><i>rest</i></span> незамкнутым, <span class=\"tex-span\"><i>cycle</i></span> — правда ли, что нам надо обрабатывать цикл, в котором мы находимся. </p><p>Если мы находимся не в вершине цикла, то обрабатываем всех детей, говоря что мы хотим, чтобы в них было по одному незакрытому пути. Пусть у нас есть <span class=\"tex-span\"><i>s</i></span> сыновей, нам надо взять и замкнуть все лишние линии, а недостающие нагенерить. То есть ответ это <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/0d44f4574076ece0d98f5fb9eff6a121a94744f5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, если <span class=\"tex-span\"><i>s</i> > <i>rest</i></span>, и <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/baab55368eb1a5170dfd60a1ac9d71462dcb4850.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> в противном случае.</p><p>Если мы находимся в вершине цикла, то либо мы покрываем этот цикл кольцом и это стоит нам <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/db52f6781c221ae5c2bf94aeab26cdd0afc89d60.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, где <span class=\"tex-span\"><i>u</i></span> — это вершина на цикле. отличная от <span class=\"tex-span\"><i>v</i></span>. Другой вариант — покрыть все участки кольца радиальными линиями. Утверждение: это всегда можно оптимально сделать ровно двумя радиальными. Пусть это не так. Тогда рассмотрим некоторую вершину, в которой радиальные линии <<подвешиваются>> к кольцу. От неё по кольцу в разные стороны уходят два тоннеля, принадлежащие этим линиям. Так как различных линий на кольце сейчас не менее трех, то мы можем перенаправить радиальные линии следующим образом: соединить куски вне кольца друг с другом, а кольцо замкнуть. На кольце останется не менее двух кусков, следовательно все линии останутся валидными, а их число не изменится. </p><p>Теперь надо выбрать две станции, из поддерева которых будут выходить радиальные ветки, покрывшее кольцо. Стоимость такой станции это <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0]</span>, а обычной — <span class=\"tex-span\"><i>d</i>[<i>u</i>][0][0]</span> (<span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][0]</span> в случае той вершины, которую мы сейчас обрабатываем) . Соответственно, нам надо выбрать две станции с максимальным значением <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0] - <i>d</i>[<i>u</i>][0][0]</span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/E\" title=\"Codeforces Round 121 (Div. 1)\">191E - Thwarting Demonstrations</a></p><p>Кратко о решении: бинарный поиск по ответу</p><p>Подробно о решении: Сделаем бинарный поиск по ответу. Нам надо посчитать количество отрезков, на которых сумма больше нашего некоторого значения. Как мы это будем делать: будем обрабатывать все отрезки в порядке увеличения правых концов. Отрезки с одинаковыми правыми концами будем обрабатывать пачками. Более подробно: мы будем поддерживать некоторую структуру данных в которой будут храниться суммы всех отрезков c фиксированным правым концом. </p><p>Для того, чтобы быстро пересчитывать, нам нужно всего добавить в множество некоторый элемент ( <span class=\"tex-span\">0</span>, если точнее) и добавить ко всем элементам множества некоторое значение (<span class=\"tex-span\"><i>a</i>[<i>i</i>]</span>, если быть точнее). Еще нам нужно уметь отвечать на запрос <<количество элементов, больших данного на отрезке>>. Все это умеет быстро реализовывать, например, декартово дерево. Но нам придется дополнительно хранить некоторую величину <span class=\"tex-span\"><i>X</i></span>, означающую <<надо прибавить к элементу из декартова дерева <span class=\"tex-span\"><i>X</i></span>, чтобы получить реальное значение>>. Тогда при добавлении элемента <span class=\"tex-span\"><i>a</i></span> в нашу структуру надо будет положить в декартово дерево величину <span class=\"tex-span\"><i>a</i> - <i>X</i></span>, а прибавление некоторой величины ко всему множеству реализуется простым изменением <span class=\"tex-span\"><i>X</i></span>. </p><p>То есть у нас есть структура данных, которая умеет все эти операции выполнять за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. То есть одна итерация внешнего бинпоиска работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, следовательно весь алгоритм работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-2225-4648\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"2225\",\n blogEntryId: \"4634\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+13</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/AlTimin\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/AlTimin\">\n AlTimin\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4634#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4634#comments\">\n 6\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4658\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (5)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"440048\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/lukamosiashvili\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/487409/avatar/4e37df5c1d58cc25.jpg'/> </a>\n <div><a href=\"/profile/lukamosiashvili\" title=\"Master lukamosiashvili\" class=\"rated-user user-orange\">lukamosiashvili</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/24/2018 17:04\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-440048\" href=\"?#comment-440048\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"440048\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"440048\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"487409\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-440048\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I wrote code for 191C but I got verdict: wrong answer on test 3. please, tell to me, why my code do not works correctly. link: <a href=\"https://codeforces.com/contest/191/submission/39604271\">https://codeforces.com/contest/191/submission/39604271</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-440048 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-440048 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-440048\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"639056\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SarthakBansal\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1212402/avatar/48e2e41dbb0f3d70.jpg'/> </a>\n <div><a href=\"/profile/SarthakBansal\" title=\"Expert SarthakBansal\" class=\"rated-user user-blue\">SarthakBansal</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/10/2020 11:10\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-639056\" href=\"?#comment-639056\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"639056\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1212402\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-639056\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><strong>English Editorial of 191A — Dynasty Puzzles</strong></p><p>We create dp[26][26] where dp[i][j] represents the max. length of a dynasty which starts at letter i and ends at letter j. Since in the question, the first and last letters are to be same, Our answer will be the maximum of dp[i][i] for 0<= i <=26.</p> <pre><code>for i:0...n\n Input a string. Now for this string let l=first character and r=last character.\n Thereby dp[l][r]=max(dp[l][r],s.length())\n for j:0...26 \n Now the string which starts at j and ends at r can be improved to a string which, starts at j \n then ends at l then re begins at l and finally ends at r (i.e. input string s also included \n while the starting ending letters remain same)\n i.e. dp[j][r]=max(dp[j][r],dp[j][l]+s.length())\n Also take care that this improvement is possible only if there already exists a string which \n starts at j and ends at l (i.e. dp[j][l] !=0 ).\n</code></pre><p>Finally , answer will be maximum of all dp[i][i] , where 0<=i<=26.</p><p><a href=\"https://codeforces.com/problemset/submission/191/83279171\">Code135</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-639056 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-639056 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-639056\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"759087\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Feb/08/2021 00:02\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-759087\" href=\"?#comment-759087\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"759087\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-759087\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Very well explained!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-759087 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-759087 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-759087\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1042874\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/theCPguy\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2764258/avatar/98ad595a357c6acb.jpg'/> </a>\n <div><a href=\"/profile/theCPguy\" title=\"Specialist theCPguy\" class=\"rated-user user-cyan\">theCPguy</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/04/2023 08:48\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1042874\" href=\"?#comment-1042874\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1042874\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2764258\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1042874\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Great Explanation Sir</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1042874 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1042874 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1042874\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"695887\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mooncrater\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/656776/avatar/d19b34b1e226e4ad.jpg'/> </a>\n <div><a href=\"/profile/Mooncrater\" title=\"Specialist Mooncrater\" class=\"rated-user user-cyan\">Mooncrater</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/14/2020 17:11\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-695887\" href=\"?#comment-695887\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"695887\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"656776\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-695887\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For anyone looking for a submission for the editorial for C, look at <a href=\"https://codeforces.com/contest/191/submission/1727922\">Shik's solution here.</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-695887 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-695887 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-695887\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4658\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" style=\"width:99%;\"></textarea>\r\n <div class=\"error error__content\"></div>\r\n <div style=\"text-align:center;\">\r\n <input type=\"button\" name=\"preview\" style=\"padding: 0.25em 1em; margin-top: 1em; min-width: 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Demonstration"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Demonstration</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>In the capital city of Berland, Bertown, demonstrations are against the recent election of the King of Berland. Berland opposition, led by Mr. Ovalny, believes that the elections were not fair enough and wants to organize a demonstration at one of the squares.</p><p>Bertown has <span class=\"tex-span\"><i>n</i></span> squares, numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>, they are numbered in the order of increasing distance between them and the city center. That is, square number <span class=\"tex-span\">1</span> is central, and square number <span class=\"tex-span\"><i>n</i></span> is the farthest from the center. Naturally, the opposition wants to hold a meeting as close to the city center as possible (that is, they want an square with the minimum number).</p><p>There are exactly <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span> days left before the demonstration. Now all squares are free. But the Bertown city administration never sleeps, and the approval of an application for the demonstration threatens to become a very complex process. The process of approval lasts several days, but every day the following procedure takes place:</p><ul> <li> The opposition shall apply to hold a demonstration at a free square (the one which isn't used by the administration). </li><li> The administration tries to move the demonstration to the worst free square left. To do this, the administration organizes some long-term activities on the square, which is specified in the application of opposition. In other words, the administration starts using the square and it is no longer free. Then the administration proposes to move the opposition demonstration to the worst free square. If the opposition has applied for the worst free square <span class=\"tex-font-style-bf\">then request is accepted and administration doesn't spend money</span>. If the administration does not have enough money to organize an event on the square in question, the opposition's application is accepted. If administration doesn't have enough money to organize activity, then rest of administration's money spends and application is accepted </li><li> If the application is not accepted, then the opposition can agree to the administration's proposal (that is, take the worst free square), or withdraw the current application and submit another one the next day. If there are no more days left before the meeting, the opposition has no choice but to agree to the proposal of City Hall. If application is accepted opposition can reject it. It means than opposition still can submit more applications later, <span class=\"tex-font-style-bf\">but square remains free</span>. </li></ul><p>In order to organize an event on the square <span class=\"tex-span\"><i>i</i></span>, the administration needs to spend <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> bourles. Because of the crisis the administration has only <span class=\"tex-span\"><i>b</i></span> bourles to confront the opposition. What is the best square that the opposition can take, if the administration will keep trying to occupy the square in question each time? Note that the administration's actions always depend only on the actions of the opposition.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> — the number of squares and days left before the meeting, correspondingly (<span class=\"tex-span\">1 ≤ <i>k</i> < <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span>).</p><p>The second line contains a single integer <span class=\"tex-span\"><i>b</i></span> — the number of bourles the administration has (<span class=\"tex-span\">1 ≤ <i>b</i> ≤ 10<sup class=\"upper-index\">18</sup></span>).</p><p>The third line contains <span class=\"tex-span\"><i>n</i></span> space-separated integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> — the sum of money, needed to organise an event on square <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>).</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum number of the square where the opposition can organize the demonstration.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 2<br/>8<br/>2 4 5 3 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 2<br/>8<br/>3 2 4 1 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>1000000000000000<br/>5 4 3 2 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the opposition can act like this. On day one it applies for square 3. The administration has to organize an event there and end up with 3 bourles. If on the second day the opposition applies for square 2, the administration won't have the money to intervene.</p><p>In the second sample the opposition has only the chance for the last square. If its first move occupies one of the first four squares, the administration is left with at least 4 bourles, which means that next day it can use its next move to move the opposition from any square to the last one.</p><p>In the third sample administration has a lot of money, so opposition can occupy only last square.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"40a10da7df78a7e61d2131d1e5df1115\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"cec91400c4d392a5994a9016975da662dcd210a1\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/192/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Brute force\">\r\n brute force\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Constructive algorithms\">\r\n constructive algorithms\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1700\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" 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|| c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"D\" data-uuid=\"ps_f5bd00d6d7f74971a6c9d833458e694a867209f6\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Demonstration</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>In the capital city of Berland, Bertown, demonstrations are against the recent election of the King of Berland. Berland opposition, led by Mr. Ovalny, believes that the elections were not fair enough and wants to organize a demonstration at one of the squares.</p><p>Bertown has <span class=\"tex-span\"><i>n</i></span> squares, numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>, they are numbered in the order of increasing distance between them and the city center. That is, square number <span class=\"tex-span\">1</span> is central, and square number <span class=\"tex-span\"><i>n</i></span> is the farthest from the center. Naturally, the opposition wants to hold a meeting as close to the city center as possible (that is, they want an square with the minimum number).</p><p>There are exactly <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(<i>k</i> < <i>n</i>)</span> days left before the demonstration. Now all squares are free. But the Bertown city administration never sleeps, and the approval of an application for the demonstration threatens to become a very complex process. The process of approval lasts several days, but every day the following procedure takes place:</p><ul> <li> The opposition shall apply to hold a demonstration at a free square (the one which isn't used by the administration). </li><li> The administration tries to move the demonstration to the worst free square left. To do this, the administration organizes some long-term activities on the square, which is specified in the application of opposition. In other words, the administration starts using the square and it is no longer free. Then the administration proposes to move the opposition demonstration to the worst free square. If the opposition has applied for the worst free square <span class=\"tex-font-style-bf\">then request is accepted and administration doesn't spend money</span>. If the administration does not have enough money to organize an event on the square in question, the opposition's application is accepted. If administration doesn't have enough money to organize activity, then rest of administration's money spends and application is accepted </li><li> If the application is not accepted, then the opposition can agree to the administration's proposal (that is, take the worst free square), or withdraw the current application and submit another one the next day. If there are no more days left before the meeting, the opposition has no choice but to agree to the proposal of City Hall. If application is accepted opposition can reject it. It means than opposition still can submit more applications later, <span class=\"tex-font-style-bf\">but square remains free</span>. </li></ul><p>In order to organize an event on the square <span class=\"tex-span\"><i>i</i></span>, the administration needs to spend <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> bourles. Because of the crisis the administration has only <span class=\"tex-span\"><i>b</i></span> bourles to confront the opposition. What is the best square that the opposition can take, if the administration will keep trying to occupy the square in question each time? Note that the administration's actions always depend only on the actions of the opposition.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> — the number of squares and days left before the meeting, correspondingly (<span class=\"tex-span\">1 ≤ <i>k</i> < <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span>).</p><p>The second line contains a single integer <span class=\"tex-span\"><i>b</i></span> — the number of bourles the administration has (<span class=\"tex-span\">1 ≤ <i>b</i> ≤ 10<sup class=\"upper-index\">18</sup></span>).</p><p>The third line contains <span class=\"tex-span\"><i>n</i></span> space-separated integers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> — the sum of money, needed to organise an event on square <span class=\"tex-span\"><i>i</i></span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>).</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum number of the square where the opposition can organize the demonstration.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 2<br />8<br />2 4 5 3 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 2<br />8<br />3 2 4 1 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />1000000000000000<br />5 4 3 2 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the opposition can act like this. On day one it applies for square 3. The administration has to organize an event there and end up with 3 bourles. If on the second day the opposition applies for square 2, the administration won't have the money to intervene.</p><p>In the second sample the opposition has only the chance for the last square. If its first move occupies one of the first four squares, the administration is left with at least 4 bourles, which means that next day it can use its next move to move the opposition from any square to the last one.</p><p>In the third sample administration has a lot of money, so opposition can occupy only last square.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=D]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n $problem.find(\".diff-notifier\").hide();\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:47</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n\r\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div>\r\n\r\n\n <div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='0e36e4ae41db037922b04beb941e4855'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on 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href=\"/profile/AlTimin\">AlTimin</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/AlTimin\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/AlTimin\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/AlTimin\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/AlTimin\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/AlTimin\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/AlTimin\" style=\"text-decoration:none;color:black !important;\">AlTimin's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4648\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4634\"> <p>Разбор Codeforces Round #121</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/AlTimin\" title=\"Expert AlTimin\" class=\"rated-user user-blue\">AlTimin</a>,\r\n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>,\r\n \r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/ru.png\" alt=\"In Russian\" title=\"In Russian\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Задача <a href=\"/contest/192/problem/A\" title=\"Codeforces Round 121 (Div. 2)\">192A - Funky Numbers</a></p><p>Кратко о решении: перебор</p><p>Подробно о решении: Нетрудно заметить, что это числа положительны, следовательно каждое из слагаемых меньше <span class=\"tex-span\"><i>N</i></span>. То есть всего различных возможных слагаемых порядка <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e13517ff4c4fef8f8f59a599e10028d5eebef947.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Это значит то, что мы взять и одно из слагаемых перебрать. Тогда нам нужно научиться проверять, является ли какое-то число треугольным. Заметим, что если мы заранее выпишем все слагаемые в порядке увеличения то мы сможем с помощью бинарного поиска в массиве искать наше число. Это даем там решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a921374df420d82523c37d44eb5dc0197ca8605.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Если перебирать первое слагаемое в порядке увеличения, то можно использовать два указателя, что дает нам решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4ddef016555085ab07bf6394739f007f3e4a716b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Задача <a href=\"/contest/192/problem/B\" title=\"Codeforces Round 121 (Div. 2)\">192B - Walking in the Rain</a></p><p>Кратко о решении: динамика.</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — количество дней, в течении которых плитка номер <span class=\"tex-span\"><i>i</i></span> доступна. Пересчет: <span class=\"tex-span\"><i>d</i>[<i>i</i>] = <i>min</i>(<i>a</i>[<i>i</i>], <i>max</i>(<i>d</i>[<i>i</i> - 1], <i>d</i>[<i>i</i> - 2]))</span></p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/A\" title=\"Codeforces Round 121 (Div. 1)\">191A - Dynasty Puzzles</a></p><p>Кратко о решении: динамика</p><p>Подробно о решении: динамика d[i][j], <span class=\"tex-span\"><i>i</i></span> — первый символ в имени династии, <span class=\"tex-span\"><i>j</i></span> — последний текущий символ. <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>j</i>]</span> — максимальная текущая длина. Переход: для слова с первой буквой <span class=\"tex-span\"><i>l</i></span>, последней буквой <span class=\"tex-span\"><i>r</i></span> и длиной <span class=\"tex-span\"><i>s</i></span> для всех возможных первых букв <span class=\"tex-span\"><i>i</i></span> состояние <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>r</i>]</span> может быть улучшено значением <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>l</i>] + <i>s</i></span>.</p><p>Ответом будет являться максимальное значение <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>i</i>]</span> для всех <span class=\"tex-span\"><i>i</i></span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i> * <i>alpha</i>)</span>, где <span class=\"tex-span\"><i>alpha</i></span> — это размер алфавита.</p><p>Задача <a href=\"/contest/191/problem/B\" title=\"Codeforces Round 121 (Div. 1)\">191B - Demonstration</a></p><p>Кратко о решении: конструктив</p><p>Подробно о решении: заметим, что на последнюю площадь никогда не выгодно подавать заявку (денег мэрии не потратим, ничего не изменится, мы просто потеряем ход). Переберем площадь, на которой мы хотим провести митинг. У нас есть <span class=\"tex-span\"><i>k</i> - 1</span> ход на то, чтобы потратить деньги мэрии (один ход нам нужен на подачу заявки на искомую площадь). Тратить деньги выгоднее всего на самых дорогих площадях, за исключением последней. Осталось научиться быстро выбирать <span class=\"tex-span\"><i>k</i> - 1</span> максимум из всего массива, за исключением данного элемента. Для этого сначала отсортируем массив и получим <span class=\"tex-span\"><i>k</i></span> максимумов (последнюю площадь мы не должны рассматривать). Проверяем, лежит ли наше текущее значение в <span class=\"tex-span\"><i>k</i> - 1</span> максимальных (бинпоиск и не только). Если лежит, то искомые <span class=\"tex-span\"><i>k</i> - 1</span> максимумов — это максимальные <span class=\"tex-span\"><i>k</i></span> элементов без нашего. Если не лежит, то это просто максимальные <span class=\"tex-span\"><i>k</i></span> элементов. </p><p>Теперь когда мы понимаем, сколько денег мэрии мы можем потратить, то тратим их и смотрим, остаются ли еще у мэрии деньги на проведение события на нашей текущей площади</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/36f470bf769107e6d8d30da09625de1ca4144c7b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/C\" title=\"Codeforces Round 121 (Div. 1)\">191C - Fools and Roads</a></p><p>Кратко о решении: lca</p><p>Подробно о решении: Разобьем каждый путь на два, строго идущих вверх к наименьшему общему предку. Теперь у нас есть только "вертикальные пути". Для каждой вершины насчитаем такую величину: количество вертикальных путей, начинающихся в ней минус количество вертикальных путей в ней заканчивающихся. Если мы насчитали эту величину, то ответ для ребра — это сумма значений в его поддереве. Насчитать такую величину довольно просто: берем для каждой пары дураков считаем lca этой пары. В города дураков прибавляем единичку, в lca значение уменьшаем на два.</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/64f2b782eb0a0a6592ebcf518601e6532901a6b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/D\" title=\"Codeforces Round 121 (Div. 1)\">191D - Metro Scheme</a></p><p>Кратко о решении: снова динамика</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][<i>cycle</i>]</span> — количество линий, которое требуется для того, чтобы в поддереве вершины <span class=\"tex-span\"><i>v</i></span> все покрасить, в <span class=\"tex-span\"><i>v</i></span> остаются <span class=\"tex-span\"><i>rest</i></span> незамкнутым, <span class=\"tex-span\"><i>cycle</i></span> — правда ли, что нам надо обрабатывать цикл, в котором мы находимся. </p><p>Если мы находимся не в вершине цикла, то обрабатываем всех детей, говоря что мы хотим, чтобы в них было по одному незакрытому пути. Пусть у нас есть <span class=\"tex-span\"><i>s</i></span> сыновей, нам надо взять и замкнуть все лишние линии, а недостающие нагенерить. То есть ответ это <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/0d44f4574076ece0d98f5fb9eff6a121a94744f5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, если <span class=\"tex-span\"><i>s</i> > <i>rest</i></span>, и <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/baab55368eb1a5170dfd60a1ac9d71462dcb4850.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> в противном случае.</p><p>Если мы находимся в вершине цикла, то либо мы покрываем этот цикл кольцом и это стоит нам <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/db52f6781c221ae5c2bf94aeab26cdd0afc89d60.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, где <span class=\"tex-span\"><i>u</i></span> — это вершина на цикле. отличная от <span class=\"tex-span\"><i>v</i></span>. Другой вариант — покрыть все участки кольца радиальными линиями. Утверждение: это всегда можно оптимально сделать ровно двумя радиальными. Пусть это не так. Тогда рассмотрим некоторую вершину, в которой радиальные линии <<подвешиваются>> к кольцу. От неё по кольцу в разные стороны уходят два тоннеля, принадлежащие этим линиям. Так как различных линий на кольце сейчас не менее трех, то мы можем перенаправить радиальные линии следующим образом: соединить куски вне кольца друг с другом, а кольцо замкнуть. На кольце останется не менее двух кусков, следовательно все линии останутся валидными, а их число не изменится. </p><p>Теперь надо выбрать две станции, из поддерева которых будут выходить радиальные ветки, покрывшее кольцо. Стоимость такой станции это <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0]</span>, а обычной — <span class=\"tex-span\"><i>d</i>[<i>u</i>][0][0]</span> (<span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][0]</span> в случае той вершины, которую мы сейчас обрабатываем) . Соответственно, нам надо выбрать две станции с максимальным значением <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0] - <i>d</i>[<i>u</i>][0][0]</span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/E\" title=\"Codeforces Round 121 (Div. 1)\">191E - Thwarting Demonstrations</a></p><p>Кратко о решении: бинарный поиск по ответу</p><p>Подробно о решении: Сделаем бинарный поиск по ответу. Нам надо посчитать количество отрезков, на которых сумма больше нашего некоторого значения. Как мы это будем делать: будем обрабатывать все отрезки в порядке увеличения правых концов. Отрезки с одинаковыми правыми концами будем обрабатывать пачками. Более подробно: мы будем поддерживать некоторую структуру данных в которой будут храниться суммы всех отрезков c фиксированным правым концом. </p><p>Для того, чтобы быстро пересчитывать, нам нужно всего добавить в множество некоторый элемент ( <span class=\"tex-span\">0</span>, если точнее) и добавить ко всем элементам множества некоторое значение (<span class=\"tex-span\"><i>a</i>[<i>i</i>]</span>, если быть точнее). Еще нам нужно уметь отвечать на запрос <<количество элементов, больших данного на отрезке>>. Все это умеет быстро реализовывать, например, декартово дерево. Но нам придется дополнительно хранить некоторую величину <span class=\"tex-span\"><i>X</i></span>, означающую <<надо прибавить к элементу из декартова дерева <span class=\"tex-span\"><i>X</i></span>, чтобы получить реальное значение>>. Тогда при добавлении элемента <span class=\"tex-span\"><i>a</i></span> в нашу структуру надо будет положить в декартово дерево величину <span class=\"tex-span\"><i>a</i> - <i>X</i></span>, а прибавление некоторой величины ко всему множеству реализуется простым изменением <span class=\"tex-span\"><i>X</i></span>. </p><p>То есть у нас есть структура данных, которая умеет все эти операции выполнять за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. То есть одна итерация внешнего бинпоиска работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, следовательно весь алгоритм работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-2225-4648\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"2225\",\n blogEntryId: \"4634\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+13</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/AlTimin\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/AlTimin\">\n AlTimin\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4634#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4634#comments\">\n 6\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4658\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (5)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"440048\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/lukamosiashvili\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/487409/avatar/4e37df5c1d58cc25.jpg'/> </a>\n <div><a href=\"/profile/lukamosiashvili\" title=\"Master lukamosiashvili\" class=\"rated-user user-orange\">lukamosiashvili</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/24/2018 17:04\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-440048\" href=\"?#comment-440048\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"440048\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"440048\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"487409\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-440048\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I wrote code for 191C but I got verdict: wrong answer on test 3. please, tell to me, why my code do not works correctly. link: <a href=\"https://codeforces.com/contest/191/submission/39604271\">https://codeforces.com/contest/191/submission/39604271</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-440048 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-440048 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-440048\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"639056\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SarthakBansal\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1212402/avatar/48e2e41dbb0f3d70.jpg'/> </a>\n <div><a href=\"/profile/SarthakBansal\" title=\"Expert SarthakBansal\" class=\"rated-user user-blue\">SarthakBansal</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/10/2020 11:10\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-639056\" href=\"?#comment-639056\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"639056\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1212402\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-639056\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><strong>English Editorial of 191A — Dynasty Puzzles</strong></p><p>We create dp[26][26] where dp[i][j] represents the max. length of a dynasty which starts at letter i and ends at letter j. Since in the question, the first and last letters are to be same, Our answer will be the maximum of dp[i][i] for 0<= i <=26.</p> <pre><code>for i:0...n\n Input a string. Now for this string let l=first character and r=last character.\n Thereby dp[l][r]=max(dp[l][r],s.length())\n for j:0...26 \n Now the string which starts at j and ends at r can be improved to a string which, starts at j \n then ends at l then re begins at l and finally ends at r (i.e. input string s also included \n while the starting ending letters remain same)\n i.e. dp[j][r]=max(dp[j][r],dp[j][l]+s.length())\n Also take care that this improvement is possible only if there already exists a string which \n starts at j and ends at l (i.e. dp[j][l] !=0 ).\n</code></pre><p>Finally , answer will be maximum of all dp[i][i] , where 0<=i<=26.</p><p><a href=\"https://codeforces.com/problemset/submission/191/83279171\">Code135</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-639056 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-639056 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-639056\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"759087\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Feb/08/2021 00:02\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-759087\" href=\"?#comment-759087\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"759087\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-759087\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Very well explained!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-759087 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-759087 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-759087\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1042874\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/theCPguy\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2764258/avatar/98ad595a357c6acb.jpg'/> </a>\n <div><a href=\"/profile/theCPguy\" title=\"Specialist theCPguy\" class=\"rated-user user-cyan\">theCPguy</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/04/2023 08:48\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1042874\" href=\"?#comment-1042874\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1042874\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2764258\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1042874\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Great Explanation Sir</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1042874 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1042874 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1042874\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"695887\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mooncrater\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/656776/avatar/d19b34b1e226e4ad.jpg'/> </a>\n <div><a href=\"/profile/Mooncrater\" title=\"Specialist Mooncrater\" class=\"rated-user user-cyan\">Mooncrater</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/14/2020 17:11\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-695887\" href=\"?#comment-695887\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"695887\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"656776\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-695887\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For anyone looking for a submission for the editorial for C, look at <a href=\"https://codeforces.com/contest/191/submission/1727922\">Shik's solution here.</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-695887 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-695887 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-695887\">\r\n 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Fools and Roads"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Fools and Roads</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>They say that Berland has exactly two problems, fools and roads. Besides, Berland has <span class=\"tex-span\"><i>n</i></span> cities, populated by the fools and connected by the roads. All Berland roads are bidirectional. As there are many fools in Berland, between each pair of cities there is a path (or else the fools would get upset). Also, between each pair of cities there is no more than one simple path (or else the fools would get lost). </p><p>But that is not the end of Berland's special features. In this country fools sometimes visit each other and thus spoil the roads. The fools aren't very smart, so they always use only the simple paths.</p><p><span class=\"tex-font-style-it\">A simple path</span> is the path which goes through every Berland city not more than once.</p><p>The Berland government knows the paths which the fools use. Help the government count for each road, how many distinct fools can go on it.</p><p>Note how the fools' paths are given in the input.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of cities. </p><p>Each of the next <span class=\"tex-span\"><i>n</i> - 1</span> lines contains two space-separated integers <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>), that means that there is a road connecting cities <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>The next line contains integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">0 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of pairs of fools who visit each other. </p><p>Next <span class=\"tex-span\"><i>k</i></span> lines contain two space-separated numbers. The <span class=\"tex-span\"><i>i</i></span>-th line <span class=\"tex-span\">(<i>i</i> > 0)</span> contains numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>). That means that the fool number <span class=\"tex-span\">2<i>i</i> - 1</span> lives in city <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and visits the fool number <span class=\"tex-span\">2<i>i</i></span>, who lives in city <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>. The given pairs describe simple paths, because between every pair of cities there is only one simple path.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i> - 1</span> integer. The integers should be separated by spaces. The <span class=\"tex-span\"><i>i</i></span>-th number should equal the number of fools who can go on the <span class=\"tex-span\"><i>i</i></span>-th road. The roads are numbered starting from one in the order, in which they occur in the input.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>1 2<br/>1 3<br/>2 4<br/>2 5<br/>2<br/>1 4<br/>3 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2 1 1 1 <br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>3 4<br/>4 5<br/>1 4<br/>2 4<br/>3<br/>2 3<br/>1 3<br/>3 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3 1 1 1 <br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the fool number one goes on the first and third road and the fool number 3 goes on the second, first and fourth ones.</p><p>In the second sample, the fools number 1, 3 and 5 go on the first road, the fool number 5 will go on the second road, on the third road goes the fool number 3, and on the fourth one goes fool number 1.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"592b7c5493c297899f45637fef84488b\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"cec91400c4d392a5994a9016975da662dcd210a1\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='592b7c5493c297899f45637fef84488b'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/192/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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data-uuid=\"ps_2bc685f089f20f09c33e0b1816491ec43413cbe1\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Fools and Roads</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>They say that Berland has exactly two problems, fools and roads. Besides, Berland has <span class=\"tex-span\"><i>n</i></span> cities, populated by the fools and connected by the roads. All Berland roads are bidirectional. As there are many fools in Berland, between each pair of cities there is a path (or else the fools would get upset). Also, between each pair of cities there is no more than one simple path (or else the fools would get lost). </p><p>But that is not the end of Berland's special features. In this country fools sometimes visit each other and thus spoil the roads. The fools aren't very smart, so they always use only the simple paths.</p><p><span class=\"tex-font-style-it\">A simple path</span> is the path which goes through every Berland city not more than once.</p><p>The Berland government knows the paths which the fools use. Help the government count for each road, how many distinct fools can go on it.</p><p>Note how the fools' paths are given in the input.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">2 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of cities. </p><p>Each of the next <span class=\"tex-span\"><i>n</i> - 1</span> lines contains two space-separated integers <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>), that means that there is a road connecting cities <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>The next line contains integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">0 ≤ <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the number of pairs of fools who visit each other. </p><p>Next <span class=\"tex-span\"><i>k</i></span> lines contain two space-separated numbers. The <span class=\"tex-span\"><i>i</i></span>-th line <span class=\"tex-span\">(<i>i</i> > 0)</span> contains numbers <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>). That means that the fool number <span class=\"tex-span\">2<i>i</i> - 1</span> lives in city <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> and visits the fool number <span class=\"tex-span\">2<i>i</i></span>, who lives in city <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>. The given pairs describe simple paths, because between every pair of cities there is only one simple path.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i> - 1</span> integer. The integers should be separated by spaces. The <span class=\"tex-span\"><i>i</i></span>-th number should equal the number of fools who can go on the <span class=\"tex-span\"><i>i</i></span>-th road. The roads are numbered starting from one in the order, in which they occur in the input.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />1 2<br />1 3<br />2 4<br />2 5<br />2<br />1 4<br />3 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2 1 1 1 <br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />3 4<br />4 5<br />1 4<br />2 4<br />3<br />2 3<br />1 3<br />3 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3 1 1 1 <br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the fool number one goes on the first and third road and the fool number 3 goes on the second, first and fourth ones.</p><p>In the second sample, the fools number 1, 3 and 5 go on the first road, the fool number 5 will go on the second road, on the 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:47</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n\r\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div>\r\n\r\n\n <div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='0e36e4ae41db037922b04beb941e4855'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" 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href=\"/profile/AlTimin\">AlTimin</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/AlTimin\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/AlTimin\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/AlTimin\">Submissions</a></li>\r\n <li><a\r\n href=\"/contests/with/AlTimin\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/AlTimin\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/AlTimin\" style=\"text-decoration:none;color:black !important;\">AlTimin's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4648\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4634\"> <p>Разбор Codeforces Round #121</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/AlTimin\" title=\"Expert AlTimin\" class=\"rated-user user-blue\">AlTimin</a>,\r\n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>,\r\n \r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/ru.png\" alt=\"In Russian\" title=\"In Russian\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Задача <a href=\"/contest/192/problem/A\" title=\"Codeforces Round 121 (Div. 2)\">192A - Funky Numbers</a></p><p>Кратко о решении: перебор</p><p>Подробно о решении: Нетрудно заметить, что это числа положительны, следовательно каждое из слагаемых меньше <span class=\"tex-span\"><i>N</i></span>. То есть всего различных возможных слагаемых порядка <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e13517ff4c4fef8f8f59a599e10028d5eebef947.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Это значит то, что мы взять и одно из слагаемых перебрать. Тогда нам нужно научиться проверять, является ли какое-то число треугольным. Заметим, что если мы заранее выпишем все слагаемые в порядке увеличения то мы сможем с помощью бинарного поиска в массиве искать наше число. Это даем там решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9a921374df420d82523c37d44eb5dc0197ca8605.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Если перебирать первое слагаемое в порядке увеличения, то можно использовать два указателя, что дает нам решение за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4ddef016555085ab07bf6394739f007f3e4a716b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Задача <a href=\"/contest/192/problem/B\" title=\"Codeforces Round 121 (Div. 2)\">192B - Walking in the Rain</a></p><p>Кратко о решении: динамика.</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — количество дней, в течении которых плитка номер <span class=\"tex-span\"><i>i</i></span> доступна. Пересчет: <span class=\"tex-span\"><i>d</i>[<i>i</i>] = <i>min</i>(<i>a</i>[<i>i</i>], <i>max</i>(<i>d</i>[<i>i</i> - 1], <i>d</i>[<i>i</i> - 2]))</span></p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/A\" title=\"Codeforces Round 121 (Div. 1)\">191A - Dynasty Puzzles</a></p><p>Кратко о решении: динамика</p><p>Подробно о решении: динамика d[i][j], <span class=\"tex-span\"><i>i</i></span> — первый символ в имени династии, <span class=\"tex-span\"><i>j</i></span> — последний текущий символ. <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>j</i>]</span> — максимальная текущая длина. Переход: для слова с первой буквой <span class=\"tex-span\"><i>l</i></span>, последней буквой <span class=\"tex-span\"><i>r</i></span> и длиной <span class=\"tex-span\"><i>s</i></span> для всех возможных первых букв <span class=\"tex-span\"><i>i</i></span> состояние <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>r</i>]</span> может быть улучшено значением <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>l</i>] + <i>s</i></span>.</p><p>Ответом будет являться максимальное значение <span class=\"tex-span\"><i>d</i>[<i>i</i>][<i>i</i>]</span> для всех <span class=\"tex-span\"><i>i</i></span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i> * <i>alpha</i>)</span>, где <span class=\"tex-span\"><i>alpha</i></span> — это размер алфавита.</p><p>Задача <a href=\"/contest/191/problem/B\" title=\"Codeforces Round 121 (Div. 1)\">191B - Demonstration</a></p><p>Кратко о решении: конструктив</p><p>Подробно о решении: заметим, что на последнюю площадь никогда не выгодно подавать заявку (денег мэрии не потратим, ничего не изменится, мы просто потеряем ход). Переберем площадь, на которой мы хотим провести митинг. У нас есть <span class=\"tex-span\"><i>k</i> - 1</span> ход на то, чтобы потратить деньги мэрии (один ход нам нужен на подачу заявки на искомую площадь). Тратить деньги выгоднее всего на самых дорогих площадях, за исключением последней. Осталось научиться быстро выбирать <span class=\"tex-span\"><i>k</i> - 1</span> максимум из всего массива, за исключением данного элемента. Для этого сначала отсортируем массив и получим <span class=\"tex-span\"><i>k</i></span> максимумов (последнюю площадь мы не должны рассматривать). Проверяем, лежит ли наше текущее значение в <span class=\"tex-span\"><i>k</i> - 1</span> максимальных (бинпоиск и не только). Если лежит, то искомые <span class=\"tex-span\"><i>k</i> - 1</span> максимумов — это максимальные <span class=\"tex-span\"><i>k</i></span> элементов без нашего. Если не лежит, то это просто максимальные <span class=\"tex-span\"><i>k</i></span> элементов. </p><p>Теперь когда мы понимаем, сколько денег мэрии мы можем потратить, то тратим их и смотрим, остаются ли еще у мэрии деньги на проведение события на нашей текущей площади</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/36f470bf769107e6d8d30da09625de1ca4144c7b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/C\" title=\"Codeforces Round 121 (Div. 1)\">191C - Fools and Roads</a></p><p>Кратко о решении: lca</p><p>Подробно о решении: Разобьем каждый путь на два, строго идущих вверх к наименьшему общему предку. Теперь у нас есть только "вертикальные пути". Для каждой вершины насчитаем такую величину: количество вертикальных путей, начинающихся в ней минус количество вертикальных путей в ней заканчивающихся. Если мы насчитали эту величину, то ответ для ребра — это сумма значений в его поддереве. Насчитать такую величину довольно просто: берем для каждой пары дураков считаем lca этой пары. В города дураков прибавляем единичку, в lca значение уменьшаем на два.</p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/64f2b782eb0a0a6592ebcf518601e6532901a6b7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Задача <a href=\"/contest/191/problem/D\" title=\"Codeforces Round 121 (Div. 1)\">191D - Metro Scheme</a></p><p>Кратко о решении: снова динамика</p><p>Подробно о решении: динамика <span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][<i>cycle</i>]</span> — количество линий, которое требуется для того, чтобы в поддереве вершины <span class=\"tex-span\"><i>v</i></span> все покрасить, в <span class=\"tex-span\"><i>v</i></span> остаются <span class=\"tex-span\"><i>rest</i></span> незамкнутым, <span class=\"tex-span\"><i>cycle</i></span> — правда ли, что нам надо обрабатывать цикл, в котором мы находимся. </p><p>Если мы находимся не в вершине цикла, то обрабатываем всех детей, говоря что мы хотим, чтобы в них было по одному незакрытому пути. Пусть у нас есть <span class=\"tex-span\"><i>s</i></span> сыновей, нам надо взять и замкнуть все лишние линии, а недостающие нагенерить. То есть ответ это <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/0d44f4574076ece0d98f5fb9eff6a121a94744f5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, если <span class=\"tex-span\"><i>s</i> > <i>rest</i></span>, и <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/baab55368eb1a5170dfd60a1ac9d71462dcb4850.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> в противном случае.</p><p>Если мы находимся в вершине цикла, то либо мы покрываем этот цикл кольцом и это стоит нам <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/db52f6781c221ae5c2bf94aeab26cdd0afc89d60.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, где <span class=\"tex-span\"><i>u</i></span> — это вершина на цикле. отличная от <span class=\"tex-span\"><i>v</i></span>. Другой вариант — покрыть все участки кольца радиальными линиями. Утверждение: это всегда можно оптимально сделать ровно двумя радиальными. Пусть это не так. Тогда рассмотрим некоторую вершину, в которой радиальные линии <<подвешиваются>> к кольцу. От неё по кольцу в разные стороны уходят два тоннеля, принадлежащие этим линиям. Так как различных линий на кольце сейчас не менее трех, то мы можем перенаправить радиальные линии следующим образом: соединить куски вне кольца друг с другом, а кольцо замкнуть. На кольце останется не менее двух кусков, следовательно все линии останутся валидными, а их число не изменится. </p><p>Теперь надо выбрать две станции, из поддерева которых будут выходить радиальные ветки, покрывшее кольцо. Стоимость такой станции это <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0]</span>, а обычной — <span class=\"tex-span\"><i>d</i>[<i>u</i>][0][0]</span> (<span class=\"tex-span\"><i>d</i>[<i>v</i>][<i>rest</i>][0]</span> в случае той вершины, которую мы сейчас обрабатываем) . Соответственно, нам надо выбрать две станции с максимальным значением <span class=\"tex-span\"><i>d</i>[<i>u</i>][2][0] - <i>d</i>[<i>u</i>][0][0]</span>.</p><p>Асимптотика решения: <span class=\"tex-span\"><i>O</i>(<i>N</i>)</span></p><p>Задача <a href=\"/contest/191/problem/E\" title=\"Codeforces Round 121 (Div. 1)\">191E - Thwarting Demonstrations</a></p><p>Кратко о решении: бинарный поиск по ответу</p><p>Подробно о решении: Сделаем бинарный поиск по ответу. Нам надо посчитать количество отрезков, на которых сумма больше нашего некоторого значения. Как мы это будем делать: будем обрабатывать все отрезки в порядке увеличения правых концов. Отрезки с одинаковыми правыми концами будем обрабатывать пачками. Более подробно: мы будем поддерживать некоторую структуру данных в которой будут храниться суммы всех отрезков c фиксированным правым концом. </p><p>Для того, чтобы быстро пересчитывать, нам нужно всего добавить в множество некоторый элемент ( <span class=\"tex-span\">0</span>, если точнее) и добавить ко всем элементам множества некоторое значение (<span class=\"tex-span\"><i>a</i>[<i>i</i>]</span>, если быть точнее). Еще нам нужно уметь отвечать на запрос <<количество элементов, больших данного на отрезке>>. Все это умеет быстро реализовывать, например, декартово дерево. Но нам придется дополнительно хранить некоторую величину <span class=\"tex-span\"><i>X</i></span>, означающую <<надо прибавить к элементу из декартова дерева <span class=\"tex-span\"><i>X</i></span>, чтобы получить реальное значение>>. Тогда при добавлении элемента <span class=\"tex-span\"><i>a</i></span> в нашу структуру надо будет положить в декартово дерево величину <span class=\"tex-span\"><i>a</i> - <i>X</i></span>, а прибавление некоторой величины ко всему множеству реализуется простым изменением <span class=\"tex-span\"><i>X</i></span>. </p><p>То есть у нас есть структура данных, которая умеет все эти операции выполнять за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9040a33098f83986b0de64475c66584fbfdf0e22.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. То есть одна итерация внешнего бинпоиска работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, следовательно весь алгоритм работает за <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Асимптотика решения: <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f13922b33b7e44125bf4d4e7e8555d95d3fb011b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-2225-4648\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"2225\",\n blogEntryId: \"4634\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+13</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4648\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/AlTimin\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/AlTimin\">\n AlTimin\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"May/26/2012 00:01\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4634#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4634#comments\">\n 6\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4658\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (5)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"440048\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/lukamosiashvili\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/487409/avatar/4e37df5c1d58cc25.jpg'/> </a>\n <div><a href=\"/profile/lukamosiashvili\" title=\"Master lukamosiashvili\" class=\"rated-user user-orange\">lukamosiashvili</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/24/2018 17:04\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-440048\" href=\"?#comment-440048\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"440048\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"440048\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"487409\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-440048\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I wrote code for 191C but I got verdict: wrong answer on test 3. please, tell to me, why my code do not works correctly. link: <a href=\"https://codeforces.com/contest/191/submission/39604271\">https://codeforces.com/contest/191/submission/39604271</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-440048 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-440048 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-440048\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"639056\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SarthakBansal\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1212402/avatar/48e2e41dbb0f3d70.jpg'/> </a>\n <div><a href=\"/profile/SarthakBansal\" title=\"Expert SarthakBansal\" class=\"rated-user user-blue\">SarthakBansal</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/10/2020 11:10\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-639056\" href=\"?#comment-639056\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"639056\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1212402\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-639056\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><strong>English Editorial of 191A — Dynasty Puzzles</strong></p><p>We create dp[26][26] where dp[i][j] represents the max. length of a dynasty which starts at letter i and ends at letter j. Since in the question, the first and last letters are to be same, Our answer will be the maximum of dp[i][i] for 0<= i <=26.</p> <pre><code>for i:0...n\n Input a string. Now for this string let l=first character and r=last character.\n Thereby dp[l][r]=max(dp[l][r],s.length())\n for j:0...26 \n Now the string which starts at j and ends at r can be improved to a string which, starts at j \n then ends at l then re begins at l and finally ends at r (i.e. input string s also included \n while the starting ending letters remain same)\n i.e. dp[j][r]=max(dp[j][r],dp[j][l]+s.length())\n Also take care that this improvement is possible only if there already exists a string which \n starts at j and ends at l (i.e. dp[j][l] !=0 ).\n</code></pre><p>Finally , answer will be maximum of all dp[i][i] , where 0<=i<=26.</p><p><a href=\"https://codeforces.com/problemset/submission/191/83279171\">Code135</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-639056 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-639056 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-639056\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"759087\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Feb/08/2021 00:02\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-759087\" href=\"?#comment-759087\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"759087\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-759087\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Very well explained!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-759087 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-759087 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-759087\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1042874\" commentParentId=\"639056\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/theCPguy\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2764258/avatar/98ad595a357c6acb.jpg'/> </a>\n <div><a href=\"/profile/theCPguy\" title=\"Specialist theCPguy\" class=\"rated-user user-cyan\">theCPguy</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/04/2023 08:48\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1042874\" href=\"?#comment-1042874\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-639056\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1042874\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2764258\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1042874\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Great Explanation Sir</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1042874 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1042874 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1042874\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"695887\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mooncrater\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/656776/avatar/d19b34b1e226e4ad.jpg'/> </a>\n <div><a href=\"/profile/Mooncrater\" title=\"Specialist Mooncrater\" class=\"rated-user user-cyan\">Mooncrater</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/14/2020 17:11\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-695887\" href=\"?#comment-695887\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"695887\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"656776\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-695887\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For anyone looking for a submission for the editorial for C, look at <a href=\"https://codeforces.com/contest/191/submission/1727922\">Shik's solution here.</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-695887 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-695887 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-695887\">\r\n 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Cutting Figure"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Cutting Figure</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've gotten an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> sheet of squared paper. Some of its squares are painted. Let's mark the set of all painted squares as <span class=\"tex-span\"><i>A</i></span>. Set <span class=\"tex-span\"><i>A</i></span> is connected. Your task is to find the minimum number of squares that we can delete from set <span class=\"tex-span\"><i>A</i></span> to make it not connected.</p><p>A set of painted squares is called <span class=\"tex-font-style-it\">connected</span>, if for every two squares <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> from this set there is a sequence of squares from the set, beginning in <span class=\"tex-span\"><i>a</i></span> and ending in <span class=\"tex-span\"><i>b</i></span>, such that in this sequence any square, except for the last one, shares a common side with the square that follows next in the sequence. An empty set and a set consisting of exactly one square are connected by definition.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 50</span>) — the sizes of the sheet of paper. </p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the sheet of paper: the <span class=\"tex-span\"><i>j</i></span>-th character of the <span class=\"tex-span\"><i>i</i></span>-th line equals either \"#\", if the corresponding square is painted (belongs to set <span class=\"tex-span\"><i>A</i></span>), or equals \".\" if the corresponding square is not painted (does not belong to set <span class=\"tex-span\"><i>A</i></span>). It is guaranteed that the set of all painted squares <span class=\"tex-span\"><i>A</i></span> is connected and isn't empty.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On the first line print the minimum number of squares that need to be deleted to make set <span class=\"tex-span\"><i>A</i></span> not connected. If it is impossible, print -1. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>####<br/>#..#<br/>#..#<br/>#..#<br/>####<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 5<br/>#####<br/>#...#<br/>#####<br/>#...#<br/>#####<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you can delete any two squares that do not share a side. After that the set of painted squares is not connected anymore.</p><p>The note to the second sample is shown on the figure below. To the left there is a picture of the initial set of squares. To the right there is a set with deleted squares. 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both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4673\" title=\"Editoral Codeforces Round #122\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1059:1060\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/193\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/193/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/193/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/193/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/193/hacks\">Hacks</a></li>\r\n 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value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"A\" data-uuid=\"ps_7c053858db3b3c2d55f2e73282044aa8a2bcb60e\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Cutting Figure</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've gotten an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> sheet of squared paper. Some of its squares are painted. Let's mark the set of all painted squares as <span class=\"tex-span\"><i>A</i></span>. Set <span class=\"tex-span\"><i>A</i></span> is connected. Your task is to find the minimum number of squares that we can delete from set <span class=\"tex-span\"><i>A</i></span> to make it not connected.</p><p>A set of painted squares is called <span class=\"tex-font-style-it\">connected</span>, if for every two squares <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> from this set there is a sequence of squares from the set, beginning in <span class=\"tex-span\"><i>a</i></span> and ending in <span class=\"tex-span\"><i>b</i></span>, such that in this sequence any square, except for the last one, shares a common side with the square that follows next in the sequence. An empty set and a set consisting of exactly one square are connected by definition.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 50</span>) — the sizes of the sheet of paper. </p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the sheet of paper: the <span class=\"tex-span\"><i>j</i></span>-th character of the <span class=\"tex-span\"><i>i</i></span>-th line equals either "#", if the corresponding square is painted (belongs to set <span class=\"tex-span\"><i>A</i></span>), or equals "." if the corresponding square is not painted (does not belong to set <span class=\"tex-span\"><i>A</i></span>). It is guaranteed that the set of all painted squares <span class=\"tex-span\"><i>A</i></span> is connected and isn't empty.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On the first line print the minimum number of squares that need to be deleted to make set <span class=\"tex-span\"><i>A</i></span> not connected. If it is impossible, print -1. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />####<br />#..#<br />#..#<br />#..#<br />####<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 5<br />#####<br />#...#<br />#####<br />#...#<br />#####<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you can delete any two squares that do not share a side. After that the set of painted squares is not connected anymore.</p><p>The note to the second sample is shown on the figure below. To the left there is a picture of the initial set of squares. To the right there is a set with deleted squares. 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:45</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Xor"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Xor</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>John Doe has four arrays: <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, and <span class=\"tex-span\"><i>p</i></span>. Each array consists of <span class=\"tex-span\"><i>n</i></span> integers. Elements of all arrays are indexed starting from <span class=\"tex-span\">1</span>. Array <span class=\"tex-span\"><i>p</i></span> is a permutation of integers <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p><p>John invented a game for his friends and himself. Initially a player is given array <span class=\"tex-span\"><i>a</i></span>. The player must consecutively execute exactly <span class=\"tex-span\"><i>u</i></span> operations on <span class=\"tex-span\"><i>a</i></span>. You are permitted to execute the following operations:</p><ul> <li> Operation 1: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1c9c42af2174608e65df454e248fb1a2d68be4f1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. Expression <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/b364f2e04c665b78b924ec10666327a4ef4635bc.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> means applying the operation of a bitwise xor to numbers <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The given operation exists in all modern programming languages, for example, in language <span class=\"tex-font-style-it\">C++</span> and <span class=\"tex-font-style-it\">Java</span> it is marked as \"^\", in <span class=\"tex-font-style-it\">Pascal</span> — as \"xor\". </li><li> Operation 2: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></sub> + <i>r</i></span>. When this operation is executed, all changes are made at the same time. </li></ul><p>After all <span class=\"tex-span\"><i>u</i></span> operations are applied, the number of points the player gets is determined by the formula <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/12fe8e063991fbe8d88a736a98a7c37de4febecf.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. </p><p>John wants to find out what maximum number of points a player can win in his game. Help him.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>u</i> ≤ 30</span>, <span class=\"tex-span\">0 ≤ <i>r</i> ≤ 100</span>) — the number of elements in each array, the number of operations and the number that describes one of the operations. </p><p>Each of the next four lines contains <span class=\"tex-span\"><i>n</i></span> space-separated integers — arrays <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>p</i></span>. The first line has array <span class=\"tex-span\"><i>a</i></span>, the second line has array <span class=\"tex-span\"><i>b</i></span>, the third line has array <span class=\"tex-span\"><i>k</i></span> and the fourth one has array <span class=\"tex-span\"><i>p</i></span>. </p><p>It is guaranteed that elements of arrays <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are positive and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> <span class=\"tex-span\">(1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup>)</span>, elements of array <span class=\"tex-span\"><i>k</i></span> do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> in the absolute value <span class=\"tex-span\">(|<i>k</i>| ≤ 10<sup class=\"upper-index\">4</sup>)</span> and <span class=\"tex-span\"><i>p</i></span> is a permutation of numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On a single line print number <span class=\"tex-span\"><i>s</i></span> — the maximum number of points that a player can win in John's game.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 2 1<br/>7 7 7<br/>8 8 8<br/>1 2 3<br/>1 3 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>96<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 1 0<br/>1 1<br/>1 1<br/>1 -1<br/>1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you should first apply the operation of the first type, then the operation of the second type.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"6a443961aaf9c7b1800498eb1ff03d8c\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"76c52514ef737ce086271e61546b7cc143ea286b\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='6a443961aaf9c7b1800498eb1ff03d8c'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/193/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = $(this).hasClass(\"la-angle-right\");\r\n const params = {\r\n action: \"setCollapsed\",\r\n sidebarFrameSimpleClassName: \"ContestVirtualFrame\",\r\n collapsed\r\n };\r\n $.each($target[0].attributes, function(i, a) {\r\n const name = a.name;\r\n if (name.startsWith(\"data-extra-key-\")) {\r\n const key = a.value;\r\n const keyIndex = parseInt(name.substring(\"data-extra-key-\".length));\r\n const value = $target.attr(\"data-extra-value-\" + keyIndex);\r\n params[key] = value;\r\n }\r\n });\r\n $.post(dataPageUrl, params, function (result) {\r\n if (result[\"success\"] !== \"true\") {\r\n Codeforces.showMessage(\"Failed to save collapsed state.\");\r\n }\r\n }, \"json\");\r\n return false;\r\n });\r\n })\r\n </script>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Problem tags\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\"padding: 0.5em;\">\r\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Brute force\">\r\n brute force\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *2000\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='6a443961aaf9c7b1800498eb1ff03d8c'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1405\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='6a443961aaf9c7b1800498eb1ff03d8c'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1405\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script type=\"text/javascript\">\r\n $(\".tag-box img\").click(function () {\r\n var tagName = $(this).attr(\"value\");\r\n Codeforces.confirm(\"Are you sure you want to remove this tag?\", function () {\r\n $(\"#removeTagForm input[name=tagName]\").val(tagName);\r\n $(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4671\" title=\"Codeforces Round #122\" target=\"_blank\">Codeforces Round #122</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1054:1055\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4673\" title=\"Editoral Codeforces Round #122\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1059:1060\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/193\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/193/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/193/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/193/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/193/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/193/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/193/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/193/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n }\r\n\r\n .testCaseMarker {\r\n position: absolute;\r\n font-weight: bold;\r\n font-size: 1rem;\r\n }\r\n\r\n .diff-popup {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n display: none;\r\n overflow: auto;\r\n }\r\n\r\n 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pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Xor</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>John Doe has four arrays: <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, and <span class=\"tex-span\"><i>p</i></span>. Each array consists of <span class=\"tex-span\"><i>n</i></span> integers. Elements of all arrays are indexed starting from <span class=\"tex-span\">1</span>. Array <span class=\"tex-span\"><i>p</i></span> is a permutation of integers <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p><p>John invented a game for his friends and himself. Initially a player is given array <span class=\"tex-span\"><i>a</i></span>. The player must consecutively execute exactly <span class=\"tex-span\"><i>u</i></span> operations on <span class=\"tex-span\"><i>a</i></span>. You are permitted to execute the following operations:</p><ul> <li> Operation 1: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1c9c42af2174608e65df454e248fb1a2d68be4f1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Expression <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/b364f2e04c665b78b924ec10666327a4ef4635bc.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> means applying the operation of a bitwise xor to numbers <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The given operation exists in all modern programming languages, for example, in language <span class=\"tex-font-style-it\">C++</span> and <span class=\"tex-font-style-it\">Java</span> it is marked as "^", in <span class=\"tex-font-style-it\">Pascal</span> — as "xor". </li><li> Operation 2: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></sub> + <i>r</i></span>. When this operation is executed, all changes are made at the same time. </li></ul><p>After all <span class=\"tex-span\"><i>u</i></span> operations are applied, the number of points the player gets is determined by the formula <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/12fe8e063991fbe8d88a736a98a7c37de4febecf.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p>John wants to find out what maximum number of points a player can win in his game. Help him.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>u</i> ≤ 30</span>, <span class=\"tex-span\">0 ≤ <i>r</i> ≤ 100</span>) — the number of elements in each array, the number of operations and the number that describes one of the operations. </p><p>Each of the next four lines contains <span class=\"tex-span\"><i>n</i></span> space-separated integers — arrays <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>p</i></span>. The first line has array <span class=\"tex-span\"><i>a</i></span>, the second line has array <span class=\"tex-span\"><i>b</i></span>, the third line has array <span class=\"tex-span\"><i>k</i></span> and the fourth one has array <span class=\"tex-span\"><i>p</i></span>. </p><p>It is guaranteed that elements of arrays <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are positive and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> <span class=\"tex-span\">(1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup>)</span>, elements of array <span class=\"tex-span\"><i>k</i></span> do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> in the absolute value <span class=\"tex-span\">(|<i>k</i>| ≤ 10<sup class=\"upper-index\">4</sup>)</span> and <span class=\"tex-span\"><i>p</i></span> is a permutation of numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On a single line print number <span class=\"tex-span\"><i>s</i></span> — the maximum number of points that a player can win in John's game.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 2 1<br />7 7 7<br />8 8 8<br />1 2 3<br />1 3 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>96<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 1 0<br />1 1<br />1 1<br />1 -1<br />1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you should first apply the operation of the first type, then the operation of the second type.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Hamming Distance"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Hamming Distance</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p><span class=\"tex-font-style-it\">Hamming distance</span> between strings <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> of equal length (denoted by <span class=\"tex-span\"><i>h</i>(<i>a</i>, <i>b</i>)</span>) is equal to the number of distinct integers <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ |<i>a</i>|)</span>, such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>b</i></span>. For example, the Hamming distance between strings \"<span class=\"tex-font-style-tt\">aba</span>\" and \"<span class=\"tex-font-style-tt\">bba</span>\" equals <span class=\"tex-span\">1</span>, they have different first symbols. For strings \"<span class=\"tex-font-style-tt\">bbba</span>\" and \"<span class=\"tex-font-style-tt\">aaab</span>\" the Hamming distance equals <span class=\"tex-span\">4</span>.</p><p>John Doe had a paper on which four strings of equal length <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">4</sub></span> were written. Each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> consisted only of lowercase letters \"<span class=\"tex-font-style-tt\">a</span>\" and \"<span class=\"tex-font-style-tt\">b</span>\". John found the Hamming distances between all pairs of strings he had. Then he lost the paper with the strings but he didn't lose the Hamming distances between all pairs.</p><p>Help John restore the strings; find some four strings <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">3</sub>, <i>s</i>'<sub class=\"lower-index\">4</sub></span> of equal length that consist only of lowercase letters \"<span class=\"tex-font-style-tt\">a</span>\" and \"<span class=\"tex-font-style-tt\">b</span>\", such that the pairwise Hamming distances between them are the same as between John's strings. More formally, set <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span> must satisfy the condition <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c4229770f30b6c0798b505843e2db014514a7205.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. </p><p>To make the strings easier to put down on a piece of paper, you should choose among all suitable sets of strings the one that has strings of <span class=\"tex-font-style-bf\">minimum length</span>. </p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">2</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The second line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The third line contains the single integer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">3</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>.</p><p>All given integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> are non-negative and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>. It is guaranteed that at least one number <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> is positive.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print -1 if there's no suitable set of strings.</p><p>Otherwise print on the first line number <span class=\"tex-span\"><i>len</i></span> — the length of each string. On the <span class=\"tex-span\"><i>i</i></span>-th of the next four lines print string <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span>. If there are multiple sets with the minimum length of the strings, print any of them. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 4 4<br/>4 4<br/>4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6<br/>aaaabb<br/>aabbaa<br/>bbaaaa<br/>bbbbbb<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"94953af48b7b96a98eb944fe63d2dc67\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"76c52514ef737ce086271e61546b7cc143ea286b\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Hamming Distance</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p><span class=\"tex-font-style-it\">Hamming distance</span> between strings <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> of equal length (denoted by <span class=\"tex-span\"><i>h</i>(<i>a</i>, <i>b</i>)</span>) is equal to the number of distinct integers <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ |<i>a</i>|)</span>, such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>b</i></span>. For example, the Hamming distance between strings "<span class=\"tex-font-style-tt\">aba</span>" and "<span class=\"tex-font-style-tt\">bba</span>" equals <span class=\"tex-span\">1</span>, they have different first symbols. For strings "<span class=\"tex-font-style-tt\">bbba</span>" and "<span class=\"tex-font-style-tt\">aaab</span>" the Hamming distance equals <span class=\"tex-span\">4</span>.</p><p>John Doe had a paper on which four strings of equal length <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">4</sub></span> were written. Each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> consisted only of lowercase letters "<span class=\"tex-font-style-tt\">a</span>" and "<span class=\"tex-font-style-tt\">b</span>". John found the Hamming distances between all pairs of strings he had. Then he lost the paper with the strings but he didn't lose the Hamming distances between all pairs.</p><p>Help John restore the strings; find some four strings <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">3</sub>, <i>s</i>'<sub class=\"lower-index\">4</sub></span> of equal length that consist only of lowercase letters "<span class=\"tex-font-style-tt\">a</span>" and "<span class=\"tex-font-style-tt\">b</span>", such that the pairwise Hamming distances between them are the same as between John's strings. More formally, set <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span> must satisfy the condition <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c4229770f30b6c0798b505843e2db014514a7205.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p>To make the strings easier to put down on a piece of paper, you should choose among all suitable sets of strings the one that has strings of <span class=\"tex-font-style-bf\">minimum length</span>. </p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">2</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The second line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The third line contains the single integer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">3</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>.</p><p>All given integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> are non-negative and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>. It is guaranteed that at least one number <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> is positive.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print -1 if there's no suitable set of strings.</p><p>Otherwise print on the first line number <span class=\"tex-span\"><i>len</i></span> — the length of each string. On the <span class=\"tex-span\"><i>i</i></span>-th of the next four lines print string <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span>. If there are multiple sets with the minimum length of the strings, print any of them. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 4 4<br />4 4<br />4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6<br />aaaabb<br />aabbaa<br />bbaaaa<br />bbbbbb<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Two Segments"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Two Segments</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>5 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Nick has some permutation consisting of <span class=\"tex-span\"><i>p</i></span> integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. A segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> (<span class=\"tex-span\"><i>l</i> ≤ <i>r</i></span>) is a set of elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> satisfying <span class=\"tex-span\"><i>l</i> ≤ <i>i</i> ≤ <i>r</i></span>.</p><p>Nick calls a pair of segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub>]</span> and <span class=\"tex-span\">[<i>b</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">1</sub>]</span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\">0</sub> ≤ <i>a</i><sub class=\"lower-index\">1</sub> < <i>b</i><sub class=\"lower-index\">0</sub> ≤ <i>b</i><sub class=\"lower-index\">1</sub> ≤ <i>n</i></span>) good if all their <span class=\"tex-span\">(<i>a</i><sub class=\"lower-index\">1</sub> - <i>a</i><sub class=\"lower-index\">0</sub> + <i>b</i><sub class=\"lower-index\">1</sub> - <i>b</i><sub class=\"lower-index\">0</sub> + 2)</span> elements, when sorted in ascending order, form an arithmetic progression with a difference of <span class=\"tex-span\">1</span>. That is, when they sorted in ascending order, the elements are in the form <span class=\"tex-span\">{<i>x</i>, <i>x</i> + 1, <i>x</i> + 2, ..., <i>x</i> + <i>m</i> - 1}</span>, for some <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>m</i></span>.</p><p>Your task is to find the number of distinct pairs of good segments in the given permutation. Two pairs of segments are considered distinct if the sets of elements contained in these pairs of segments are distinct. For example, any segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> <span class=\"tex-span\">(<i>l</i> < <i>r</i>)</span> can be represented as a pair of segments, as <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> and <span class=\"tex-span\">[<i>i</i> + 1, <i>r</i>]</span> (<span class=\"tex-span\"><i>l</i> ≤ <i>i</i> ≤ <i>r</i></span>). As all these pairs consist of the same set of elements, they are considered identical.</p><p>See the notes accompanying the sample tests for clarification.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3·10<sup class=\"upper-index\">5</sup></span>) — the permutation size. The second line contains <span class=\"tex-span\"><i>n</i></span> space-separated distinct integers <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>, (<span class=\"tex-span\">1 ≤ <i>p</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>).</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the number of good pairs of segments of permutation <span class=\"tex-span\"><i>p</i></span>.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>1 2 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>1 4 5 3 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>5 4 3 1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the following pairs of segments are good: (<span class=\"tex-span\">[1, 1]</span>, <span class=\"tex-span\">[2, 2]</span>); (<span class=\"tex-span\">[2, 2]</span>, <span class=\"tex-span\">[3, 3]</span>); (<span class=\"tex-span\">[1, 2]</span>, <span class=\"tex-span\">[3, 3]</span>). Pair of segments (<span class=\"tex-span\">[1, 1]</span>, <span class=\"tex-span\">[2, 3]</span>) is by definition equivalent to pair (<span class=\"tex-span\">[1, 2]</span>, <span class=\"tex-span\">[3, 3]</span>), since both of them covers the same set of elements, namely <span class=\"tex-span\">{1, 2, 3}</span>.</p><p>In the third sample the following pairs of segments are good: (<span class=\"tex-span\">[4, 4]</span>, <span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[3, 3]</span>,<span class=\"tex-span\">[4, 5]</span>); (<span class=\"tex-span\">[2, 2]</span>,<span class=\"tex-span\">[3, 5]</span>); (<span class=\"tex-span\">[1, 1]</span>,<span class=\"tex-span\">[2, 5]</span>); (<span class=\"tex-span\">[3, 3]</span>,<span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[2, 3]</span>,<span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[1, 3]</span>,<span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[2, 2]</span>,<span class=\"tex-span\">[3, 3]</span>); (<span class=\"tex-span\">[1, 1]</span>,<span class=\"tex-span\">[2, 3]</span>); (<span class=\"tex-span\">[1, 1]</span>,<span class=\"tex-span\">[2, 2]</span>). </p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"73186cc597505e9baf425bc6a91b370b\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"76c52514ef737ce086271e61546b7cc143ea286b\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='73186cc597505e9baf425bc6a91b370b'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/193/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = $(this).hasClass(\"la-angle-right\");\r\n const params = {\r\n action: \"setCollapsed\",\r\n sidebarFrameSimpleClassName: \"ContestVirtualFrame\",\r\n collapsed\r\n };\r\n $.each($target[0].attributes, function(i, a) {\r\n const name = a.name;\r\n if (name.startsWith(\"data-extra-key-\")) {\r\n const key = a.value;\r\n const keyIndex = parseInt(name.substring(\"data-extra-key-\".length));\r\n const value = $target.attr(\"data-extra-value-\" + keyIndex);\r\n params[key] = value;\r\n }\r\n });\r\n $.post(dataPageUrl, params, function (result) {\r\n if (result[\"success\"] !== \"true\") {\r\n Codeforces.showMessage(\"Failed to save collapsed state.\");\r\n }\r\n }, \"json\");\r\n return false;\r\n });\r\n })\r\n </script>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Problem tags\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\"padding: 0.5em;\">\r\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Heaps, binary search trees, segment trees, hash tables, etc\">\r\n data structures\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *2900\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='73186cc597505e9baf425bc6a91b370b'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1407\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='73186cc597505e9baf425bc6a91b370b'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1407\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script type=\"text/javascript\">\r\n $(\".tag-box img\").click(function () {\r\n var tagName = $(this).attr(\"value\");\r\n Codeforces.confirm(\"Are you sure you want to remove this tag?\", function () {\r\n $(\"#removeTagForm input[name=tagName]\").val(tagName);\r\n $(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4671\" title=\"Codeforces Round #122\" target=\"_blank\">Codeforces Round #122</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1054:1055\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4673\" title=\"Editoral Codeforces Round #122\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1059:1060\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/193\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/193/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/193/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/193/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/193/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/193/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/193/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/193/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n }\r\n\r\n .testCaseMarker {\r\n position: absolute;\r\n font-weight: bold;\r\n font-size: 1rem;\r\n }\r\n\r\n .diff-popup {\r\n width: 90vw;\r\n max-width: 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\"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"D\" data-uuid=\"ps_8f2971be7dc38490147eaeeda02ec84300c122a1\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Two Segments</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>5 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Nick has some permutation consisting of <span class=\"tex-span\"><i>p</i></span> integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>. A segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> (<span class=\"tex-span\"><i>l</i> ≤ <i>r</i></span>) is a set of elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> satisfying <span class=\"tex-span\"><i>l</i> ≤ <i>i</i> ≤ <i>r</i></span>.</p><p>Nick calls a pair of segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub>]</span> and <span class=\"tex-span\">[<i>b</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">1</sub>]</span> (<span class=\"tex-span\">1 ≤ <i>a</i><sub class=\"lower-index\">0</sub> ≤ <i>a</i><sub class=\"lower-index\">1</sub> < <i>b</i><sub class=\"lower-index\">0</sub> ≤ <i>b</i><sub class=\"lower-index\">1</sub> ≤ <i>n</i></span>) good if all their <span class=\"tex-span\">(<i>a</i><sub class=\"lower-index\">1</sub> - <i>a</i><sub class=\"lower-index\">0</sub> + <i>b</i><sub class=\"lower-index\">1</sub> - <i>b</i><sub class=\"lower-index\">0</sub> + 2)</span> elements, when sorted in ascending order, form an arithmetic progression with a difference of <span class=\"tex-span\">1</span>. That is, when they sorted in ascending order, the elements are in the form <span class=\"tex-span\">{<i>x</i>, <i>x</i> + 1, <i>x</i> + 2, ..., <i>x</i> + <i>m</i> - 1}</span>, for some <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>m</i></span>.</p><p>Your task is to find the number of distinct pairs of good segments in the given permutation. Two pairs of segments are considered distinct if the sets of elements contained in these pairs of segments are distinct. For example, any segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> <span class=\"tex-span\">(<i>l</i> < <i>r</i>)</span> can be represented as a pair of segments, as <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> and <span class=\"tex-span\">[<i>i</i> + 1, <i>r</i>]</span> (<span class=\"tex-span\"><i>l</i> ≤ <i>i</i> ≤ <i>r</i></span>). As all these pairs consist of the same set of elements, they are considered identical.</p><p>See the notes accompanying the sample tests for clarification.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 3·10<sup class=\"upper-index\">5</sup></span>) — the permutation size. The second line contains <span class=\"tex-span\"><i>n</i></span> space-separated distinct integers <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>, (<span class=\"tex-span\">1 ≤ <i>p</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>).</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single integer — the number of good pairs of segments of permutation <span class=\"tex-span\"><i>p</i></span>.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />1 2 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />1 4 5 3 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />5 4 3 1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>10<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the following pairs of segments are good: (<span class=\"tex-span\">[1, 1]</span>, <span class=\"tex-span\">[2, 2]</span>); (<span class=\"tex-span\">[2, 2]</span>, <span class=\"tex-span\">[3, 3]</span>); (<span class=\"tex-span\">[1, 2]</span>, <span class=\"tex-span\">[3, 3]</span>). Pair of segments (<span class=\"tex-span\">[1, 1]</span>, <span class=\"tex-span\">[2, 3]</span>) is by definition equivalent to pair (<span class=\"tex-span\">[1, 2]</span>, <span class=\"tex-span\">[3, 3]</span>), since both of them covers the same set of elements, namely <span class=\"tex-span\">{1, 2, 3}</span>.</p><p>In the third sample the following pairs of segments are good: (<span class=\"tex-span\">[4, 4]</span>, <span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[3, 3]</span>,<span class=\"tex-span\">[4, 5]</span>); (<span class=\"tex-span\">[2, 2]</span>,<span class=\"tex-span\">[3, 5]</span>); (<span class=\"tex-span\">[1, 1]</span>,<span class=\"tex-span\">[2, 5]</span>); (<span class=\"tex-span\">[3, 3]</span>,<span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[2, 3]</span>,<span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[1, 3]</span>,<span class=\"tex-span\">[5, 5]</span>); (<span class=\"tex-span\">[2, 2]</span>,<span class=\"tex-span\">[3, 3]</span>); (<span class=\"tex-span\">[1, 1]</span>,<span class=\"tex-span\">[2, 3]</span>); (<span class=\"tex-span\">[1, 1]</span>,<span class=\"tex-span\">[2, 2]</span>). </p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=D]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n $problem.find(\".diff-notifier\").hide();\r\n });\r\n\r\n $problem.find(\"a.view-changes\").click(function() {\r\n $.post(\"/data/diff\", {action: \"getDiff\", a: 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Fibonacci Number"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Fibonacci Number</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>3 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>John Doe has a list of all Fibonacci numbers modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>. This list is infinite, it starts with numbers <span class=\"tex-span\">0</span> and <span class=\"tex-span\">1</span>. Each number in the list, apart from the first two, is a sum of previous two modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>. That is, John's list is made from the Fibonacci numbers' list by replacing each number there by the remainder when divided by <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>. </p><p>John got interested in number <span class=\"tex-span\"><i>f</i></span> (<span class=\"tex-span\">0 ≤ <i>f</i> < 10<sup class=\"upper-index\">13</sup></span>) and now wants to find its first occurrence in the list given above. Help John and find the number of the first occurence of number <span class=\"tex-span\"><i>f</i></span> in the list or otherwise state that number <span class=\"tex-span\"><i>f</i></span> does not occur in the list. </p><p>The numeration in John's list starts from zero. There, the <span class=\"tex-span\">0</span>-th position is the number <span class=\"tex-span\">0</span>, the <span class=\"tex-span\">1</span>-st position is the number <span class=\"tex-span\">1</span>, the <span class=\"tex-span\">2</span>-nd position is the number <span class=\"tex-span\">1</span>, the <span class=\"tex-span\">3</span>-rd position is the number <span class=\"tex-span\">2</span>, the <span class=\"tex-span\">4</span>-th position is the number <span class=\"tex-span\">3</span> and so on. Thus, the beginning of the list looks like this: <span class=\"tex-span\">0, 1, 1, 2, 3, 5, 8, 13, 21, ...</span></p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains the single integer <span class=\"tex-span\"><i>f</i></span> (<span class=\"tex-span\">0 ≤ <i>f</i> < 10<sup class=\"upper-index\">13</sup></span>) — the number, which position in the list we should find.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the number of the first occurrence of the given number in John's list. If this number doesn't occur in John's list, print -1.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>13<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>7<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>377<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>14<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"ebd68b216c853ee31b79cb5e241c5dd2\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"76c52514ef737ce086271e61546b7cc143ea286b\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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}\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"E\" data-uuid=\"ps_4381db00a3214585d283e74bab0637c1e213e284\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Fibonacci Number</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>3 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>John Doe has a list of all Fibonacci numbers modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>. This list is infinite, it starts with numbers <span class=\"tex-span\">0</span> and <span class=\"tex-span\">1</span>. Each number in the list, apart from the first two, is a sum of previous two modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>. That is, John's list is made from the Fibonacci numbers' list by replacing each number there by the remainder when divided by <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>. </p><p>John got interested in number <span class=\"tex-span\"><i>f</i></span> (<span class=\"tex-span\">0 ≤ <i>f</i> < 10<sup class=\"upper-index\">13</sup></span>) and now wants to find its first occurrence in the list given above. Help John and find the number of the first occurence of number <span class=\"tex-span\"><i>f</i></span> in the list or otherwise state that number <span class=\"tex-span\"><i>f</i></span> does not occur in the list. </p><p>The numeration in John's list starts from zero. There, the <span class=\"tex-span\">0</span>-th position is the number <span class=\"tex-span\">0</span>, the <span class=\"tex-span\">1</span>-st position is the number <span class=\"tex-span\">1</span>, the <span class=\"tex-span\">2</span>-nd position is the number <span class=\"tex-span\">1</span>, the <span class=\"tex-span\">3</span>-rd position is the number <span class=\"tex-span\">2</span>, the <span class=\"tex-span\">4</span>-th position is the number <span class=\"tex-span\">3</span> and so on. Thus, the beginning of the list looks like this: <span class=\"tex-span\">0, 1, 1, 2, 3, 5, 8, 13, 21, ...</span></p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains the single integer <span class=\"tex-span\"><i>f</i></span> (<span class=\"tex-span\">0 ≤ <i>f</i> < 10<sup class=\"upper-index\">13</sup></span>) — the number, which position in the list we should find.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the number of the first occurrence of the given number in John's list. If this number doesn't occur in John's list, print -1.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>13<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>7<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>377<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>14<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=E]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:45</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final 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style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New 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title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/shivam565\" title=\"Specialist shivam565\" class=\"rated-user user-cyan\">shivam565</a> →\r\n <a href=\"/blog/entry/108348\">Total number of subarrays with sum atmost k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n </ul>\r\n </div>\r\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/recent-actions\">Detailed →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n</div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li><a\r\n href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Exams"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Exams</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>One day the Codeforces round author sat exams. He had <span class=\"tex-span\"><i>n</i></span> exams and he needed to get an integer from <span class=\"tex-span\">2</span> to <span class=\"tex-span\">5</span> for each exam. He will have to re-sit each failed exam, i.e. the exam that gets mark <span class=\"tex-span\">2</span>. </p><p>The author would need to spend too much time and effort to make the sum of his marks strictly more than <span class=\"tex-span\"><i>k</i></span>. That could have spoilt the Codeforces round. On the other hand, if the sum of his marks is strictly less than <span class=\"tex-span\"><i>k</i></span>, the author's mum won't be pleased at all. </p><p>The Codeforces authors are very smart and they always get the mark they choose themselves. Also, the Codeforces authors just hate re-sitting exams. </p><p>Help the author and find the minimum number of exams he will have to re-sit if he passes the exams in the way that makes the sum of marks for all <span class=\"tex-span\"><i>n</i></span> exams equal exactly <span class=\"tex-span\"><i>k</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single input line contains space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 50</span>, <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 250</span>) — the number of exams and the required sum of marks.</p><p>It is guaranteed that there exists a way to pass <span class=\"tex-span\"><i>n</i></span> exams in the way that makes the sum of marks equal exactly <span class=\"tex-span\"><i>k</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the single number — the minimum number of exams that the author will get a <span class=\"tex-span\">2</span> for, considering that the sum of marks for all exams must equal <span class=\"tex-span\"><i>k</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 10<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the author has to get a <span class=\"tex-span\">2</span> for all his exams.</p><p>In the second sample he should get a <span class=\"tex-span\">3</span> for two exams and a <span class=\"tex-span\">2</span> for two more.</p><p>In the third sample he should get a <span class=\"tex-span\">3</span> for one exam.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"5ac0d47a9e5ebac9da1e4c618809158e\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - A - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"61d7bde3d3882aad15cc4fba3641c9e313b8e9bf\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/194\">Codeforces Round 122 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? 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It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/194/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, simulation\">\r\n implementation\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Mathematics including integration, differential equations, etc\">\r\n math\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *900\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form 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class=\"delete-resource-link\" resourceIds=\"1058:1061\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/194\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/194/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/194/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/194/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/194/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/194/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/194/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/194/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n }\r\n\r\n .testCaseMarker {\r\n position: absolute;\r\n font-weight: bold;\r\n font-size: 1rem;\r\n }\r\n\r\n .diff-popup {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n display: none;\r\n overflow: auto;\r\n }\r\n\r\n .input-output-copier {\r\n font-size: 1.2rem;\r\n float: right;\r\n color: #888 !important;\r\n cursor: pointer;\r\n border: 1px solid rgb(185, 185, 185);\r\n padding: 3px;\r\n margin: 1px;\r\n line-height: 1.1rem;\r\n text-transform: none;\r\n }\r\n\r\n .input-output-copier:hover {\r\n background-color: #def;\r\n }\r\n\r\n .test-explanation textarea {\r\n width: 100%;\r\n height: 1.5em;\r\n }\r\n\r\n .pending-submission-message {\r\n color: darkorange !important;\r\n }\r\n </style>\r\n <script>\r\n const OPENING_SPACE = String.fromCharCode(1001);\r\n const CLOSING_SPACE = String.fromCharCode(1002);\r\n\r\n const 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result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"A\" data-uuid=\"ps_6f459396a300802cf2d5b4b88ea309ab7cc624f0\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Exams</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>One day the Codeforces round author sat exams. He had <span class=\"tex-span\"><i>n</i></span> exams and he needed to get an integer from <span class=\"tex-span\">2</span> to <span class=\"tex-span\">5</span> for each exam. He will have to re-sit each failed exam, i.e. the exam that gets mark <span class=\"tex-span\">2</span>. </p><p>The author would need to spend too much time and effort to make the sum of his marks strictly more than <span class=\"tex-span\"><i>k</i></span>. That could have spoilt the Codeforces round. On the other hand, if the sum of his marks is strictly less than <span class=\"tex-span\"><i>k</i></span>, the author's mum won't be pleased at all. </p><p>The Codeforces authors are very smart and they always get the mark they choose themselves. Also, the Codeforces authors just hate re-sitting exams. </p><p>Help the author and find the minimum number of exams he will have to re-sit if he passes the exams in the way that makes the sum of marks for all <span class=\"tex-span\"><i>n</i></span> exams equal exactly <span class=\"tex-span\"><i>k</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single input line contains space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 50</span>, <span class=\"tex-span\">1 ≤ <i>k</i> ≤ 250</span>) — the number of exams and the required sum of marks.</p><p>It is guaranteed that there exists a way to pass <span class=\"tex-span\"><i>n</i></span> exams in the way that makes the sum of marks equal exactly <span class=\"tex-span\"><i>k</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the single number — the minimum number of exams that the author will get a <span class=\"tex-span\">2</span> for, considering that the sum of marks for all exams must equal <span class=\"tex-span\"><i>k</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 10<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the author has to get a <span class=\"tex-span\">2</span> for all his exams.</p><p>In the second sample he should get a <span class=\"tex-span\">3</span> for two exams and a <span class=\"tex-span\">2</span> for two more.</p><p>In the third sample he should get a <span class=\"tex-span\">3</span> for one exam.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=A]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n $problem.find(\".diff-notifier\").hide();\r\n });\r\n\r\n $problem.find(\"a.view-changes\").click(function() {\r\n $.post(\"/data/diff\", {action: \"getDiff\", a: 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class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Square"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Square</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>There is a square painted on a piece of paper, the square's side equals <span class=\"tex-span\"><i>n</i></span> meters. John Doe draws crosses on the square's perimeter. John paints the first cross in the lower left corner of the square. Then John moves along the square's perimeter in the clockwise direction (first upwards, then to the right, then downwards, then to the left and so on). Every time he walks <span class=\"tex-span\">(<i>n</i> + 1)</span> meters, he draws a cross (see picture for clarifications).</p><p>John Doe stops only when the lower left corner of the square has two crosses. How many crosses will John draw?</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/6ae91f26bedb8332876df568deba2ff2ff3f20f8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <span class=\"tex-font-size-script\"> The figure shows the order in which John draws crosses for a square with side <span class=\"tex-span\">4</span>. The lower left square has two crosses. Overall John paints <span class=\"tex-span\">17</span> crosses. </span> </center></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>t</i></span> (<span class=\"tex-span\">1 ≤ <i>t</i> ≤ 10<sup class=\"upper-index\">4</sup></span>) — the number of test cases. </p><p>The second line contains <span class=\"tex-span\"><i>t</i></span> space-separated integers <span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>n</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the sides of the square for each test sample.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each test sample print on a single line the answer to it, that is, the number of crosses John will draw as he will move along the square of the corresponding size. Print the answers to the samples in the order in which the samples are given in the input.</p><p>Please do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>4 8 100<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17<br/>33<br/>401<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"65f1ce5f87ca5276b312c1829c766e67\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"61d7bde3d3882aad15cc4fba3641c9e313b8e9bf\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='65f1ce5f87ca5276b312c1829c766e67'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/194/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Mathematics including integration, differential equations, etc\">\r\n math\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1200\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='65f1ce5f87ca5276b312c1829c766e67'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1410\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='65f1ce5f87ca5276b312c1829c766e67'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1410\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script type=\"text/javascript\">\r\n $(\".tag-box img\").click(function () {\r\n var tagName = $(this).attr(\"value\");\r\n Codeforces.confirm(\"Are you sure you want to remove this tag?\", function () {\r\n $(\"#removeTagForm input[name=tagName]\").val(tagName);\r\n $(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4671\" title=\"Codeforces Round #122\" target=\"_blank\">Codeforces Round #122</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1056:1057\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4673\" title=\"Editoral Codeforces Round #122\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1058:1061\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/194\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/194/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/194/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/194/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/194/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/194/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/194/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/194/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n }\r\n\r\n .testCaseMarker {\r\n position: absolute;\r\n font-weight: bold;\r\n font-size: 1rem;\r\n }\r\n\r\n .diff-popup {\r\n width: 90vw;\r\n max-width: 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\"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"B\" data-uuid=\"ps_12872c56f39550e443500aaeab94e44f131920c5\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Square</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>There is a square painted on a piece of paper, the square's side equals <span class=\"tex-span\"><i>n</i></span> meters. John Doe draws crosses on the square's perimeter. John paints the first cross in the lower left corner of the square. Then John moves along the square's perimeter in the clockwise direction (first upwards, then to the right, then downwards, then to the left and so on). Every time he walks <span class=\"tex-span\">(<i>n</i> + 1)</span> meters, he draws a cross (see picture for clarifications).</p><p>John Doe stops only when the lower left corner of the square has two crosses. How many crosses will John draw?</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/6ae91f26bedb8332876df568deba2ff2ff3f20f8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-font-size-script\"> The figure shows the order in which John draws crosses for a square with side <span class=\"tex-span\">4</span>. The lower left square has two crosses. Overall John paints <span class=\"tex-span\">17</span> crosses. </span> </center></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>t</i></span> (<span class=\"tex-span\">1 ≤ <i>t</i> ≤ 10<sup class=\"upper-index\">4</sup></span>) — the number of test cases. </p><p>The second line contains <span class=\"tex-span\"><i>t</i></span> space-separated integers <span class=\"tex-span\"><i>n</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>n</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the sides of the square for each test sample.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each test sample print on a single line the answer to it, that is, the number of crosses John will draw as he will move along the square of the corresponding size. Print the answers to the samples in the order in which the samples are given in the input.</p><p>Please do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />4 8 100<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>17<br />33<br />401<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=B]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Cutting Figure"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Cutting Figure</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've gotten an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> sheet of squared paper. Some of its squares are painted. Let's mark the set of all painted squares as <span class=\"tex-span\"><i>A</i></span>. Set <span class=\"tex-span\"><i>A</i></span> is connected. Your task is to find the minimum number of squares that we can delete from set <span class=\"tex-span\"><i>A</i></span> to make it not connected.</p><p>A set of painted squares is called <span class=\"tex-font-style-it\">connected</span>, if for every two squares <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> from this set there is a sequence of squares from the set, beginning in <span class=\"tex-span\"><i>a</i></span> and ending in <span class=\"tex-span\"><i>b</i></span>, such that in this sequence any square, except for the last one, shares a common side with the square that follows next in the sequence. An empty set and a set consisting of exactly one square are connected by definition.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 50</span>) — the sizes of the sheet of paper. </p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the sheet of paper: the <span class=\"tex-span\"><i>j</i></span>-th character of the <span class=\"tex-span\"><i>i</i></span>-th line equals either \"#\", if the corresponding square is painted (belongs to set <span class=\"tex-span\"><i>A</i></span>), or equals \".\" if the corresponding square is not painted (does not belong to set <span class=\"tex-span\"><i>A</i></span>). It is guaranteed that the set of all painted squares <span class=\"tex-span\"><i>A</i></span> is connected and isn't empty.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On the first line print the minimum number of squares that need to be deleted to make set <span class=\"tex-span\"><i>A</i></span> not connected. If it is impossible, print -1. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>####<br/>#..#<br/>#..#<br/>#..#<br/>####<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 5<br/>#####<br/>#...#<br/>#####<br/>#...#<br/>#####<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you can delete any two squares that do not share a side. After that the set of painted squares is not connected anymore.</p><p>The note to the second sample is shown on the figure below. To the left there is a picture of the initial set of squares. To the right there is a set with deleted squares. The deleted squares are marked with crosses. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2389a4600c1049a63418d3e9d1d414a2c633eda8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"dc0ca1e9a5f13814ab8e854f41646fbd\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"61d7bde3d3882aad15cc4fba3641c9e313b8e9bf\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/194\">Codeforces Round 122 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? 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It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/194/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Constructive algorithms\">\r\n constructive algorithms\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Dfs and similar\">\r\n dfs and similar\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Graphs\">\r\n graphs\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, 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both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4673\" title=\"Editoral Codeforces Round #122\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1058:1061\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/194\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/194/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/194/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/194/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/194/hacks\">Hacks</a></li>\r\n 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value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"C\" data-uuid=\"ps_f4054cbc78ff5fe2825ecaaf938a0d6e1d86861e\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Cutting Figure</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've gotten an <span class=\"tex-span\"><i>n</i> × <i>m</i></span> sheet of squared paper. Some of its squares are painted. Let's mark the set of all painted squares as <span class=\"tex-span\"><i>A</i></span>. Set <span class=\"tex-span\"><i>A</i></span> is connected. Your task is to find the minimum number of squares that we can delete from set <span class=\"tex-span\"><i>A</i></span> to make it not connected.</p><p>A set of painted squares is called <span class=\"tex-font-style-it\">connected</span>, if for every two squares <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> from this set there is a sequence of squares from the set, beginning in <span class=\"tex-span\"><i>a</i></span> and ending in <span class=\"tex-span\"><i>b</i></span>, such that in this sequence any square, except for the last one, shares a common side with the square that follows next in the sequence. An empty set and a set consisting of exactly one square are connected by definition.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 50</span>) — the sizes of the sheet of paper. </p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the sheet of paper: the <span class=\"tex-span\"><i>j</i></span>-th character of the <span class=\"tex-span\"><i>i</i></span>-th line equals either "#", if the corresponding square is painted (belongs to set <span class=\"tex-span\"><i>A</i></span>), or equals "." if the corresponding square is not painted (does not belong to set <span class=\"tex-span\"><i>A</i></span>). It is guaranteed that the set of all painted squares <span class=\"tex-span\"><i>A</i></span> is connected and isn't empty.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On the first line print the minimum number of squares that need to be deleted to make set <span class=\"tex-span\"><i>A</i></span> not connected. If it is impossible, print -1. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />####<br />#..#<br />#..#<br />#..#<br />####<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 5<br />#####<br />#...#<br />#####<br />#...#<br />#####<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you can delete any two squares that do not share a side. After that the set of painted squares is not connected anymore.</p><p>The note to the second sample is shown on the figure below. To the left there is a picture of the initial set of squares. To the right there is a set with deleted squares. The deleted squares are marked with crosses. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2389a4600c1049a63418d3e9d1d414a2c633eda8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n $problem.find(\".diff-notifier\").hide();\r\n });\r\n\r\n $problem.find(\"a.view-changes\").click(function() {\r\n $.post(\"/data/diff\", 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class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Xor"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Xor</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>John Doe has four arrays: <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, and <span class=\"tex-span\"><i>p</i></span>. Each array consists of <span class=\"tex-span\"><i>n</i></span> integers. Elements of all arrays are indexed starting from <span class=\"tex-span\">1</span>. Array <span class=\"tex-span\"><i>p</i></span> is a permutation of integers <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p><p>John invented a game for his friends and himself. Initially a player is given array <span class=\"tex-span\"><i>a</i></span>. The player must consecutively execute exactly <span class=\"tex-span\"><i>u</i></span> operations on <span class=\"tex-span\"><i>a</i></span>. You are permitted to execute the following operations:</p><ul> <li> Operation 1: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1c9c42af2174608e65df454e248fb1a2d68be4f1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. Expression <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/b364f2e04c665b78b924ec10666327a4ef4635bc.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> means applying the operation of a bitwise xor to numbers <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The given operation exists in all modern programming languages, for example, in language <span class=\"tex-font-style-it\">C++</span> and <span class=\"tex-font-style-it\">Java</span> it is marked as \"^\", in <span class=\"tex-font-style-it\">Pascal</span> — as \"xor\". </li><li> Operation 2: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></sub> + <i>r</i></span>. When this operation is executed, all changes are made at the same time. </li></ul><p>After all <span class=\"tex-span\"><i>u</i></span> operations are applied, the number of points the player gets is determined by the formula <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/12fe8e063991fbe8d88a736a98a7c37de4febecf.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. </p><p>John wants to find out what maximum number of points a player can win in his game. Help him.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>u</i> ≤ 30</span>, <span class=\"tex-span\">0 ≤ <i>r</i> ≤ 100</span>) — the number of elements in each array, the number of operations and the number that describes one of the operations. </p><p>Each of the next four lines contains <span class=\"tex-span\"><i>n</i></span> space-separated integers — arrays <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>p</i></span>. The first line has array <span class=\"tex-span\"><i>a</i></span>, the second line has array <span class=\"tex-span\"><i>b</i></span>, the third line has array <span class=\"tex-span\"><i>k</i></span> and the fourth one has array <span class=\"tex-span\"><i>p</i></span>. </p><p>It is guaranteed that elements of arrays <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are positive and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> <span class=\"tex-span\">(1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup>)</span>, elements of array <span class=\"tex-span\"><i>k</i></span> do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> in the absolute value <span class=\"tex-span\">(|<i>k</i>| ≤ 10<sup class=\"upper-index\">4</sup>)</span> and <span class=\"tex-span\"><i>p</i></span> is a permutation of numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On a single line print number <span class=\"tex-span\"><i>s</i></span> — the maximum number of points that a player can win in John's game.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 2 1<br/>7 7 7<br/>8 8 8<br/>1 2 3<br/>1 3 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>96<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 1 0<br/>1 1<br/>1 1<br/>1 -1<br/>1 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you should first apply the operation of the first type, then the operation of the second type.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"2a8ff6067d15166e36463ac79b825de1\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"61d7bde3d3882aad15cc4fba3641c9e313b8e9bf\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='2a8ff6067d15166e36463ac79b825de1'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/194/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = $(this).hasClass(\"la-angle-right\");\r\n const params = {\r\n action: \"setCollapsed\",\r\n sidebarFrameSimpleClassName: \"ContestVirtualFrame\",\r\n collapsed\r\n };\r\n $.each($target[0].attributes, function(i, a) {\r\n const name = a.name;\r\n if (name.startsWith(\"data-extra-key-\")) {\r\n const key = a.value;\r\n const keyIndex = parseInt(name.substring(\"data-extra-key-\".length));\r\n const value = $target.attr(\"data-extra-value-\" + keyIndex);\r\n params[key] = value;\r\n }\r\n });\r\n $.post(dataPageUrl, params, function (result) {\r\n if (result[\"success\"] !== \"true\") {\r\n Codeforces.showMessage(\"Failed to save collapsed state.\");\r\n }\r\n }, \"json\");\r\n return false;\r\n });\r\n })\r\n </script>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Problem tags\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\"padding: 0.5em;\">\r\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *2000\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='2a8ff6067d15166e36463ac79b825de1'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1412\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='2a8ff6067d15166e36463ac79b825de1'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1412\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script type=\"text/javascript\">\r\n $(\".tag-box img\").click(function () {\r\n var tagName = $(this).attr(\"value\");\r\n Codeforces.confirm(\"Are you sure you want to remove this tag?\", function () {\r\n $(\"#removeTagForm input[name=tagName]\").val(tagName);\r\n $(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4671\" title=\"Codeforces Round #122\" target=\"_blank\">Codeforces Round #122</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1056:1057\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4673\" title=\"Editoral Codeforces Round #122\" target=\"_blank\">Tutorial</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1058:1061\" resourceName=\"Tutorial\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/194\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/194/submit\">Submit Code</a></li>\r\n <li><a\r\n 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(!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"D\" data-uuid=\"ps_40a840b70ad10f777ea2355fa0b2a207c21e70e7\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Xor</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>John Doe has four arrays: <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, and <span class=\"tex-span\"><i>p</i></span>. Each array consists of <span class=\"tex-span\"><i>n</i></span> integers. Elements of all arrays are indexed starting from <span class=\"tex-span\">1</span>. Array <span class=\"tex-span\"><i>p</i></span> is a permutation of integers <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p><p>John invented a game for his friends and himself. Initially a player is given array <span class=\"tex-span\"><i>a</i></span>. The player must consecutively execute exactly <span class=\"tex-span\"><i>u</i></span> operations on <span class=\"tex-span\"><i>a</i></span>. You are permitted to execute the following operations:</p><ul> <li> Operation 1: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1c9c42af2174608e65df454e248fb1a2d68be4f1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Expression <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/b364f2e04c665b78b924ec10666327a4ef4635bc.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> means applying the operation of a bitwise xor to numbers <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The given operation exists in all modern programming languages, for example, in language <span class=\"tex-font-style-it\">C++</span> and <span class=\"tex-font-style-it\">Java</span> it is marked as "^", in <span class=\"tex-font-style-it\">Pascal</span> — as "xor". </li><li> Operation 2: For each <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/71d27c8a997496ba958994239acaa8e1e4573b36.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> change <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> into <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></sub> + <i>r</i></span>. When this operation is executed, all changes are made at the same time. </li></ul><p>After all <span class=\"tex-span\"><i>u</i></span> operations are applied, the number of points the player gets is determined by the formula <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/12fe8e063991fbe8d88a736a98a7c37de4febecf.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p>John wants to find out what maximum number of points a player can win in his game. Help him.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>u</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>u</i> ≤ 30</span>, <span class=\"tex-span\">0 ≤ <i>r</i> ≤ 100</span>) — the number of elements in each array, the number of operations and the number that describes one of the operations. </p><p>Each of the next four lines contains <span class=\"tex-span\"><i>n</i></span> space-separated integers — arrays <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>p</i></span>. The first line has array <span class=\"tex-span\"><i>a</i></span>, the second line has array <span class=\"tex-span\"><i>b</i></span>, the third line has array <span class=\"tex-span\"><i>k</i></span> and the fourth one has array <span class=\"tex-span\"><i>p</i></span>. </p><p>It is guaranteed that elements of arrays <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are positive and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> <span class=\"tex-span\">(1 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">4</sup>)</span>, elements of array <span class=\"tex-span\"><i>k</i></span> do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">4</sup></span> in the absolute value <span class=\"tex-span\">(|<i>k</i>| ≤ 10<sup class=\"upper-index\">4</sup>)</span> and <span class=\"tex-span\"><i>p</i></span> is a permutation of numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On a single line print number <span class=\"tex-span\"><i>s</i></span> — the maximum number of points that a player can win in John's game.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 2 1<br />7 7 7<br />8 8 8<br />1 2 3<br />1 3 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>96<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 1 0<br />1 1<br />1 1<br />1 -1<br />1 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you should first apply the operation of the first type, then the operation of the second type.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Hamming Distance"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Hamming Distance</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p><span class=\"tex-font-style-it\">Hamming distance</span> between strings <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> of equal length (denoted by <span class=\"tex-span\"><i>h</i>(<i>a</i>, <i>b</i>)</span>) is equal to the number of distinct integers <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ |<i>a</i>|)</span>, such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>b</i></span>. For example, the Hamming distance between strings \"<span class=\"tex-font-style-tt\">aba</span>\" and \"<span class=\"tex-font-style-tt\">bba</span>\" equals <span class=\"tex-span\">1</span>, they have different first symbols. For strings \"<span class=\"tex-font-style-tt\">bbba</span>\" and \"<span class=\"tex-font-style-tt\">aaab</span>\" the Hamming distance equals <span class=\"tex-span\">4</span>.</p><p>John Doe had a paper on which four strings of equal length <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">4</sub></span> were written. Each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> consisted only of lowercase letters \"<span class=\"tex-font-style-tt\">a</span>\" and \"<span class=\"tex-font-style-tt\">b</span>\". John found the Hamming distances between all pairs of strings he had. Then he lost the paper with the strings but he didn't lose the Hamming distances between all pairs.</p><p>Help John restore the strings; find some four strings <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">3</sub>, <i>s</i>'<sub class=\"lower-index\">4</sub></span> of equal length that consist only of lowercase letters \"<span class=\"tex-font-style-tt\">a</span>\" and \"<span class=\"tex-font-style-tt\">b</span>\", such that the pairwise Hamming distances between them are the same as between John's strings. More formally, set <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span> must satisfy the condition <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c4229770f30b6c0798b505843e2db014514a7205.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>. </p><p>To make the strings easier to put down on a piece of paper, you should choose among all suitable sets of strings the one that has strings of <span class=\"tex-font-style-bf\">minimum length</span>. </p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">2</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The second line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The third line contains the single integer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">3</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>.</p><p>All given integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> are non-negative and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>. It is guaranteed that at least one number <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> is positive.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print -1 if there's no suitable set of strings.</p><p>Otherwise print on the first line number <span class=\"tex-span\"><i>len</i></span> — the length of each string. On the <span class=\"tex-span\"><i>i</i></span>-th of the next four lines print string <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span>. If there are multiple sets with the minimum length of the strings, print any of them. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 4 4<br/>4 4<br/>4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6<br/>aaaabb<br/>aabbaa<br/>bbaaaa<br/>bbbbbb<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"90b7736652cf92d0d0e02547bb825bd6\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"61d7bde3d3882aad15cc4fba3641c9e313b8e9bf\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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\"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"E\" data-uuid=\"ps_9d06cb56bfeb2cc0e455cbf96c251f26f35c592f\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Hamming Distance</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p><span class=\"tex-font-style-it\">Hamming distance</span> between strings <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> of equal length (denoted by <span class=\"tex-span\"><i>h</i>(<i>a</i>, <i>b</i>)</span>) is equal to the number of distinct integers <span class=\"tex-span\"><i>i</i></span> <span class=\"tex-span\">(1 ≤ <i>i</i> ≤ |<i>a</i>|)</span>, such that <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span>, where <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> is the <span class=\"tex-span\"><i>i</i></span>-th symbol of string <span class=\"tex-span\"><i>b</i></span>. For example, the Hamming distance between strings "<span class=\"tex-font-style-tt\">aba</span>" and "<span class=\"tex-font-style-tt\">bba</span>" equals <span class=\"tex-span\">1</span>, they have different first symbols. For strings "<span class=\"tex-font-style-tt\">bbba</span>" and "<span class=\"tex-font-style-tt\">aaab</span>" the Hamming distance equals <span class=\"tex-span\">4</span>.</p><p>John Doe had a paper on which four strings of equal length <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">4</sub></span> were written. Each string <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub></span> consisted only of lowercase letters "<span class=\"tex-font-style-tt\">a</span>" and "<span class=\"tex-font-style-tt\">b</span>". John found the Hamming distances between all pairs of strings he had. Then he lost the paper with the strings but he didn't lose the Hamming distances between all pairs.</p><p>Help John restore the strings; find some four strings <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">2</sub></span>, <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\">3</sub>, <i>s</i>'<sub class=\"lower-index\">4</sub></span> of equal length that consist only of lowercase letters "<span class=\"tex-font-style-tt\">a</span>" and "<span class=\"tex-font-style-tt\">b</span>", such that the pairwise Hamming distances between them are the same as between John's strings. More formally, set <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span> must satisfy the condition <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c4229770f30b6c0798b505843e2db014514a7205.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p>To make the strings easier to put down on a piece of paper, you should choose among all suitable sets of strings the one that has strings of <span class=\"tex-font-style-bf\">minimum length</span>. </p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">2</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span>, <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The second line contains space-separated integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>. The third line contains the single integer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">3</sub>, <i>s</i><sub class=\"lower-index\">4</sub>)</span>.</p><p>All given integers <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> are non-negative and do not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>. It is guaranteed that at least one number <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> is positive.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print -1 if there's no suitable set of strings.</p><p>Otherwise print on the first line number <span class=\"tex-span\"><i>len</i></span> — the length of each string. On the <span class=\"tex-span\"><i>i</i></span>-th of the next four lines print string <span class=\"tex-span\"><i>s</i>'<sub class=\"lower-index\"><i>i</i></sub></span>. If there are multiple sets with the minimum length of the strings, print any of them. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 4 4<br />4 4<br />4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6<br />aaaabb<br />aabbaa<br />bbaaaa<br />bbbbbb<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=E]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='90a98a05eea86ac7779e4a9253fb1262'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/tunyash\">tunyash</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/tunyash\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/tunyash\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/tunyash\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/tunyash\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/tunyash\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/tunyash\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/tunyash\" style=\"text-decoration:none;color:black !important;\">tunyash's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4687\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4673\"> <p>Editoral Codeforces Round #122</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a>,\r\n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p>Please, report me about every grammar mistake, you see. Thank you.</p><p><strong>Problem <></strong></p><p>Let's notice that <span class=\"tex-span\">2<i>n</i> ≤ <i>k</i> ≤ 5<i>n</i></span>. If <span class=\"tex-span\"><i>k</i> < 3<i>n</i></span> author has to get <span class=\"tex-span\">2</span> on some exams. There are <span class=\"tex-span\">3<i>n</i> - <i>k</i></span> such exams and that's the answer). If <span class=\"tex-span\">3<i>n</i> ≤ <i>k</i></span> author will pass all exams (answer is <span class=\"tex-span\">0</span>).</p><p><strong>Problem <></strong></p><p>Let the pencil move by the line and put crosses through every <span class=\"tex-span\">(<i>n</i> + 1)</span> point. Lets associate every point on the line with point on square perimeter. Namely, point <span class=\"tex-span\"><i>x</i></span> on the line will be associated with point on square perimeter that we will reach if we move pencil around square to <span class=\"tex-span\"><i>x</i></span> clockwise. Then lower left corner will be associated with all points <span class=\"tex-span\">4<i>np</i></span> for every non-negative integer <span class=\"tex-span\"><i>p</i></span>. Crosses will be associated with points <span class=\"tex-span\"><i>k</i>(<i>n</i> + 1)</span> for some non-negative <span class=\"tex-span\"><i>k</i></span>. Nearest point of overlap of two families of points will be in point LCM(<span class=\"tex-span\"><i>n</i> + 1</span>, <span class=\"tex-span\">4<i>n</i></span>). Then we will put <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ed247dc18de8de3d9e5056ef969c141f37e8d7c5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> crosses.</p><p><strong>Problem "Cutting Figure"</strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: using the fact that the answer cannot be greater than 2, check answer 1.</p><p>Let's proof that the answer is not greater than 2. Let area of the figure be greater than 3. Let's examine the leftmost of all topmost squares. There is no neighbors left or up to it. So, number of its neighbors is not more than 2. Thus, if we delete its neighbors, we shall disconnect the figure. If the area is equal to 3, we always can disconnect the figure by deletion of one square. It can be proofed by considering all two primary cases. If the area is not greater than 2, there is no way to disconnect the figure.</p><p>The algorithm: Check answer 1. We can simply brute-force the square to delete, and for each instance start dfs from any existing square. If during the dfs we visited not all of the remaining squares, we have found the square to delete. The answer is 1 if our bruteforce succeeded, and 2 otherwise.</p><p>That was necessary to consider the case when there is no answer.</p><p>The complexity of the described algorithm is <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">4</sup>)</span>. That was possible to search for articulation points and solve the problem in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>, but in my opinion that required more time and effort.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: bruteforce in complexity <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span> where <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>u</i></sub></span> if fibonacci number at position <span class=\"tex-span\"><i>u</i></span>.</p><p>This problem had complex statements. We have an array <span class=\"tex-span\"><i>a</i></span>, and we can transform it in two ways. The goal was to maximize the sum of all its elements with given multipliers after exactly <span class=\"tex-span\"><i>u</i></span> operations. </p><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup> * <i>nu</i>)</span>, what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>u</i></sup><i>n</i>)</span>. Actually, the correct solution is not too far from this algorithm.</p><p>There is just one conjecture: every two successive xor operations change nothing, and we can move them to any place of the combination. Thus, it will be enough to bruteforce only combinations in which every pair of successive xor operations is at the end.</p><p>It could be done using recoursive bruteforce. We must change in previous solution two things. First, we must n't put xor after xor. Besides that, we should update answer if number <span class=\"tex-span\"><i>u</i> - <i>l</i></span> is even, where <span class=\"tex-span\"><i>l</i></span> is current level of recoursion (all remaining operations in the end separates to pairs of xors).</p><p>Let's calculate complexity of this algo. There are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub></span> sequences of length <span class=\"tex-span\"><i>i</i></span> without two consecutive xors. It's easy to proof, you can calculate some dp to see it. That's why, complexity of our algo is <span class=\"tex-span\"><i>O</i>(<i>F</i><sub class=\"lower-index\"><i>u</i></sub><i>n</i>)</span>. </p><p><strong>Problem "Hamming distance"</strong></p><p>Main idea: reduction to system of linear equations and solving it using Gauss algorithm.</p><p>Let's notice that order of columns in answer doesn't matter. That's why there is only one important thing — quantity of every type of column. There is only <span class=\"tex-span\">2<sup class=\"upper-index\">4</sup> = 16</span> different columns. </p><p>Let's represent Hamming distance between every pair of strings as sum of quantities of types of columns. It's possible because every column adds to every distance between pairs <span class=\"tex-span\">0</span> or <span class=\"tex-span\">1</span>. </p><p>Now we have system of 6 linear equations with 16 variables. It's not good, let's decrease number of variables. First, some columns adds same values to every Hamming distance. For example strings "abbb" and "baaa". For every column <span class=\"tex-span\"><i>q</i></span> we can replace all letters "a" by letters "b" and all letters "b" by letters "a" and reach column that adds same values to every distance. We reduced number of variables to 8. We also can notice that columns "aaaa" and "bbbb" is useless and reduce number of variables to 7.</p><p>This system can be solved using Gauss algorithm. One variable steel be free. Let's fix it. It's value can't be more than maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>We can solve system of equations in integers because coefficients of equation is little.</p><p>Complexity of this solution if <span class=\"tex-span\"><i>O</i>(<i>max</i>(<i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)))</span>. If we solve it in rational numbers complexity will change to <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/8c8d27d62748b457b309b76aa23e79966ee1e196.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem "Two segments"</strong></p><p>Main idea: inverse the permutation and solve simplified problem (see below), consider function "quantity of segments of permutation that form the given segment of natural series".</p><p>In order to solve this problem, we suggest solve another: <<we have a permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>n</i></sub></span>, we have to calculate the count of segments such that their elements form one or two segments of natural series>>.</p><p>If we solve the inverse problem for some permutation <span class=\"tex-span\"><i>q</i><sub class=\"lower-index\"><i>n</i></sub></span> such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d035fefe105b0588db40032492d1b1ab7ca95d34.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, we shall get the answer for the initial problem and initial permutation <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>. </p><p>Straight-forward algo: let's bruteforce the segment of permutation and mark its elements in a boolean array. Check that in that array there is not more than two marked segments. This algo has complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">3</sup>)</span>.</p><p>Let's notice that during the changeover from <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span> to <span class=\"tex-span\">[<i>l</i>, <i>r</i> + 1]</span> the quantity of segments changes in some predictable way. Let <span class=\"tex-span\"><i>s</i>([<i>a</i>, <i>b</i>])</span> be quantity of segments that form segment <span class=\"tex-span\">[<i>a</i>, <i>b</i>]</span> of permutation. There are three cases (see picture below):</p> <ul> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> is between two marked elements (that is, both elements with values <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> - 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub> + 1</span> belong to segment <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>), then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) - 1</span>. The new element will <> the segments near it.</li> <li>If the new element <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> has only one neighbor with value belonging to <span class=\"tex-span\">[<i>l</i>, <i>r</i>]</span>, then <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>])</span>. The new element will lengthen one of existing segments.</li> <li>If there are no marked elements near <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span> the new element forms a new segment, <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> + 1]) = <i>s</i>([<i>l</i>, <i>r</i>]) + 1</span>.</li> </ul><p><img alt=\" \" src=\"/predownloaded/63/6d/636d98a90f49e3fa5e674121e4d502e05a8e3618.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>The new element is red, elements that are marked to this moment are black.</p><p>Improved algo: Let's bruteforce position of the left border and for each instance move the right border from left to right. During each move we shall recount the actual quantity of segments forming the current segment of permutation (<span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>). Now we have a solution in complexity <span class=\"tex-span\"><i>O</i>(<i>n</i><sup class=\"upper-index\">2</sup>)</span>. It works fast enough even when <span class=\"tex-span\"><i>n</i> = 20000</span>. Obviously, that is not enough to get AC.</p><p>Move on full solution. It is based on previous. Now we can calc <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span> using <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i> - 1])</span>. Now we should look at way of changing <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>r</i>])</span> as compared with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>r</i>])</span>. Let's move left border of segment from the right to left and support some data structure with <span class=\"tex-span\"><i>s</i>([<i>l</i>, <i>i</i>])</span> for every <span class=\"tex-span\"><i>i</i></span> satisfying <span class=\"tex-span\"><i>l</i> < <i>i</i> ≤ <i>n</i></span> and current <span class=\"tex-span\"><i>l</i></span>. This structure should answer queries "count numbers 1 and 2 in structure", that is count segments <span class=\"tex-span\">[<i>l</i>, <i>i</i>]</span> that generates one or two segments in the original permutaton.</p><p>Let <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> be <span class=\"tex-span\"><i>s</i>([<i>l</i> - 1, <i>i</i>]) - <i>s</i>([<i>l</i>, <i>i</i>])</span>. <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>l</i></sub></span> will be equal to <span class=\"tex-span\">1</span> because one element form one segment in permutation (notice that in final answer we must not consider 1-element segments, that's why we must subtract <span class=\"tex-span\"><i>n</i></span> from answer in the end of solution). </p><p><span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> determined by the number of neighbors of element <span class=\"tex-span\"><i>l</i> - 1</span> in the segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span>. Neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> is elements <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> + 1</span> and <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>l</i> - 1</sub> - 1</span> if they're exist.</p> <ul> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> hasn't neighbors in this segment, <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> froms new 1-element segment.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has one neighbor in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 0</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> join to existing segment of its neighbor.</li> <li>If <span class=\"tex-span\"><i>l</i> - 1</span> has two neighbors in this segment <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = - 1</span>, because <span class=\"tex-span\"><i>l</i> - 1</span> connect segments of its neighbors.</li> </ul><p>Number of neighbors in segment <span class=\"tex-span\">[<i>l</i> - 1, <i>i</i>]</span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That's why <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> non-decreasing with increasing <span class=\"tex-span\"><i>i</i></span>. That means that there are only three segments of equivalence of <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span>. We are interested only in neighbors of <span class=\"tex-span\"><i>l</i> - 1</span> which positions are right than <span class=\"tex-span\"><i>l</i> - 1</span>. Let <span class=\"tex-span\"><i>a</i></span> is position of first neighbor, <span class=\"tex-span\"><i>b</i></span> is position of second neighbor, without loss of generality <span class=\"tex-span\"><i>a</i> < <i>b</i></span>. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/196acd457c455039600c692a2f84a622ba51f16c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/962708738f03f3591ae84f208f649e8101c678c9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/91357537046f76bf751c6f556d5246a9380d982c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. (elements of permutation are numbered from 0). If <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> aren't exist, for all <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/03d019de4889cef11a72c48f2cb062b2d1bd7fc5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub> = 1</span>. If only <span class=\"tex-span\"><i>b</i></span> isn't exist for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/07a7d36022c3752127f986d73b10d82226702d20.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, for <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/7f4b3528cb4825b47ea13d31b3974a52b48e4349.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. </p><p><img alt=\" \" src=\"/predownloaded/2c/c5/2cc5622df7a3aab914c096e58d9a9cafff3c8096.jpg\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Look at example to clear your understanding. (<span class=\"tex-span\">Δ<sub class=\"lower-index\"><i>i</i></sub></span> is in top right corners, <span class=\"tex-span\"><i>l</i> = 3, <i>p</i><sub class=\"lower-index\"><i>l</i></sub> = 5</span>)</p><p>Using this facts we can code data structure support following operations:</p> <ul> <li>Add +1 or -1 on segment</li> <li>Calc number of 1 and 2 in the structure.</li> </ul><p>Sum of answers of structure in every iteration (for every <span class=\"tex-span\"><i>l</i></span>) is answer to problem.</p><p>Let's notice that all numbers in structure will be positive. That's why elements 1 and 2 will be minimal of pre-minimal in the structure. Using this fact we can code segment tree, supports these operations.</p><p>Complexity of this solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>We also can code sqrt-decomposition and obtain complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/eeb414762bec13ea211d26f02e9c7a6ee1a32fab.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><strong>Problem <></strong></p><p>Translation by <a class=\"rated-user user-violet\" href=\"/profile/fdoer\" title=\"Candidate Master fdoer\">fdoer</a></p><p>Main idea: baby-step-giant-step.</p><p>In this problem we had some Fibonacci number modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> <span class=\"tex-span\"><i>f</i></span>, and we had to determine the position of its first occurence in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p> <ul> <li>Let <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> be two different coprime modula — divisors of <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</li> <li>Let <span class=\"tex-span\"><i>F</i></span> be the actual Fibonacci number such that <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d9ce8bd6dfc05bcffe4c5adfab52889f39344e5b.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Then <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/58b7a9fcb7965b72f8014a6dd64ad3a2ccdeab98.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> and <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/267e7cf7d50f13239a730ed84115ae776abc9cb9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1caa04438fa9a47dedb0da3e3719343de6771dd5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> period.</li> <li>Find all occurences of number <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/3047ade922687e0deaa664084be4e4f9094cbb35.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> in Fibonacci sequence modulo <span class=\"tex-span\"><i>b</i></span> period.</li> <li>Let's fix a pair of such occurences. Let the occurence modulo <span class=\"tex-span\"><i>a</i></span> be in position <span class=\"tex-span\"><i>i</i></span>, and the occurence modulo <span class=\"tex-span\"><i>b</i></span> be in position <span class=\"tex-span\"><i>j</i></span>.</li> <li>Let <span class=\"tex-span\"><i>t</i>(<i>m</i>)</span> be Fibonacci sequence modulo <span class=\"tex-span\"><i>m</i></span> period.</li> <li>From the Chinese Remainder Theorem, it follows that <span class=\"tex-span\"><i>t</i>(<i>ab</i>) = <i>LCM</i>(<i>t</i>(<i>a</i>), <i>t</i>(<i>b</i>))</span> (remember that <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> are coprime).</li> <li>Then from fixed occurences of <span class=\"tex-span\"><i>f</i></span> in periods of sequences modulo <span class=\"tex-span\"><i>a</i></span> and <span class=\"tex-span\"><i>b</i></span> we can recover the position of occurence of <span class=\"tex-span\"><i>f</i></span> in period of sequence modulo <span class=\"tex-span\"><i>ab</i></span>. It could be done by solving the following Diophantine equation: <span class=\"tex-span\"><i>i</i> + <i>t</i>(<i>a</i>) * <i>x</i> = <i>j</i> + <i>t</i>(<i>b</i>) * <i>y</i></span>. We can solve it using a simple bruteforce of one of the roots.</li> <li>If the occurence in sequence modulo <span class=\"tex-span\"><i>ab</i></span> period ( we have just found it) is <span class=\"tex-span\"><i>u</i></span>, then every occurence <span class=\"tex-span\"><i>f</i></span> in Fibonacci sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period can be represented as <span class=\"tex-span\"><i>t</i>(<i>ab</i>) * <i>k</i> + <i>u</i></span>. Then let's bruteforce <span class=\"tex-span\"><i>k</i></span> and find all occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span> period. To determine Fibonacci number on position <span class=\"tex-span\">α + <i>t</i>(<i>ab</i>)</span> from known Fibonacci number on position <span class=\"tex-span\">α</span>, we need to multiply the vector (<span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">α</sub>, <i>F</i><sub class=\"lower-index\">α + 1</sub></span>) and some matrix.</li> <li>Let's choose <span class=\"tex-span\"><i>a</i> = 5<sup class=\"upper-index\">9</sup></span> and <span class=\"tex-span\"><i>b</i> = 2<sup class=\"upper-index\">13</sup></span>. Note that there is no number that occur Fibonacci sequence modulo <span class=\"tex-span\"><i>a</i></span> or <span class=\"tex-span\"><i>b</i></span> period more than <span class=\"tex-span\">8</span> times. That means that total count of pairs will never be greater than <span class=\"tex-span\">64</span>. For each occurence we'll bruteforce not more than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6df6b79db0ecaf3bc5b2b44480122999f452471.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> numbers. That was the author's solution.</li> </ul><p>Also that was possible to use the fact that for any number the count of its occurences in period of sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>p</i></sup></span> (for any natural <span class=\"tex-span\"><i>p</i></span>) is not big more efficiently. From occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i></sup></span> period we could get occurences in sequence modulo <span class=\"tex-span\">10<sup class=\"upper-index\"><i>i</i> + 1</sup></span> period using the method we use to jump from modulus <span class=\"tex-span\"><i>ab</i></span> to modulus <span class=\"tex-span\">10<sup class=\"upper-index\">13</sup></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/193\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/194\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 122 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4634-4687\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4634\",\n blogEntryId: \"4673\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editoral\" class=\"tag notice\" style=\"text-decoration: none;\">editoral</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=round122\" class=\"tag notice\" style=\"text-decoration: none;\">round122</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+116</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4687\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/tunyash\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/tunyash\">\n tunyash\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/03/2012 21:55\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4673#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4673#comments\">\n 21\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4697\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (21)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95281\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2012 01:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95281\" href=\"?#comment-95281\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95281\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95281\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I did it in O(n^2). I always do. It was a really nice problem, everyone got hacked :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95281 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95281 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95281\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95324\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:13\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95324\" href=\"?#comment-95324\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95324\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95324\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Is Problem “Hamming distance” perfectly designed?</p><p>I mean if the number of strings is not 4,such as 5,6,7 or bigger,the number of variables is much bigger than equation number.How can we solve it in this situation?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95324 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95324 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95324\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95325\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95325\" href=\"?#comment-95325\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95325\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95325\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>It's solvable, yes. We have system of linear equations and limitations (all values must be non-negative). In that case you can use simplex-mathod and Homori method. I can't tell you more because i'm not sure how it works. But it's so hard for me, and it's not beautiful in my opinion. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95325 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95325 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95325\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95326\" commentParentId=\"95324\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:18\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95326\" href=\"?#comment-95326\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95324\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95326\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95326\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think this solution still works but you have to set a new equation system, and it's going to be more than 7 variables. The rest of the algorithm should be the same.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95326 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95326 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95326\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95330\" commentParentId=\"95326\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/RealEyes\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1534/avatar/70225c828a24d271.jpg'/> </a>\n <div><a href=\"/profile/RealEyes\" title=\"Master RealEyes\" class=\"rated-user user-orange\">RealEyes</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:35\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95330\" href=\"?#comment-95330\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95326\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95330\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"1534\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95330\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>But in this solution,we need to enumerate more than one free variables.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95330 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95330 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95330\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95327\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:22\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95327\" href=\"?#comment-95327\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95327\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95327\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That was exactly my solution for xor but I got TLE...</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95327 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95327 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95327\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95328\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/sping128\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2315/avatar/18796f3cc861cd0c.jpg'/> </a>\n <div><a href=\"/profile/sping128\" title=\"Candidate Master sping128\" class=\"rated-user user-violet\">sping128</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95328\" href=\"?#comment-95328\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95328\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95328\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2315\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95328\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Maybe, you didn't really cut off the branches which have two xors in a row in the recursive tree.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95328 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95328 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95328\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95329\" commentParentId=\"95327\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:30\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95329\" href=\"?#comment-95329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95327\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95329\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your solution have right complexity, yes. But it's so slow because of using vector as parameter in recoursive function. Test 3 is not maximal test. Optimise your solution, remove vectors, long longs etc. And it will pass the tests.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95332\" commentParentId=\"95329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:43\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95332\" href=\"?#comment-95332\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-95329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"95332\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95332\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>ah thanks</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95332 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95332 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95332\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"95333\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Matjaz\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Matjaz\" title=\"Expert Matjaz\" class=\"rated-user user-blue\">Matjaz</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2012 00:58\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-95333\" href=\"?#comment-95333\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"95333\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"95333\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4171\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-95333\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><blockquote><p>A simple bruteforce of all combinations of operations with subsequent modeling leads to complexity O(2^u * nu), what is not fast enough. That was possible to optimize it by modeling parallel to recursive bruteforce. Now we have complexity O(2^u*n).</p> </blockquote><p>I don't quite get this. How do you get rid of the <em>u</em> factor?</p><p>Edit : Ah nvm. I see it now :).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-95333 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-95333 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-95333\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96850\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 10:23\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96850\" href=\"?#comment-96850\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96850\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96850\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>One variable steel be free. Let’s fix it. It’s value can’t be more than maximum of h(si, sj) because column adds positive value to one or more Hamming distance. For every fixed value we should check if all variables take non-negative integer value and choose the best answer.</p><p>what do you mean ?？?？ which variable?？?？</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96850 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96850 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96850\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96901\" commentParentId=\"96850\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 20:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96901\" href=\"?#comment-96901\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96850\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96901\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"12\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+12</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96901\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We have six linear equations with seven variables. Number of variables greater than number of equations. Because of this we have one free variable. In other words we can represent every variable except for free as <span class=\"tex-span\"><i>f</i>(<i>x</i>)</span> where x is free variable.</p><p>For example there are one free variable in this system of linear equations:</p> <ul> <li><span class=\"tex-span\"><i>x</i> + <i>y</i> = 5</span></li> <li><span class=\"tex-span\"><i>x</i> + <i>z</i> = 6</span></li> </ul><p><span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span> and <span class=\"tex-span\"><i>z</i></span> can be free because we can represent any two variables as <span class=\"tex-span\"><i>f</i>(<i>a</i>)</span> where a is free variable. Is it clear?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96901 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96901 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96901\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96920\" commentParentId=\"96901\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/yinthewind\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/29052/avatar/a12ca717beaba01.jpg'/> </a>\n <div><a href=\"/profile/yinthewind\" title=\"Expert yinthewind\" class=\"rated-user user-blue\">yinthewind</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 09:53\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96920\" href=\"?#comment-96920\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96901\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96920\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96920\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"29052\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96920\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry for my English..</p><p>I mean how did you get the last restriction ?</p><p>The number of columns is fixed ？ </p><p>Why it can’t be more than maximum of h(si, sj)?</p><p>I think your prove might be insufficient,because the column's contributions to hamming distances are not arbitrary,it have some pattern.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96920 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96920 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96920\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96924\" commentParentId=\"96920\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 11:07\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96924\" href=\"?#comment-96924\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96920\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96924\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"8\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96924\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Look, every column except <> and <> (we don't use it) add 1 to some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> because there are two different letters in every such column. For example, if we add column <> to the answer <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">0</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase by one (<span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">1</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> and <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\">2</sub>, <i>s</i><sub class=\"lower-index\">3</sub>)</span> will increase too). Therefore number of every type of columns doesn't exceed <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span> if letter <span class=\"tex-span\"><i>i</i></span> differs with letter <span class=\"tex-span\"><i>j</i></span> in this column. We obtain that number of every type of columns doesn't exceed some <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. Then number of every column doesn't exceed maximum of <span class=\"tex-span\"><i>h</i>(<i>s</i><sub class=\"lower-index\"><i>i</i></sub>, <i>s</i><sub class=\"lower-index\"><i>j</i></sub>)</span>. </p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96924 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96924 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96924\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"110392\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/pty\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/pty\" title=\"International Master pty\" class=\"rated-user user-orange\">pty</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Nov/03/2012 13:47\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-110392\" href=\"?#comment-110392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"110392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"28722\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-110392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>about div1 Problem E, how to count t(10^13)?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-110392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-110392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-110392\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767329\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 10:37\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767329\" href=\"?#comment-767329\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"767329\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"767329\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767329\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In ques A of Div 1, let us say the grid/matrix :![ ](<a href=\"https://ibb.co/FKXjL37\"><img alt=\"txx\" border=\"0\" src=\"/predownloaded/fb/15/fb157e21d6ab0f59131a162518ed521c4174bda7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></a>)</p><p>How can deleting 2 cells eventually disconnect the whole component? If corner of the grid is deleted, then also some column will certainly have a colored cell sharing a side, just beneath it. Am I doing it right?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767329 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767329 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767329\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767415\" commentParentId=\"767329\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 15:23\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767415\" href=\"?#comment-767415\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767329\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767415\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767415\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>We denote the row number from up to down as 1,2,..., and the column number from left to right as 1,2,.... If we delete (row=1,column=2)-th and (row=2,column=1)-th cells, the original graph will be disconnected, since the (row=1,column=1)-th cell has been isolated from the other part.</p><p>As a feasible solution, we could check the degree of each cell, and if some cell has degree-1, then the answer is 1 by deleting its unique neighbor; otherwise, we could find a cell with degree-2, and deleting its two neighbors gives answer 2. If can be proved that there exists at least one cell with degree-2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767415 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767415 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767415\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"767577\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Believer_Ayush\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/908276/avatar/2214e7fe79a3922a.jpg'/> </a>\n <div><a href=\"/profile/Believer_Ayush\" title=\"Expert Believer_Ayush\" class=\"rated-user user-blue\">Believer_Ayush</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/03/2021 21:05\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-767577\" href=\"?#comment-767577\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"767577\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"908276\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-767577\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Got it.Thanks!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-767577 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-767577 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-767577\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043104\" commentParentId=\"767415\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 11:17\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043104\" href=\"?#comment-1043104\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-767415\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043104\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043104\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>it will fail on TC-7</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043104 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043104 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043104\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043122\" commentParentId=\"1043104\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/SummerSky\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/419016/avatar/8ddf3c5c2dc6bf44.jpg'/> </a>\n <div><a href=\"/profile/SummerSky\" title=\"Expert SummerSky\" class=\"rated-user user-blue\">SummerSky</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 14:19\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043122\" href=\"?#comment-1043122\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043104\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043122\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"419016\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043122\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>You are right, and thank you for pointing out my mistake. Test 7 is a nice counter-example to my solution described above. I think the correct one is to run tarjan algorithm to find if there exists a cutting node. If yes, the answer is 1, and ohterwise it should be 2.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043122 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043122 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043122\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1043131\" commentParentId=\"1043122\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_Aryan_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2420415/avatar/d1fdc5cf179d4e49.jpg'/> </a>\n <div><a href=\"/profile/_Aryan_\" title=\"Expert _Aryan_\" class=\"rated-user user-blue\">_Aryan_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/05/2023 15:46\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1043131\" href=\"?#comment-1043131\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-1043122\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1043131\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2420415\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1043131\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>yes</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1043131 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1043131 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1043131\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4697\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n 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Let's Watch Football"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Let's Watch Football</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Valeric and Valerko missed the last Euro football game, so they decided to watch the game's key moments on the Net. They want to start watching as soon as possible but the connection speed is too low. If they turn on the video right now, it will \"hang up\" as the size of data to watch per second will be more than the size of downloaded data per second.</p><p>The guys want to watch the whole video without any pauses, so they have to wait some <span class=\"tex-font-style-bf\">integer</span> number of seconds for a part of the video to download. After this number of seconds passes, they can start watching. Waiting for the whole video to download isn't necessary as the video can download after the guys started to watch.</p><p>Let's suppose that video's length is <span class=\"tex-span\"><i>c</i></span> seconds and Valeric and Valerko wait <span class=\"tex-span\"><i>t</i></span> seconds before the watching. Then for any moment of time <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>t</i> ≤ <i>t</i><sub class=\"lower-index\">0</sub> ≤ <i>c</i> + <i>t</i></span>, the following condition must fulfill: the size of data received in <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> seconds is not less than the size of data needed to watch <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub> - <i>t</i></span> seconds of the video.</p><p>Of course, the guys want to wait as little as possible, so your task is to find the minimum integer number of seconds to wait before turning the video on. The guys must watch the video without pauses.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains three space-separated integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span> and <span class=\"tex-span\"><i>c</i></span> <span class=\"tex-span\">(1 ≤ <i>a</i>, <i>b</i>, <i>c</i> ≤ 1000, <i>a</i> > <i>b</i>)</span>. The first number (<span class=\"tex-span\"><i>a</i></span>) denotes the size of data needed to watch one second of the video. The second number (<span class=\"tex-span\"><i>b</i></span>) denotes the size of data Valeric and Valerko can download from the Net per second. The third number (<span class=\"tex-span\"><i>c</i></span>) denotes the video's length in seconds.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum integer number of seconds that Valeric and Valerko must wait to watch football without pauses.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>10 3 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>13 12 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample video's length is 1 second and it is necessary 4 units of data for watching 1 second of video, so guys should download 4 <span class=\"tex-span\">·</span> 1 = 4 units of data to watch the whole video. The most optimal way is to wait 3 seconds till 3 units of data will be downloaded and then start watching. While guys will be watching video 1 second, one unit of data will be downloaded and Valerik and Valerko will have 4 units of data by the end of watching. Also every moment till the end of video guys will have more data then necessary for watching.</p><p>In the second sample guys need 2 <span class=\"tex-span\">·</span> 10 = 20 units of data, so they have to wait 5 seconds and after that they will have 20 units before the second second ends. However, if guys wait 4 seconds, they will be able to watch first second of video without pauses, but they will download 18 units of data by the end of second second and it is less then necessary.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"1a23b803dc57f5e7584c340e0b5244d3\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - A - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"58a7c348d38b4b6c230b07f082e4eef04e204c50\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/195\">Codeforces Round 123 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='1a23b803dc57f5e7584c340e0b5244d3'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/195/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Binary search\">\r\n binary search\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Brute force\">\r\n brute force\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Mathematics including integration, differential equations, etc\">\r\n math\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1000\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='1a23b803dc57f5e7584c340e0b5244d3'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1419\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='1a23b803dc57f5e7584c340e0b5244d3'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1419\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script 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0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4696\" title=\"Codeforces Round #123 (Div. 2)\" target=\"_blank\">Announcement #1 <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1068\" resourceName=\"Codeforces Round #123 (Div. 2)\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"http://www.codeforces.com/blog/entry/4696\" title=\"HolkinPV\" target=\"_blank\">HolkinPV <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1070\" resourceName=\"HolkinPV\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4699\" title=\"Codeforces Round #123 (Div. 2) Разбор Задач\" target=\"_blank\">Tutorial <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1071\" resourceName=\"Codeforces Round #123 (Div. 2) Разбор Задач\"\r\nresourceManual=\"true\" 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alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Let's Watch Football</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Valeric and Valerko missed the last Euro football game, so they decided to watch the game's key moments on the Net. They want to start watching as soon as possible but the connection speed is too low. If they turn on the video right now, it will "hang up" as the size of data to watch per second will be more than the size of downloaded data per second.</p><p>The guys want to watch the whole video without any pauses, so they have to wait some <span class=\"tex-font-style-bf\">integer</span> number of seconds for a part of the video to download. After this number of seconds passes, they can start watching. Waiting for the whole video to download isn't necessary as the video can download after the guys started to watch.</p><p>Let's suppose that video's length is <span class=\"tex-span\"><i>c</i></span> seconds and Valeric and Valerko wait <span class=\"tex-span\"><i>t</i></span> seconds before the watching. Then for any moment of time <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>t</i> ≤ <i>t</i><sub class=\"lower-index\">0</sub> ≤ <i>c</i> + <i>t</i></span>, the following condition must fulfill: the size of data received in <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> seconds is not less than the size of data needed to watch <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub> - <i>t</i></span> seconds of the video.</p><p>Of course, the guys want to wait as little as possible, so your task is to find the minimum integer number of seconds to wait before turning the video on. The guys must watch the video without pauses.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains three space-separated integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span> and <span class=\"tex-span\"><i>c</i></span> <span class=\"tex-span\">(1 ≤ <i>a</i>, <i>b</i>, <i>c</i> ≤ 1000, <i>a</i> > <i>b</i>)</span>. The first number (<span class=\"tex-span\"><i>a</i></span>) denotes the size of data needed to watch one second of the video. The second number (<span class=\"tex-span\"><i>b</i></span>) denotes the size of data Valeric and Valerko can download from the Net per second. The third number (<span class=\"tex-span\"><i>c</i></span>) denotes the video's length in seconds.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum integer number of seconds that Valeric and Valerko must wait to watch football without pauses.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>10 3 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>13 12 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample video's length is 1 second and it is necessary 4 units of data for watching 1 second of video, so guys should download 4 <span class=\"tex-span\">·</span> 1 = 4 units of data to watch the whole video. The most optimal way is to wait 3 seconds till 3 units of data will be downloaded and then start watching. While guys will be watching video 1 second, one unit of data will be downloaded and Valerik and Valerko will have 4 units of data by the end of watching. Also every moment till the end of video guys will have more data then necessary for watching.</p><p>In the second sample guys need 2 <span class=\"tex-span\">·</span> 10 = 20 units of data, so they have to wait 5 seconds and after that they will have 20 units before the second second ends. However, if guys wait 4 seconds, they will be able to watch first second of video without pauses, but they will download 18 units of data by the end of second second and it is less then necessary.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=A]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n $problem.find(\".diff-notifier\").hide();\r\n });\r\n\r\n $problem.find(\"a.view-changes\").click(function() {\r\n $.post(\"/data/diff\", {action: \"getDiff\", a: 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='6255412dbf162e74a4677e79357bb071'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/HolkinPV\">HolkinPV</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/HolkinPV\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/HolkinPV\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/HolkinPV\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/HolkinPV\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/HolkinPV\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/HolkinPV\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/HolkinPV\" style=\"text-decoration:none;color:black !important;\">HolkinPV's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4713\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4699\"> <p>Codeforces Round #123 (Div. 2) Tutorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/HolkinPV\" title=\"Candidate Master HolkinPV\" class=\"rated-user user-violet\">HolkinPV</a>,\r\n <span class=\"format-humantime\" title=\"Jun/10/2012 22:36\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/195/problem/A\" title=\"Codeforces Round 123 (Div. 2)\">195A - Let's Watch Football</a></p><p>The whole video will be downloaded in <span class=\"tex-span\"><i>all</i> = (<i>c</i>·<i>a</i> + <i>b</i> - 1) / <i>b</i></span> seconds. In this problem you can choose every <span class=\"tex-span\">1 < = <i>t</i> < = <i>all</i></span> as an answer. To fulfill coditions of the problem it is enough to check the condition <span class=\"tex-span\"><i>t</i>0·<i>b</i> > = (<i>t</i>0 - <i>t</i>)·<i>a</i></span> at the moment of time t0 = all.</p><p><a href=\"/contest/195/problem/B\" title=\"Codeforces Round 123 (Div. 2)\">195B - After Training</a></p><p>In this problem you should carefully implement the given process. Firstly note that ball number <span class=\"tex-span\"><i>i</i> > <i>m</i></span> will be in the same basket as ball number <span class=\"tex-span\"><i>i</i> - <i>m</i></span>. Therefore it is enough to distribute first <span class=\"tex-span\"><i>m</i></span> balls. It can be done using two pointers <span class=\"tex-span\"><i>lf</i></span>, <span class=\"tex-span\"><i>rg</i></span> from the middle. Alternately put one ball to the left and to the right and shift pointers. In only case you should shift left pointer twice in the first moment of time if <span class=\"tex-span\"><i>m</i></span> is odd.</p><p><a href=\"/contest/195/problem/C\" title=\"Codeforces Round 123 (Div. 2)\">195C - Try and Catch</a></p><p>In this problem you was to implement what was writen in the statement. In my solution I did the following. Erase all spaces from the text except spaces in messages in try-catch blocks. Then when we get word "try" we put number of the new try-catch block in stack. When we get word "throw" we remember it's type and current state of stack (that is what try-catch blocks are opened). For example, put these number in set. When we get word "catch" if it's type equals to type of operator "throw" and the number of current try-catch block is in your set then write the answer now else erase this try-catch block from stack. If there was no suitable try-catch block write "Unhandled Exception".</p><p><a href=\"/contest/195/problem/D\" title=\"Codeforces Round 123 (Div. 2)\">195D - Analyzing Polyline</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Igor_Kudryashov\" title=\"Candidate Master Igor_Kudryashov\">Igor_Kudryashov</a></p><p>In fact in this problem we were given lines <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = <i>k</i><sub class=\"lower-index\"><i>i</i></sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> but negative values were replaced by zero. Your task was to find the number of angles that do not equal 180 degrees in the graph s(x), that is the sum of the given functions.</p><p>Firstly note that sum of two lines is also line. Indeed <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub> + <i>y</i><sub class=\"lower-index\">2</sub></span> is <span class=\"tex-span\"><i>y</i> = <i>k</i><sub class=\"lower-index\">1</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">2</sub> = (<i>k</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub>) * <i>x</i> + (<i>b</i><sub class=\"lower-index\">1</sub> + <i>b</i><sub class=\"lower-index\">2</sub>)</span>.</p><p>Consider points where <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = 0</span>, that is <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> = - <i>b</i><sub class=\"lower-index\"><i>i</i></sub> / <i>k</i><sub class=\"lower-index\"><i>i</i></sub></span>. While we assume that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't equal to 0. Then line number <span class=\"tex-span\"><i>i</i></span> is divided in two lines one of which identically equals to 0. Consider all different points <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and sort them. Then, obviously, the sum of the given functions between two consecutive points is line. Find the equation of the line. Assume that we consider point <span class=\"tex-span\"><i>i</i></span> from the left. Then equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span> will not be equal to equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> - 1</span>. That is in point <span class=\"tex-span\"><i>i</i></span> is formed an angle that doesn't equal 180 degrees.</p><p>So we should find equations of lines between every pair of points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span>. It can be easily done using two arrays with queries of increasing value on the interval offline.</p><p><a href=\"/contest/195/problem/E\" title=\"Codeforces Round 123 (Div. 2)\">195E - Building Forest</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Fefer_Ivan\" title=\"Candidate Master Fefer_Ivan\">Fefer_Ivan</a></p><p>The longest operation in this problem is to find the root of some vertex and the sum of the path to this root. To find these values fast we will use compression ways heuristics which is used in data structure "disjoint-set-union".</p><p>For every vertex v we keep two values : <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> and <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span>. <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>v</i></span>, if <span class=\"tex-span\"><i>v</i></span> — root, else <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> — next vertex on path from <span class=\"tex-span\"><i>v</i></span> to root. <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span> = sum of lengths of edges on path from <span class=\"tex-span\"><i>v</i></span> to <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span>.</p><p>To add new edge from <span class=\"tex-span\"><i>u</i></span> to <span class=\"tex-span\"><i>v</i></span> of length <span class=\"tex-span\"><i>w</i></span> it is enough to do <span class=\"tex-span\"><i>c</i>[<i>u</i>] = <i>v</i></span> and <span class=\"tex-span\"><i>sum</i>[<i>u</i>] = <i>w</i></span>.</p><p>Note that we only add new edges (we don't erase edges).</p><p>That is, if we find <span class=\"tex-span\"><i>root</i>(<i>v</i>)</span> and <span class=\"tex-span\"><i>depth</i>(<i>v</i>)</span> for some vertex <span class=\"tex-span\"><i>v</i></span> we can assign <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>root</i>(<i>v</i>)</span>, </p><p>Unable to parse markup [type=CF_TEX]</p> time. The approximate implementation is shown below. <pre><code>int root(int v){ \n if(c[v] == v){ \n return v; \n }else{ \n int u = root(c[v]); \n sum[v] = (sum[c[v]] + sum[v]) % M; \n c[v] = u; \n return u; \n } \n} \n</code></pre><p>It can proved that such implementation works using <span class=\"tex-span\"><i>O</i>(<i>log</i>(<i>n</i>))</span> time for every query. The complexity of the solution is <span class=\"tex-span\"><i>O</i>(<i>n</i> * <i>log</i>(<i>n</i>))</span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-230-4713\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"230\",\n blogEntryId: \"4699\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a 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style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+27</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4713\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/HolkinPV\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/HolkinPV\">\n HolkinPV\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication 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{document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":966,"cells":{"problem_id":{"kind":"string","value":"195B"},"contest":{"kind":"string","value":"195"},"problem":{"kind":"string","value":"B"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"B. After Training"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. After Training</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>After a team finished their training session on Euro football championship, Valeric was commissioned to gather the balls and sort them into baskets. Overall the stadium has <span class=\"tex-span\"><i>n</i></span> balls and <span class=\"tex-span\"><i>m</i></span> baskets. The baskets are positioned in a row from left to right and they are numbered with numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>, correspondingly. The balls are numbered with numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p><p>Valeric decided to sort the balls in the order of increasing of their numbers by the following scheme. He will put each new ball in the basket with the least number of balls. And if he's got several variants, he chooses the basket which stands closer to the middle. That means that he chooses the basket for which <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f9d0b92b5db1d7995ab93882f3948ffd8b213597.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> is minimum, where <span class=\"tex-span\"><i>i</i></span> is the number of the basket. If in this case Valeric still has multiple variants, he chooses the basket with the minimum number.</p><p>For every ball print the number of the basket where it will go according to Valeric's scheme.</p><p>Note that the balls are sorted into baskets in the order of increasing numbers, that is, the first ball goes first, then goes the second ball and so on.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>m</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i>, <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> — the number of balls and baskets, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> numbers, one per line. The <span class=\"tex-span\"><i>i</i></span>-th line must contain the number of the basket for the <span class=\"tex-span\"><i>i</i></span>-th ball.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>1<br/>3<br/>2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>1<br/>1<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"a85b52e176631c55a16c3fbd916115a6\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"58a7c348d38b4b6c230b07f082e4eef04e204c50\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/195\">Codeforces Round 123 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='a85b52e176631c55a16c3fbd916115a6'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/195/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Heaps, binary search trees, segment trees, hash tables, etc\">\r\n data structures\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, simulation\">\r\n implementation\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Mathematics including integration, differential equations, etc\">\r\n math\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1300\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='a85b52e176631c55a16c3fbd916115a6'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1420\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='a85b52e176631c55a16c3fbd916115a6'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" 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0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4696\" title=\"Codeforces Round #123 (Div. 2)\" target=\"_blank\">Announcement #1 <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1068\" resourceName=\"Codeforces Round #123 (Div. 2)\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"http://www.codeforces.com/blog/entry/4696\" title=\"HolkinPV\" target=\"_blank\">HolkinPV <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1070\" resourceName=\"HolkinPV\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4699\" title=\"Codeforces Round #123 (Div. 2) Разбор Задач\" target=\"_blank\">Tutorial <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1071\" resourceName=\"Codeforces Round #123 (Div. 2) Разбор Задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/195\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/195/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/195/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/195/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/195/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/195/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/195/standings\">Standings</a></li>\r\n <li><a\r\n 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result.push(CLOSING_SPACE);\r\n }\r\n\r\n return result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"B\" data-uuid=\"ps_763fcfb34776f146943faba06bae8c8b0979b21f\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. After Training</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>After a team finished their training session on Euro football championship, Valeric was commissioned to gather the balls and sort them into baskets. Overall the stadium has <span class=\"tex-span\"><i>n</i></span> balls and <span class=\"tex-span\"><i>m</i></span> baskets. The baskets are positioned in a row from left to right and they are numbered with numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>m</i></span>, correspondingly. The balls are numbered with numbers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>.</p><p>Valeric decided to sort the balls in the order of increasing of their numbers by the following scheme. He will put each new ball in the basket with the least number of balls. And if he's got several variants, he chooses the basket which stands closer to the middle. That means that he chooses the basket for which <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/f9d0b92b5db1d7995ab93882f3948ffd8b213597.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> is minimum, where <span class=\"tex-span\"><i>i</i></span> is the number of the basket. If in this case Valeric still has multiple variants, he chooses the basket with the minimum number.</p><p>For every ball print the number of the basket where it will go according to Valeric's scheme.</p><p>Note that the balls are sorted into baskets in the order of increasing numbers, that is, the first ball goes first, then goes the second ball and so on.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>m</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i>, <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> — the number of balls and baskets, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> numbers, one per line. The <span class=\"tex-span\"><i>i</i></span>-th line must contain the number of the basket for the <span class=\"tex-span\"><i>i</i></span>-th ball.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />1<br />3<br />2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />1<br />1<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=B]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='6255412dbf162e74a4677e79357bb071'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/HolkinPV\">HolkinPV</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/HolkinPV\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/HolkinPV\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/HolkinPV\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/HolkinPV\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/HolkinPV\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/HolkinPV\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/HolkinPV\" style=\"text-decoration:none;color:black !important;\">HolkinPV's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4713\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4699\"> <p>Codeforces Round #123 (Div. 2) Tutorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/HolkinPV\" title=\"Candidate Master HolkinPV\" class=\"rated-user user-violet\">HolkinPV</a>,\r\n <span class=\"format-humantime\" title=\"Jun/10/2012 22:36\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/195/problem/A\" title=\"Codeforces Round 123 (Div. 2)\">195A - Let's Watch Football</a></p><p>The whole video will be downloaded in <span class=\"tex-span\"><i>all</i> = (<i>c</i>·<i>a</i> + <i>b</i> - 1) / <i>b</i></span> seconds. In this problem you can choose every <span class=\"tex-span\">1 < = <i>t</i> < = <i>all</i></span> as an answer. To fulfill coditions of the problem it is enough to check the condition <span class=\"tex-span\"><i>t</i>0·<i>b</i> > = (<i>t</i>0 - <i>t</i>)·<i>a</i></span> at the moment of time t0 = all.</p><p><a href=\"/contest/195/problem/B\" title=\"Codeforces Round 123 (Div. 2)\">195B - After Training</a></p><p>In this problem you should carefully implement the given process. Firstly note that ball number <span class=\"tex-span\"><i>i</i> > <i>m</i></span> will be in the same basket as ball number <span class=\"tex-span\"><i>i</i> - <i>m</i></span>. Therefore it is enough to distribute first <span class=\"tex-span\"><i>m</i></span> balls. It can be done using two pointers <span class=\"tex-span\"><i>lf</i></span>, <span class=\"tex-span\"><i>rg</i></span> from the middle. Alternately put one ball to the left and to the right and shift pointers. In only case you should shift left pointer twice in the first moment of time if <span class=\"tex-span\"><i>m</i></span> is odd.</p><p><a href=\"/contest/195/problem/C\" title=\"Codeforces Round 123 (Div. 2)\">195C - Try and Catch</a></p><p>In this problem you was to implement what was writen in the statement. In my solution I did the following. Erase all spaces from the text except spaces in messages in try-catch blocks. Then when we get word "try" we put number of the new try-catch block in stack. When we get word "throw" we remember it's type and current state of stack (that is what try-catch blocks are opened). For example, put these number in set. When we get word "catch" if it's type equals to type of operator "throw" and the number of current try-catch block is in your set then write the answer now else erase this try-catch block from stack. If there was no suitable try-catch block write "Unhandled Exception".</p><p><a href=\"/contest/195/problem/D\" title=\"Codeforces Round 123 (Div. 2)\">195D - Analyzing Polyline</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Igor_Kudryashov\" title=\"Candidate Master Igor_Kudryashov\">Igor_Kudryashov</a></p><p>In fact in this problem we were given lines <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = <i>k</i><sub class=\"lower-index\"><i>i</i></sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> but negative values were replaced by zero. Your task was to find the number of angles that do not equal 180 degrees in the graph s(x), that is the sum of the given functions.</p><p>Firstly note that sum of two lines is also line. Indeed <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub> + <i>y</i><sub class=\"lower-index\">2</sub></span> is <span class=\"tex-span\"><i>y</i> = <i>k</i><sub class=\"lower-index\">1</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">2</sub> = (<i>k</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub>) * <i>x</i> + (<i>b</i><sub class=\"lower-index\">1</sub> + <i>b</i><sub class=\"lower-index\">2</sub>)</span>.</p><p>Consider points where <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = 0</span>, that is <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> = - <i>b</i><sub class=\"lower-index\"><i>i</i></sub> / <i>k</i><sub class=\"lower-index\"><i>i</i></sub></span>. While we assume that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't equal to 0. Then line number <span class=\"tex-span\"><i>i</i></span> is divided in two lines one of which identically equals to 0. Consider all different points <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and sort them. Then, obviously, the sum of the given functions between two consecutive points is line. Find the equation of the line. Assume that we consider point <span class=\"tex-span\"><i>i</i></span> from the left. Then equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span> will not be equal to equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> - 1</span>. That is in point <span class=\"tex-span\"><i>i</i></span> is formed an angle that doesn't equal 180 degrees.</p><p>So we should find equations of lines between every pair of points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span>. It can be easily done using two arrays with queries of increasing value on the interval offline.</p><p><a href=\"/contest/195/problem/E\" title=\"Codeforces Round 123 (Div. 2)\">195E - Building Forest</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Fefer_Ivan\" title=\"Candidate Master Fefer_Ivan\">Fefer_Ivan</a></p><p>The longest operation in this problem is to find the root of some vertex and the sum of the path to this root. To find these values fast we will use compression ways heuristics which is used in data structure "disjoint-set-union".</p><p>For every vertex v we keep two values : <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> and <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span>. <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>v</i></span>, if <span class=\"tex-span\"><i>v</i></span> — root, else <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> — next vertex on path from <span class=\"tex-span\"><i>v</i></span> to root. <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span> = sum of lengths of edges on path from <span class=\"tex-span\"><i>v</i></span> to <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span>.</p><p>To add new edge from <span class=\"tex-span\"><i>u</i></span> to <span class=\"tex-span\"><i>v</i></span> of length <span class=\"tex-span\"><i>w</i></span> it is enough to do <span class=\"tex-span\"><i>c</i>[<i>u</i>] = <i>v</i></span> and <span class=\"tex-span\"><i>sum</i>[<i>u</i>] = <i>w</i></span>.</p><p>Note that we only add new edges (we don't erase edges).</p><p>That is, if we find <span class=\"tex-span\"><i>root</i>(<i>v</i>)</span> and <span class=\"tex-span\"><i>depth</i>(<i>v</i>)</span> for some vertex <span class=\"tex-span\"><i>v</i></span> we can assign <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>root</i>(<i>v</i>)</span>, </p><p>Unable to parse markup [type=CF_TEX]</p> time. The approximate implementation is shown below. <pre><code>int root(int v){ \n if(c[v] == v){ \n return v; \n }else{ \n int u = root(c[v]); \n sum[v] = (sum[c[v]] + sum[v]) % M; \n c[v] = u; \n return u; \n } \n} \n</code></pre><p>It can proved that such implementation works using <span class=\"tex-span\"><i>O</i>(<i>log</i>(<i>n</i>))</span> time for every query. The complexity of the solution is <span class=\"tex-span\"><i>O</i>(<i>n</i> * <i>log</i>(<i>n</i>))</span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-230-4713\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"230\",\n blogEntryId: \"4699\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a 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style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+27</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4713\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/HolkinPV\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/HolkinPV\">\n HolkinPV\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication 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Try and Catch"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Try and Catch</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Vasya is developing his own programming language VPL (Vasya Programming Language). Right now he is busy making the system of exceptions. He thinks that the system of exceptions must function like that.</p><p>The exceptions are processed by try-catch-blocks. There are two operators that work with the blocks:</p><ol><li> The <span class=\"tex-font-style-tt\">try</span> operator. It opens a new try-catch-block. </li><li> The <span class=\"tex-font-style-tt\">catch(<exception_type>, <message>)</span> operator. It closes the try-catch-block that was started last and haven't yet been closed. This block can be activated only via exception of type <exception_type>. When we activate this block, the screen displays the <message>. If at the given moment there is no open try-catch-block, then we can't use the <span class=\"tex-font-style-tt\">catch</span> operator.</li></ol><p>The exceptions can occur in the program in only one case: when we use the <span class=\"tex-font-style-tt\">throw</span> operator. The <span class=\"tex-font-style-tt\">throw(<exception_type>)</span> operator creates the exception of the given type.</p><p>Let's suggest that as a result of using some <span class=\"tex-font-style-tt\">throw</span> operator the program created an exception of type <span class=\"tex-span\"><i>a</i></span>. In this case a try-catch-block is activated, such that this block's <span class=\"tex-font-style-tt\">try</span> operator was described in the program earlier than the used <span class=\"tex-font-style-tt\">throw</span> operator. Also, this block's <span class=\"tex-font-style-tt\">catch</span> operator was given an exception type <span class=\"tex-span\"><i>a</i></span> as a parameter and this block's <span class=\"tex-font-style-tt\">catch</span> operator is described later that the used <span class=\"tex-font-style-tt\">throw</span> operator. If there are several such try-catch-blocks, then the system activates the block whose <span class=\"tex-font-style-tt\">catch</span> operator occurs earlier than others. If no try-catch-block was activated, then the screen displays message \"<span class=\"tex-font-style-tt\">Unhandled Exception</span>\".</p><p>To test the system, Vasya wrote a program that contains only <span class=\"tex-font-style-tt\">try</span>, <span class=\"tex-font-style-tt\">catch</span> and <span class=\"tex-font-style-tt\">throw</span> operators, one line contains no more than one operator, the whole program contains exactly one <span class=\"tex-font-style-tt\">throw</span> operator.</p><p>Your task is: given a program in VPL, determine, what message will be displayed on the screen.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer: <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> the number of lines in the program. Next <span class=\"tex-span\"><i>n</i></span> lines contain the program in language VPL. Each line contains no more than one operator. It means that input file can contain empty lines and lines, consisting only of spaces.</p><p>The program contains only operators <span class=\"tex-font-style-tt\">try</span>, <span class=\"tex-font-style-tt\">catch</span> and <span class=\"tex-font-style-tt\">throw</span>. It is guaranteed that the program is correct. It means that each started try-catch-block was closed, the <span class=\"tex-font-style-tt\">catch</span> operators aren't used unless there is an open try-catch-block. The program has exactly one <span class=\"tex-font-style-tt\">throw</span> operator. The program may have spaces at the beginning of a line, at the end of a line, before and after a bracket, a comma or a quote mark.</p><p>The exception type is a nonempty string, that consists only of upper and lower case english letters. The length of the string does not exceed 20 symbols. Message is a nonempty string, that consists only of upper and lower case english letters, digits and spaces. Message is surrounded with quote marks. Quote marks shouldn't be printed. The length of the string does not exceed 20 symbols.</p><p>Length of any line in the input file does not exceed 50 symbols. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the message the screen will show after the given program is executed.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>8<br/>try<br/> try<br/> throw ( AE ) <br/> catch ( BE, \"BE in line 3\")<br/><br/> try<br/> catch(AE, \"AE in line 5\") <br/>catch(AE,\"AE somewhere\")<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>AE somewhere<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br/>try<br/> try<br/> throw ( AE ) <br/> catch ( AE, \"AE in line 3\")<br/><br/> try<br/> catch(BE, \"BE in line 5\") <br/>catch(AE,\"AE somewhere\")<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>AE in line 3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br/>try<br/> try<br/> throw ( CE ) <br/> catch ( BE, \"BE in line 3\")<br/><br/> try<br/> catch(AE, \"AE in line 5\") <br/>catch(AE,\"AE somewhere\")<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Unhandled Exception<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample there are 2 try-catch-blocks such that <span class=\"tex-font-style-tt\">try</span> operator is described earlier than <span class=\"tex-font-style-tt\">throw</span> operator and <span class=\"tex-font-style-tt\">catch</span> operator is described later than <span class=\"tex-font-style-tt\">throw</span> operator: <span class=\"tex-font-style-tt\">try-catch(BE,\"BE in line 3\")</span> and <span class=\"tex-font-style-tt\">try-catch(AE,\"AE somewhere\")</span>. Exception type is AE, so the second block will be activated, because operator <span class=\"tex-font-style-tt\">catch(AE,\"AE somewhere\")</span> has exception type AE as parameter and operator <span class=\"tex-font-style-tt\">catch(BE,\"BE in line 3\")</span> has exception type BE.</p><p>In the second sample there are 2 try-catch-blocks such that <span class=\"tex-font-style-tt\">try</span> operator is described earlier than <span class=\"tex-font-style-tt\">throw</span> operator and <span class=\"tex-font-style-tt\">catch</span> operator is described later than <span class=\"tex-font-style-tt\">throw</span> operator: <span class=\"tex-font-style-tt\">try-catch(AE,\"AE in line 3\")</span> and <span class=\"tex-font-style-tt\">try-catch(AE,\"AE somewhere\")</span>. Exception type is AE, so both blocks can be activated, but only the first one will be activated, because operator <span class=\"tex-font-style-tt\">catch(AE,\"AE in line 3\")</span> is described earlier than <span class=\"tex-font-style-tt\">catch(AE,\"AE somewhere\")</span></p><p>In the third sample there is no blocks that can be activated by an exception of type CE.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"2178acc0ed1e18d37d835950134c9cf7\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"58a7c348d38b4b6c230b07f082e4eef04e204c50\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/195\">Codeforces Round 123 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? 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It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/195/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Parsing expression grammar\">\r\n expression parsing\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, simulation\">\r\n implementation\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1800\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" 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\"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4696\" title=\"Codeforces Round #123 (Div. 2)\" target=\"_blank\">Announcement #1 <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1068\" resourceName=\"Codeforces Round #123 (Div. 2)\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"http://www.codeforces.com/blog/entry/4696\" title=\"HolkinPV\" target=\"_blank\">HolkinPV <span 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text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"C\" data-uuid=\"ps_dec9a6062acdc9d8d4925cfe852133f3a0ed675a\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Try and Catch</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Vasya is developing his own programming language VPL (Vasya Programming Language). Right now he is busy making the system of exceptions. He thinks that the system of exceptions must function like that.</p><p>The exceptions are processed by try-catch-blocks. There are two operators that work with the blocks:</p><ol><li> The <span class=\"tex-font-style-tt\">try</span> operator. It opens a new try-catch-block. </li><li> The <span class=\"tex-font-style-tt\">catch(<exception_type>, <message>)</span> operator. It closes the try-catch-block that was started last and haven't yet been closed. This block can be activated only via exception of type <exception_type>. When we activate this block, the screen displays the <message>. If at the given moment there is no open try-catch-block, then we can't use the <span class=\"tex-font-style-tt\">catch</span> operator.</li></ol><p>The exceptions can occur in the program in only one case: when we use the <span class=\"tex-font-style-tt\">throw</span> operator. The <span class=\"tex-font-style-tt\">throw(<exception_type>)</span> operator creates the exception of the given type.</p><p>Let's suggest that as a result of using some <span class=\"tex-font-style-tt\">throw</span> operator the program created an exception of type <span class=\"tex-span\"><i>a</i></span>. In this case a try-catch-block is activated, such that this block's <span class=\"tex-font-style-tt\">try</span> operator was described in the program earlier than the used <span class=\"tex-font-style-tt\">throw</span> operator. Also, this block's <span class=\"tex-font-style-tt\">catch</span> operator was given an exception type <span class=\"tex-span\"><i>a</i></span> as a parameter and this block's <span class=\"tex-font-style-tt\">catch</span> operator is described later that the used <span class=\"tex-font-style-tt\">throw</span> operator. If there are several such try-catch-blocks, then the system activates the block whose <span class=\"tex-font-style-tt\">catch</span> operator occurs earlier than others. If no try-catch-block was activated, then the screen displays message "<span class=\"tex-font-style-tt\">Unhandled Exception</span>".</p><p>To test the system, Vasya wrote a program that contains only <span class=\"tex-font-style-tt\">try</span>, <span class=\"tex-font-style-tt\">catch</span> and <span class=\"tex-font-style-tt\">throw</span> operators, one line contains no more than one operator, the whole program contains exactly one <span class=\"tex-font-style-tt\">throw</span> operator.</p><p>Your task is: given a program in VPL, determine, what message will be displayed on the screen.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer: <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> the number of lines in the program. Next <span class=\"tex-span\"><i>n</i></span> lines contain the program in language VPL. Each line contains no more than one operator. It means that input file can contain empty lines and lines, consisting only of spaces.</p><p>The program contains only operators <span class=\"tex-font-style-tt\">try</span>, <span class=\"tex-font-style-tt\">catch</span> and <span class=\"tex-font-style-tt\">throw</span>. It is guaranteed that the program is correct. It means that each started try-catch-block was closed, the <span class=\"tex-font-style-tt\">catch</span> operators aren't used unless there is an open try-catch-block. The program has exactly one <span class=\"tex-font-style-tt\">throw</span> operator. The program may have spaces at the beginning of a line, at the end of a line, before and after a bracket, a comma or a quote mark.</p><p>The exception type is a nonempty string, that consists only of upper and lower case english letters. The length of the string does not exceed 20 symbols. Message is a nonempty string, that consists only of upper and lower case english letters, digits and spaces. Message is surrounded with quote marks. Quote marks shouldn't be printed. The length of the string does not exceed 20 symbols.</p><p>Length of any line in the input file does not exceed 50 symbols. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the message the screen will show after the given program is executed.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>8<br />try<br /> try<br /> throw ( AE ) <br /> catch ( BE, "BE in line 3")<br /><br /> try<br /> catch(AE, "AE in line 5") <br />catch(AE,"AE somewhere")<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>AE somewhere<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br />try<br /> try<br /> throw ( AE ) <br /> catch ( AE, "AE in line 3")<br /><br /> try<br /> catch(BE, "BE in line 5") <br />catch(AE,"AE somewhere")<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>AE in line 3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>8<br />try<br /> try<br /> throw ( CE ) <br /> catch ( BE, "BE in line 3")<br /><br /> try<br /> catch(AE, "AE in line 5") <br />catch(AE,"AE somewhere")<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Unhandled Exception<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample there are 2 try-catch-blocks such that <span class=\"tex-font-style-tt\">try</span> operator is described earlier than <span class=\"tex-font-style-tt\">throw</span> operator and <span class=\"tex-font-style-tt\">catch</span> operator is described later than <span class=\"tex-font-style-tt\">throw</span> operator: <span class=\"tex-font-style-tt\">try-catch(BE,"BE in line 3")</span> and <span class=\"tex-font-style-tt\">try-catch(AE,"AE somewhere")</span>. Exception type is AE, so the second block will be activated, because operator <span class=\"tex-font-style-tt\">catch(AE,"AE somewhere")</span> has exception type AE as parameter and operator <span class=\"tex-font-style-tt\">catch(BE,"BE in line 3")</span> has exception type BE.</p><p>In the second sample there are 2 try-catch-blocks such that <span class=\"tex-font-style-tt\">try</span> operator is described earlier than <span class=\"tex-font-style-tt\">throw</span> operator and <span class=\"tex-font-style-tt\">catch</span> operator is described later than <span class=\"tex-font-style-tt\">throw</span> operator: <span class=\"tex-font-style-tt\">try-catch(AE,"AE in line 3")</span> and <span class=\"tex-font-style-tt\">try-catch(AE,"AE somewhere")</span>. Exception type is AE, so both blocks can be activated, but only the first one will be activated, because operator <span class=\"tex-font-style-tt\">catch(AE,"AE in line 3")</span> is described earlier than <span class=\"tex-font-style-tt\">catch(AE,"AE somewhere")</span></p><p>In the third sample there is no blocks that can be activated by an exception of type CE.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:43</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='6255412dbf162e74a4677e79357bb071'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/HolkinPV\">HolkinPV</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/HolkinPV\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/HolkinPV\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/HolkinPV\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/HolkinPV\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/HolkinPV\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/HolkinPV\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/HolkinPV\" style=\"text-decoration:none;color:black !important;\">HolkinPV's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4713\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4699\"> <p>Codeforces Round #123 (Div. 2) Tutorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/HolkinPV\" title=\"Candidate Master HolkinPV\" class=\"rated-user user-violet\">HolkinPV</a>,\r\n <span class=\"format-humantime\" title=\"Jun/10/2012 22:36\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/195/problem/A\" title=\"Codeforces Round 123 (Div. 2)\">195A - Let's Watch Football</a></p><p>The whole video will be downloaded in <span class=\"tex-span\"><i>all</i> = (<i>c</i>·<i>a</i> + <i>b</i> - 1) / <i>b</i></span> seconds. In this problem you can choose every <span class=\"tex-span\">1 < = <i>t</i> < = <i>all</i></span> as an answer. To fulfill coditions of the problem it is enough to check the condition <span class=\"tex-span\"><i>t</i>0·<i>b</i> > = (<i>t</i>0 - <i>t</i>)·<i>a</i></span> at the moment of time t0 = all.</p><p><a href=\"/contest/195/problem/B\" title=\"Codeforces Round 123 (Div. 2)\">195B - After Training</a></p><p>In this problem you should carefully implement the given process. Firstly note that ball number <span class=\"tex-span\"><i>i</i> > <i>m</i></span> will be in the same basket as ball number <span class=\"tex-span\"><i>i</i> - <i>m</i></span>. Therefore it is enough to distribute first <span class=\"tex-span\"><i>m</i></span> balls. It can be done using two pointers <span class=\"tex-span\"><i>lf</i></span>, <span class=\"tex-span\"><i>rg</i></span> from the middle. Alternately put one ball to the left and to the right and shift pointers. In only case you should shift left pointer twice in the first moment of time if <span class=\"tex-span\"><i>m</i></span> is odd.</p><p><a href=\"/contest/195/problem/C\" title=\"Codeforces Round 123 (Div. 2)\">195C - Try and Catch</a></p><p>In this problem you was to implement what was writen in the statement. In my solution I did the following. Erase all spaces from the text except spaces in messages in try-catch blocks. Then when we get word "try" we put number of the new try-catch block in stack. When we get word "throw" we remember it's type and current state of stack (that is what try-catch blocks are opened). For example, put these number in set. When we get word "catch" if it's type equals to type of operator "throw" and the number of current try-catch block is in your set then write the answer now else erase this try-catch block from stack. If there was no suitable try-catch block write "Unhandled Exception".</p><p><a href=\"/contest/195/problem/D\" title=\"Codeforces Round 123 (Div. 2)\">195D - Analyzing Polyline</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Igor_Kudryashov\" title=\"Candidate Master Igor_Kudryashov\">Igor_Kudryashov</a></p><p>In fact in this problem we were given lines <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = <i>k</i><sub class=\"lower-index\"><i>i</i></sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> but negative values were replaced by zero. Your task was to find the number of angles that do not equal 180 degrees in the graph s(x), that is the sum of the given functions.</p><p>Firstly note that sum of two lines is also line. Indeed <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub> + <i>y</i><sub class=\"lower-index\">2</sub></span> is <span class=\"tex-span\"><i>y</i> = <i>k</i><sub class=\"lower-index\">1</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">2</sub> = (<i>k</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub>) * <i>x</i> + (<i>b</i><sub class=\"lower-index\">1</sub> + <i>b</i><sub class=\"lower-index\">2</sub>)</span>.</p><p>Consider points where <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = 0</span>, that is <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> = - <i>b</i><sub class=\"lower-index\"><i>i</i></sub> / <i>k</i><sub class=\"lower-index\"><i>i</i></sub></span>. While we assume that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't equal to 0. Then line number <span class=\"tex-span\"><i>i</i></span> is divided in two lines one of which identically equals to 0. Consider all different points <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and sort them. Then, obviously, the sum of the given functions between two consecutive points is line. Find the equation of the line. Assume that we consider point <span class=\"tex-span\"><i>i</i></span> from the left. Then equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span> will not be equal to equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> - 1</span>. That is in point <span class=\"tex-span\"><i>i</i></span> is formed an angle that doesn't equal 180 degrees.</p><p>So we should find equations of lines between every pair of points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span>. It can be easily done using two arrays with queries of increasing value on the interval offline.</p><p><a href=\"/contest/195/problem/E\" title=\"Codeforces Round 123 (Div. 2)\">195E - Building Forest</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Fefer_Ivan\" title=\"Candidate Master Fefer_Ivan\">Fefer_Ivan</a></p><p>The longest operation in this problem is to find the root of some vertex and the sum of the path to this root. To find these values fast we will use compression ways heuristics which is used in data structure "disjoint-set-union".</p><p>For every vertex v we keep two values : <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> and <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span>. <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>v</i></span>, if <span class=\"tex-span\"><i>v</i></span> — root, else <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> — next vertex on path from <span class=\"tex-span\"><i>v</i></span> to root. <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span> = sum of lengths of edges on path from <span class=\"tex-span\"><i>v</i></span> to <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span>.</p><p>To add new edge from <span class=\"tex-span\"><i>u</i></span> to <span class=\"tex-span\"><i>v</i></span> of length <span class=\"tex-span\"><i>w</i></span> it is enough to do <span class=\"tex-span\"><i>c</i>[<i>u</i>] = <i>v</i></span> and <span class=\"tex-span\"><i>sum</i>[<i>u</i>] = <i>w</i></span>.</p><p>Note that we only add new edges (we don't erase edges).</p><p>That is, if we find <span class=\"tex-span\"><i>root</i>(<i>v</i>)</span> and <span class=\"tex-span\"><i>depth</i>(<i>v</i>)</span> for some vertex <span class=\"tex-span\"><i>v</i></span> we can assign <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>root</i>(<i>v</i>)</span>, </p><p>Unable to parse markup [type=CF_TEX]</p> time. The approximate implementation is shown below. <pre><code>int root(int v){ \n if(c[v] == v){ \n return v; \n }else{ \n int u = root(c[v]); \n sum[v] = (sum[c[v]] + sum[v]) % M; \n c[v] = u; \n return u; \n } \n} \n</code></pre><p>It can proved that such implementation works using <span class=\"tex-span\"><i>O</i>(<i>log</i>(<i>n</i>))</span> time for every query. 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Analyzing Polyline"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Analyzing Polyline</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>As Valeric and Valerko were watching one of the last Euro Championship games in a sports bar, they broke a mug. Of course, the guys paid for it but the barman said that he will let them watch football in his bar only if they help his son complete a programming task. The task goes like that.</p><p>Let's consider a set of functions of the following form: </p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6f8951b8e4ae583d0fea0c48524efbb9c9d38134.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/></center> Let's define a sum of <span class=\"tex-span\"><i>n</i></span> functions <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub>(<i>x</i>), ..., <i>y</i><sub class=\"lower-index\"><i>n</i></sub>(<i>x</i>)</span> of the given type as function <span class=\"tex-span\"><i>s</i>(<i>x</i>) = <i>y</i><sub class=\"lower-index\">1</sub>(<i>x</i>) + ... + <i>y</i><sub class=\"lower-index\"><i>n</i></sub>(<i>x</i>)</span> for any <span class=\"tex-span\"><i>x</i></span>. It's easy to show that in this case the graph <span class=\"tex-span\"><i>s</i>(<i>x</i>)</span> is a polyline. You are given <span class=\"tex-span\"><i>n</i></span> functions of the given type, your task is to find the number of angles that do not equal 180 degrees, in the graph <span class=\"tex-span\"><i>s</i>(<i>x</i>)</span>, that is the sum of the given functions.<p>Valeric and Valerko really want to watch the next Euro Championship game, so they asked you to help them.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> — the number of functions. Each of the following <span class=\"tex-span\"><i>n</i></span> lines contains two space-separated integer numbers <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">( - 10<sup class=\"upper-index\">9</sup> ≤ <i>k</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup>)</span> that determine the <span class=\"tex-span\"><i>i</i></span>-th function.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the number of angles that do not equal 180 degrees in the graph of the polyline that equals the sum of the given functions.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>1<br/>1 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>1 0<br/>0 2<br/>-1 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>-2 -4<br/>1 7<br/>-5 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"360496ac92affadb02fd252501c4f11d\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"58a7c348d38b4b6c230b07f082e4eef04e204c50\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/195\">Codeforces Round 123 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='360496ac92affadb02fd252501c4f11d'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/195/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Analyzing Polyline</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>As Valeric and Valerko were watching one of the last Euro Championship games in a sports bar, they broke a mug. Of course, the guys paid for it but the barman said that he will let them watch football in his bar only if they help his son complete a programming task. The task goes like that.</p><p>Let's consider a set of functions of the following form: </p><center class=\"tex-equation\"><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6f8951b8e4ae583d0fea0c48524efbb9c9d38134.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></center> Let's define a sum of <span class=\"tex-span\"><i>n</i></span> functions <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub>(<i>x</i>), ..., <i>y</i><sub class=\"lower-index\"><i>n</i></sub>(<i>x</i>)</span> of the given type as function <span class=\"tex-span\"><i>s</i>(<i>x</i>) = <i>y</i><sub class=\"lower-index\">1</sub>(<i>x</i>) + ... + <i>y</i><sub class=\"lower-index\"><i>n</i></sub>(<i>x</i>)</span> for any <span class=\"tex-span\"><i>x</i></span>. It's easy to show that in this case the graph <span class=\"tex-span\"><i>s</i>(<i>x</i>)</span> is a polyline. You are given <span class=\"tex-span\"><i>n</i></span> functions of the given type, your task is to find the number of angles that do not equal 180 degrees, in the graph <span class=\"tex-span\"><i>s</i>(<i>x</i>)</span>, that is the sum of the given functions.<p>Valeric and Valerko really want to watch the next Euro Championship game, so they asked you to help them.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> — the number of functions. Each of the following <span class=\"tex-span\"><i>n</i></span> lines contains two space-separated integer numbers <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> <span class=\"tex-span\">( - 10<sup class=\"upper-index\">9</sup> ≤ <i>k</i><sub class=\"lower-index\"><i>i</i></sub>, <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup>)</span> that determine the <span class=\"tex-span\"><i>i</i></span>-th function.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the number of angles that do not equal 180 degrees in the graph of the polyline that equals the sum of the given functions.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>1<br />1 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />1 0<br />0 2<br />-1 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />-2 -4<br />1 7<br />-5 1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=D]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:43</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='6255412dbf162e74a4677e79357bb071'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/HolkinPV\">HolkinPV</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/HolkinPV\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/HolkinPV\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/HolkinPV\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/HolkinPV\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/HolkinPV\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/HolkinPV\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/HolkinPV\" style=\"text-decoration:none;color:black !important;\">HolkinPV's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4713\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4699\"> <p>Codeforces Round #123 (Div. 2) Tutorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/HolkinPV\" title=\"Candidate Master HolkinPV\" class=\"rated-user user-violet\">HolkinPV</a>,\r\n <span class=\"format-humantime\" title=\"Jun/10/2012 22:36\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/195/problem/A\" title=\"Codeforces Round 123 (Div. 2)\">195A - Let's Watch Football</a></p><p>The whole video will be downloaded in <span class=\"tex-span\"><i>all</i> = (<i>c</i>·<i>a</i> + <i>b</i> - 1) / <i>b</i></span> seconds. In this problem you can choose every <span class=\"tex-span\">1 < = <i>t</i> < = <i>all</i></span> as an answer. To fulfill coditions of the problem it is enough to check the condition <span class=\"tex-span\"><i>t</i>0·<i>b</i> > = (<i>t</i>0 - <i>t</i>)·<i>a</i></span> at the moment of time t0 = all.</p><p><a href=\"/contest/195/problem/B\" title=\"Codeforces Round 123 (Div. 2)\">195B - After Training</a></p><p>In this problem you should carefully implement the given process. Firstly note that ball number <span class=\"tex-span\"><i>i</i> > <i>m</i></span> will be in the same basket as ball number <span class=\"tex-span\"><i>i</i> - <i>m</i></span>. Therefore it is enough to distribute first <span class=\"tex-span\"><i>m</i></span> balls. It can be done using two pointers <span class=\"tex-span\"><i>lf</i></span>, <span class=\"tex-span\"><i>rg</i></span> from the middle. Alternately put one ball to the left and to the right and shift pointers. In only case you should shift left pointer twice in the first moment of time if <span class=\"tex-span\"><i>m</i></span> is odd.</p><p><a href=\"/contest/195/problem/C\" title=\"Codeforces Round 123 (Div. 2)\">195C - Try and Catch</a></p><p>In this problem you was to implement what was writen in the statement. In my solution I did the following. Erase all spaces from the text except spaces in messages in try-catch blocks. Then when we get word "try" we put number of the new try-catch block in stack. When we get word "throw" we remember it's type and current state of stack (that is what try-catch blocks are opened). For example, put these number in set. When we get word "catch" if it's type equals to type of operator "throw" and the number of current try-catch block is in your set then write the answer now else erase this try-catch block from stack. If there was no suitable try-catch block write "Unhandled Exception".</p><p><a href=\"/contest/195/problem/D\" title=\"Codeforces Round 123 (Div. 2)\">195D - Analyzing Polyline</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Igor_Kudryashov\" title=\"Candidate Master Igor_Kudryashov\">Igor_Kudryashov</a></p><p>In fact in this problem we were given lines <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = <i>k</i><sub class=\"lower-index\"><i>i</i></sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> but negative values were replaced by zero. Your task was to find the number of angles that do not equal 180 degrees in the graph s(x), that is the sum of the given functions.</p><p>Firstly note that sum of two lines is also line. Indeed <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub> + <i>y</i><sub class=\"lower-index\">2</sub></span> is <span class=\"tex-span\"><i>y</i> = <i>k</i><sub class=\"lower-index\">1</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">2</sub> = (<i>k</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub>) * <i>x</i> + (<i>b</i><sub class=\"lower-index\">1</sub> + <i>b</i><sub class=\"lower-index\">2</sub>)</span>.</p><p>Consider points where <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = 0</span>, that is <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> = - <i>b</i><sub class=\"lower-index\"><i>i</i></sub> / <i>k</i><sub class=\"lower-index\"><i>i</i></sub></span>. While we assume that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't equal to 0. Then line number <span class=\"tex-span\"><i>i</i></span> is divided in two lines one of which identically equals to 0. Consider all different points <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and sort them. Then, obviously, the sum of the given functions between two consecutive points is line. Find the equation of the line. Assume that we consider point <span class=\"tex-span\"><i>i</i></span> from the left. Then equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span> will not be equal to equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> - 1</span>. That is in point <span class=\"tex-span\"><i>i</i></span> is formed an angle that doesn't equal 180 degrees.</p><p>So we should find equations of lines between every pair of points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span>. It can be easily done using two arrays with queries of increasing value on the interval offline.</p><p><a href=\"/contest/195/problem/E\" title=\"Codeforces Round 123 (Div. 2)\">195E - Building Forest</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Fefer_Ivan\" title=\"Candidate Master Fefer_Ivan\">Fefer_Ivan</a></p><p>The longest operation in this problem is to find the root of some vertex and the sum of the path to this root. To find these values fast we will use compression ways heuristics which is used in data structure "disjoint-set-union".</p><p>For every vertex v we keep two values : <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> and <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span>. <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>v</i></span>, if <span class=\"tex-span\"><i>v</i></span> — root, else <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> — next vertex on path from <span class=\"tex-span\"><i>v</i></span> to root. <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span> = sum of lengths of edges on path from <span class=\"tex-span\"><i>v</i></span> to <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span>.</p><p>To add new edge from <span class=\"tex-span\"><i>u</i></span> to <span class=\"tex-span\"><i>v</i></span> of length <span class=\"tex-span\"><i>w</i></span> it is enough to do <span class=\"tex-span\"><i>c</i>[<i>u</i>] = <i>v</i></span> and <span class=\"tex-span\"><i>sum</i>[<i>u</i>] = <i>w</i></span>.</p><p>Note that we only add new edges (we don't erase edges).</p><p>That is, if we find <span class=\"tex-span\"><i>root</i>(<i>v</i>)</span> and <span class=\"tex-span\"><i>depth</i>(<i>v</i>)</span> for some vertex <span class=\"tex-span\"><i>v</i></span> we can assign <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>root</i>(<i>v</i>)</span>, </p><p>Unable to parse markup [type=CF_TEX]</p> time. The approximate implementation is shown below. <pre><code>int root(int v){ \n if(c[v] == v){ \n return v; \n }else{ \n int u = root(c[v]); \n sum[v] = (sum[c[v]] + sum[v]) % M; \n c[v] = u; \n return u; \n } \n} \n</code></pre><p>It can proved that such implementation works using <span class=\"tex-span\"><i>O</i>(<i>log</i>(<i>n</i>))</span> time for every query. The complexity of the solution is <span class=\"tex-span\"><i>O</i>(<i>n</i> * <i>log</i>(<i>n</i>))</span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-230-4713\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"230\",\n blogEntryId: \"4699\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a 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{document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":969,"cells":{"problem_id":{"kind":"string","value":"195E"},"contest":{"kind":"string","value":"195"},"problem":{"kind":"string","value":"E"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"E. Building Forest"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Building Forest</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>An <span class=\"tex-font-style-it\">oriented weighted forest</span> is an acyclic weighted digraph in which from each vertex at most one edge goes.</p><p>The <span class=\"tex-font-style-it\">root</span> of vertex <span class=\"tex-span\"><i>v</i></span> of an oriented weighted forest is a vertex from which no edge goes and which can be reached from vertex <span class=\"tex-span\"><i>v</i></span> moving along the edges of the weighted oriented forest. We denote the root of vertex <span class=\"tex-span\"><i>v</i></span> as <span class=\"tex-span\"><i>root</i>(<i>v</i>)</span>.</p><p>The <span class=\"tex-font-style-it\">depth</span> of vertex <span class=\"tex-span\"><i>v</i></span> is the sum of weights of paths passing from the vertex <span class=\"tex-span\"><i>v</i></span> to its root. Let's denote the depth of the vertex <span class=\"tex-span\"><i>v</i></span> as <span class=\"tex-span\"><i>depth</i>(<i>v</i>)</span>.</p><p>Let's consider the process of constructing a weighted directed forest. Initially, the forest does not contain vertices. Vertices are added sequentially one by one. Overall, there are <span class=\"tex-span\"><i>n</i></span> performed operations of adding. The <span class=\"tex-span\"><i>i</i></span>-th <span class=\"tex-span\">(<i>i</i> > 0)</span> adding operation is described by a set of numbers <span class=\"tex-span\">(<i>k</i>, <i>v</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">1</sub>, <i>v</i><sub class=\"lower-index\">2</sub>, <i>x</i><sub class=\"lower-index\">2</sub>, ... , <i>v</i><sub class=\"lower-index\"><i>k</i></sub>, <i>x</i><sub class=\"lower-index\"><i>k</i></sub>)</span> and means that we should add vertex number <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>k</i></span> edges to the graph: an edge from vertex <span class=\"tex-span\"><i>root</i>(<i>v</i><sub class=\"lower-index\">1</sub>)</span> to vertex <span class=\"tex-span\"><i>i</i></span> with weight <span class=\"tex-span\"><i>depth</i>(<i>v</i><sub class=\"lower-index\">1</sub>) + <i>x</i><sub class=\"lower-index\">1</sub></span>, an edge from vertex <span class=\"tex-span\"><i>root</i>(<i>v</i><sub class=\"lower-index\">2</sub>)</span> to vertex <span class=\"tex-span\"><i>i</i></span> with weight <span class=\"tex-span\"><i>depth</i>(<i>v</i><sub class=\"lower-index\">2</sub>) + <i>x</i><sub class=\"lower-index\">2</sub></span> and so on. If <span class=\"tex-span\"><i>k</i> = 0</span>, then only vertex <span class=\"tex-span\"><i>i</i></span> is added to the graph, there are no added edges.</p><p>Your task is like this: given the operations of adding vertices, calculate the sum of the weights of all edges of the forest, resulting after the application of all defined operations, modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> — the number of operations of adding a vertex.</p><p>Next <span class=\"tex-span\"><i>n</i></span> lines contain descriptions of the operations, the <span class=\"tex-span\"><i>i</i></span>-th line contains the description of the operation of adding the <span class=\"tex-span\"><i>i</i></span>-th vertex in the following format: the first number of a line is an integer <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(0 ≤ <i>k</i> ≤ <i>i</i> - 1)</span>, then follow <span class=\"tex-span\">2<i>k</i></span> space-separated integers: <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">1</sub>, <i>v</i><sub class=\"lower-index\">2</sub>, <i>x</i><sub class=\"lower-index\">2</sub>, ... , <i>v</i><sub class=\"lower-index\"><i>k</i></sub>, <i>x</i><sub class=\"lower-index\"><i>k</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>v</i><sub class=\"lower-index\"><i>j</i></sub> ≤ <i>i</i> - 1, |<i>x</i><sub class=\"lower-index\"><i>j</i></sub>| ≤ 10<sup class=\"upper-index\">9</sup>)</span>. </p><p>The operations are given in the order, in which they should be applied to the graph. It is guaranteed that sum <span class=\"tex-span\"><i>k</i></span> of all operations does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>, also that applying operations of adding vertexes does not result in loops and multiple edges. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the sum of weights of all edges of the resulting graph modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>6<br/>0<br/>0<br/>1 2 1<br/>2 1 5 2 2<br/>1 1 2<br/>1 3 4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>30<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br/>0<br/>1 1 5<br/>0<br/>0<br/>2 3 1 4 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Conside the first sample:</p><ol><li> Vertex <span class=\"tex-span\">1</span> is added. <span class=\"tex-span\"><i>k</i> = 0</span>, thus no edges are added.</li><li> Vertex <span class=\"tex-span\">2</span> is added. <span class=\"tex-span\"><i>k</i> = 0</span>, thus no edges are added.</li><li> Vertex <span class=\"tex-span\">3</span> is added. <span class=\"tex-span\"><i>k</i> = 1</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 2</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 1</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(2) = 2</span> to vertex <span class=\"tex-span\">3</span> with weight <span class=\"tex-span\"><i>depth</i>(2) + <i>x</i><sub class=\"lower-index\">1</sub> = 0 + 1 = 1</span> is added. </li><li> Vertex <span class=\"tex-span\">4</span> is added. <span class=\"tex-span\"><i>k</i> = 2</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 1</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 5</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(1) = 1</span> to vertex <span class=\"tex-span\">4</span> with weight <span class=\"tex-span\"><i>depth</i>(1) + <i>x</i><sub class=\"lower-index\">1</sub> = 0 + 5 = 5</span> is added. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">2</sub> = 2</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub> = 2</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(2) = 3</span> to vertex <span class=\"tex-span\">4</span> with weight <span class=\"tex-span\"><i>depth</i>(2) + <i>x</i><sub class=\"lower-index\">1</sub> = 1 + 2 = 3</span> is added.</li><li> Vertex <span class=\"tex-span\">5</span> is added. <span class=\"tex-span\"><i>k</i> = 1</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 1</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 2</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(1) = 4</span> to vertex <span class=\"tex-span\">5</span> with weight <span class=\"tex-span\"><i>depth</i>(1) + <i>x</i><sub class=\"lower-index\">1</sub> = 5 + 2 = 7</span> is added.</li><li> Vertex <span class=\"tex-span\">6</span> is added. <span class=\"tex-span\"><i>k</i> = 1</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 3</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 4</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(3) = 5</span> to vertex <span class=\"tex-span\">6</span> with weight <span class=\"tex-span\"><i>depth</i>(3) + <i>x</i><sub class=\"lower-index\">1</sub> = 10 + 4 = 14</span> is added.</li></ol><p>The resulting graph is shown on the pictore below: <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/0e06fef96694f14d20fdca3e3e44623b8e0c4bf1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/></p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"324dbe0d97f858e07cc033bab1cf7de9\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"58a7c348d38b4b6c230b07f082e4eef04e204c50\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"http://www.codeforces.com/blog/entry/4696\" title=\"HolkinPV\" target=\"_blank\">HolkinPV <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1070\" resourceName=\"HolkinPV\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4699\" title=\"Codeforces Round #123 (Div. 2) Разбор Задач\" target=\"_blank\">Tutorial <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1071\" resourceName=\"Codeforces Round #123 (Div. 2) Разбор Задач\"\r\nresourceManual=\"true\" 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}\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"E\" data-uuid=\"ps_c87d5629069e4b050e530ce1698f3bbd759b3093\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Building Forest</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>An <span class=\"tex-font-style-it\">oriented weighted forest</span> is an acyclic weighted digraph in which from each vertex at most one edge goes.</p><p>The <span class=\"tex-font-style-it\">root</span> of vertex <span class=\"tex-span\"><i>v</i></span> of an oriented weighted forest is a vertex from which no edge goes and which can be reached from vertex <span class=\"tex-span\"><i>v</i></span> moving along the edges of the weighted oriented forest. We denote the root of vertex <span class=\"tex-span\"><i>v</i></span> as <span class=\"tex-span\"><i>root</i>(<i>v</i>)</span>.</p><p>The <span class=\"tex-font-style-it\">depth</span> of vertex <span class=\"tex-span\"><i>v</i></span> is the sum of weights of paths passing from the vertex <span class=\"tex-span\"><i>v</i></span> to its root. Let's denote the depth of the vertex <span class=\"tex-span\"><i>v</i></span> as <span class=\"tex-span\"><i>depth</i>(<i>v</i>)</span>.</p><p>Let's consider the process of constructing a weighted directed forest. Initially, the forest does not contain vertices. Vertices are added sequentially one by one. Overall, there are <span class=\"tex-span\"><i>n</i></span> performed operations of adding. The <span class=\"tex-span\"><i>i</i></span>-th <span class=\"tex-span\">(<i>i</i> > 0)</span> adding operation is described by a set of numbers <span class=\"tex-span\">(<i>k</i>, <i>v</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">1</sub>, <i>v</i><sub class=\"lower-index\">2</sub>, <i>x</i><sub class=\"lower-index\">2</sub>, ... , <i>v</i><sub class=\"lower-index\"><i>k</i></sub>, <i>x</i><sub class=\"lower-index\"><i>k</i></sub>)</span> and means that we should add vertex number <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>k</i></span> edges to the graph: an edge from vertex <span class=\"tex-span\"><i>root</i>(<i>v</i><sub class=\"lower-index\">1</sub>)</span> to vertex <span class=\"tex-span\"><i>i</i></span> with weight <span class=\"tex-span\"><i>depth</i>(<i>v</i><sub class=\"lower-index\">1</sub>) + <i>x</i><sub class=\"lower-index\">1</sub></span>, an edge from vertex <span class=\"tex-span\"><i>root</i>(<i>v</i><sub class=\"lower-index\">2</sub>)</span> to vertex <span class=\"tex-span\"><i>i</i></span> with weight <span class=\"tex-span\"><i>depth</i>(<i>v</i><sub class=\"lower-index\">2</sub>) + <i>x</i><sub class=\"lower-index\">2</sub></span> and so on. If <span class=\"tex-span\"><i>k</i> = 0</span>, then only vertex <span class=\"tex-span\"><i>i</i></span> is added to the graph, there are no added edges.</p><p>Your task is like this: given the operations of adding vertices, calculate the sum of the weights of all edges of the forest, resulting after the application of all defined operations, modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup>)</span> — the number of operations of adding a vertex.</p><p>Next <span class=\"tex-span\"><i>n</i></span> lines contain descriptions of the operations, the <span class=\"tex-span\"><i>i</i></span>-th line contains the description of the operation of adding the <span class=\"tex-span\"><i>i</i></span>-th vertex in the following format: the first number of a line is an integer <span class=\"tex-span\"><i>k</i></span> <span class=\"tex-span\">(0 ≤ <i>k</i> ≤ <i>i</i> - 1)</span>, then follow <span class=\"tex-span\">2<i>k</i></span> space-separated integers: <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">1</sub>, <i>v</i><sub class=\"lower-index\">2</sub>, <i>x</i><sub class=\"lower-index\">2</sub>, ... , <i>v</i><sub class=\"lower-index\"><i>k</i></sub>, <i>x</i><sub class=\"lower-index\"><i>k</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>v</i><sub class=\"lower-index\"><i>j</i></sub> ≤ <i>i</i> - 1, |<i>x</i><sub class=\"lower-index\"><i>j</i></sub>| ≤ 10<sup class=\"upper-index\">9</sup>)</span>. </p><p>The operations are given in the order, in which they should be applied to the graph. It is guaranteed that sum <span class=\"tex-span\"><i>k</i></span> of all operations does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>, also that applying operations of adding vertexes does not result in loops and multiple edges. </p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the sum of weights of all edges of the resulting graph modulo <span class=\"tex-span\">1000000007</span> <span class=\"tex-span\">(10<sup class=\"upper-index\">9</sup> + 7)</span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>6<br />0<br />0<br />1 2 1<br />2 1 5 2 2<br />1 1 2<br />1 3 4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>30<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5<br />0<br />1 1 5<br />0<br />0<br />2 3 1 4 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Conside the first sample:</p><ol><li> Vertex <span class=\"tex-span\">1</span> is added. <span class=\"tex-span\"><i>k</i> = 0</span>, thus no edges are added.</li><li> Vertex <span class=\"tex-span\">2</span> is added. <span class=\"tex-span\"><i>k</i> = 0</span>, thus no edges are added.</li><li> Vertex <span class=\"tex-span\">3</span> is added. <span class=\"tex-span\"><i>k</i> = 1</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 2</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 1</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(2) = 2</span> to vertex <span class=\"tex-span\">3</span> with weight <span class=\"tex-span\"><i>depth</i>(2) + <i>x</i><sub class=\"lower-index\">1</sub> = 0 + 1 = 1</span> is added. </li><li> Vertex <span class=\"tex-span\">4</span> is added. <span class=\"tex-span\"><i>k</i> = 2</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 1</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 5</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(1) = 1</span> to vertex <span class=\"tex-span\">4</span> with weight <span class=\"tex-span\"><i>depth</i>(1) + <i>x</i><sub class=\"lower-index\">1</sub> = 0 + 5 = 5</span> is added. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">2</sub> = 2</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub> = 2</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(2) = 3</span> to vertex <span class=\"tex-span\">4</span> with weight <span class=\"tex-span\"><i>depth</i>(2) + <i>x</i><sub class=\"lower-index\">1</sub> = 1 + 2 = 3</span> is added.</li><li> Vertex <span class=\"tex-span\">5</span> is added. <span class=\"tex-span\"><i>k</i> = 1</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 1</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 2</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(1) = 4</span> to vertex <span class=\"tex-span\">5</span> with weight <span class=\"tex-span\"><i>depth</i>(1) + <i>x</i><sub class=\"lower-index\">1</sub> = 5 + 2 = 7</span> is added.</li><li> Vertex <span class=\"tex-span\">6</span> is added. <span class=\"tex-span\"><i>k</i> = 1</span>. <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\">1</sub> = 3</span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = 4</span>. Edge from vertex <span class=\"tex-span\"><i>root</i>(3) = 5</span> to vertex <span class=\"tex-span\">6</span> with weight <span class=\"tex-span\"><i>depth</i>(3) + <i>x</i><sub class=\"lower-index\">1</sub> = 10 + 4 = 14</span> is added.</li></ol><p>The resulting graph is shown on the pictore below: <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/0e06fef96694f14d20fdca3e3e44623b8e0c4bf1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=E]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='6255412dbf162e74a4677e79357bb071'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/HolkinPV\">HolkinPV</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/HolkinPV\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/HolkinPV\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/HolkinPV\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/HolkinPV\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/HolkinPV\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/HolkinPV\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/HolkinPV\" style=\"text-decoration:none;color:black !important;\">HolkinPV's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4713\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4699\"> <p>Codeforces Round #123 (Div. 2) Tutorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/HolkinPV\" title=\"Candidate Master HolkinPV\" class=\"rated-user user-violet\">HolkinPV</a>,\r\n <span class=\"format-humantime\" title=\"Jun/10/2012 22:36\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/195/problem/A\" title=\"Codeforces Round 123 (Div. 2)\">195A - Let's Watch Football</a></p><p>The whole video will be downloaded in <span class=\"tex-span\"><i>all</i> = (<i>c</i>·<i>a</i> + <i>b</i> - 1) / <i>b</i></span> seconds. In this problem you can choose every <span class=\"tex-span\">1 < = <i>t</i> < = <i>all</i></span> as an answer. To fulfill coditions of the problem it is enough to check the condition <span class=\"tex-span\"><i>t</i>0·<i>b</i> > = (<i>t</i>0 - <i>t</i>)·<i>a</i></span> at the moment of time t0 = all.</p><p><a href=\"/contest/195/problem/B\" title=\"Codeforces Round 123 (Div. 2)\">195B - After Training</a></p><p>In this problem you should carefully implement the given process. Firstly note that ball number <span class=\"tex-span\"><i>i</i> > <i>m</i></span> will be in the same basket as ball number <span class=\"tex-span\"><i>i</i> - <i>m</i></span>. Therefore it is enough to distribute first <span class=\"tex-span\"><i>m</i></span> balls. It can be done using two pointers <span class=\"tex-span\"><i>lf</i></span>, <span class=\"tex-span\"><i>rg</i></span> from the middle. Alternately put one ball to the left and to the right and shift pointers. In only case you should shift left pointer twice in the first moment of time if <span class=\"tex-span\"><i>m</i></span> is odd.</p><p><a href=\"/contest/195/problem/C\" title=\"Codeforces Round 123 (Div. 2)\">195C - Try and Catch</a></p><p>In this problem you was to implement what was writen in the statement. In my solution I did the following. Erase all spaces from the text except spaces in messages in try-catch blocks. Then when we get word "try" we put number of the new try-catch block in stack. When we get word "throw" we remember it's type and current state of stack (that is what try-catch blocks are opened). For example, put these number in set. When we get word "catch" if it's type equals to type of operator "throw" and the number of current try-catch block is in your set then write the answer now else erase this try-catch block from stack. If there was no suitable try-catch block write "Unhandled Exception".</p><p><a href=\"/contest/195/problem/D\" title=\"Codeforces Round 123 (Div. 2)\">195D - Analyzing Polyline</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Igor_Kudryashov\" title=\"Candidate Master Igor_Kudryashov\">Igor_Kudryashov</a></p><p>In fact in this problem we were given lines <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = <i>k</i><sub class=\"lower-index\"><i>i</i></sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\"><i>i</i></sub></span> but negative values were replaced by zero. Your task was to find the number of angles that do not equal 180 degrees in the graph s(x), that is the sum of the given functions.</p><p>Firstly note that sum of two lines is also line. Indeed <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub> + <i>y</i><sub class=\"lower-index\">2</sub></span> is <span class=\"tex-span\"><i>y</i> = <i>k</i><sub class=\"lower-index\">1</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub> * <i>x</i> + <i>b</i><sub class=\"lower-index\">2</sub> = (<i>k</i><sub class=\"lower-index\">1</sub> + <i>k</i><sub class=\"lower-index\">2</sub>) * <i>x</i> + (<i>b</i><sub class=\"lower-index\">1</sub> + <i>b</i><sub class=\"lower-index\">2</sub>)</span>.</p><p>Consider points where <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub> = 0</span>, that is <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> = - <i>b</i><sub class=\"lower-index\"><i>i</i></sub> / <i>k</i><sub class=\"lower-index\"><i>i</i></sub></span>. While we assume that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\"><i>i</i></sub></span> doesn't equal to 0. Then line number <span class=\"tex-span\"><i>i</i></span> is divided in two lines one of which identically equals to 0. Consider all different points <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and sort them. Then, obviously, the sum of the given functions between two consecutive points is line. Find the equation of the line. Assume that we consider point <span class=\"tex-span\"><i>i</i></span> from the left. Then equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span> will not be equal to equation of the line between points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> - 1</span>. That is in point <span class=\"tex-span\"><i>i</i></span> is formed an angle that doesn't equal 180 degrees.</p><p>So we should find equations of lines between every pair of points <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span>. It can be easily done using two arrays with queries of increasing value on the interval offline.</p><p><a href=\"/contest/195/problem/E\" title=\"Codeforces Round 123 (Div. 2)\">195E - Building Forest</a></p><p>Tutorial by author <a class=\"rated-user user-violet\" href=\"/profile/Fefer_Ivan\" title=\"Candidate Master Fefer_Ivan\">Fefer_Ivan</a></p><p>The longest operation in this problem is to find the root of some vertex and the sum of the path to this root. To find these values fast we will use compression ways heuristics which is used in data structure "disjoint-set-union".</p><p>For every vertex v we keep two values : <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> and <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span>. <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>v</i></span>, if <span class=\"tex-span\"><i>v</i></span> — root, else <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span> — next vertex on path from <span class=\"tex-span\"><i>v</i></span> to root. <span class=\"tex-span\"><i>sum</i>[<i>v</i>]</span> = sum of lengths of edges on path from <span class=\"tex-span\"><i>v</i></span> to <span class=\"tex-span\"><i>c</i>[<i>v</i>]</span>.</p><p>To add new edge from <span class=\"tex-span\"><i>u</i></span> to <span class=\"tex-span\"><i>v</i></span> of length <span class=\"tex-span\"><i>w</i></span> it is enough to do <span class=\"tex-span\"><i>c</i>[<i>u</i>] = <i>v</i></span> and <span class=\"tex-span\"><i>sum</i>[<i>u</i>] = <i>w</i></span>.</p><p>Note that we only add new edges (we don't erase edges).</p><p>That is, if we find <span class=\"tex-span\"><i>root</i>(<i>v</i>)</span> and <span class=\"tex-span\"><i>depth</i>(<i>v</i>)</span> for some vertex <span class=\"tex-span\"><i>v</i></span> we can assign <span class=\"tex-span\"><i>c</i>[<i>v</i>] = <i>root</i>(<i>v</i>)</span>, </p><p>Unable to parse markup [type=CF_TEX]</p> time. The approximate implementation is shown below. <pre><code>int root(int v){ \n if(c[v] == v){ \n return v; \n }else{ \n int u = root(c[v]); \n sum[v] = (sum[c[v]] + sum[v]) % M; \n c[v] = u; \n return u; \n } \n} \n</code></pre><p>It can proved that such implementation works using <span class=\"tex-span\"><i>O</i>(<i>log</i>(<i>n</i>))</span> time for every query. The complexity of the solution is <span class=\"tex-span\"><i>O</i>(<i>n</i> * <i>log</i>(<i>n</i>))</span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-230-4713\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"230\",\n blogEntryId: \"4699\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a 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style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+27</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4713\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/HolkinPV\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/HolkinPV\">\n HolkinPV\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication 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{document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":970,"cells":{"problem_id":{"kind":"string","value":"196A"},"contest":{"kind":"string","value":"196"},"problem":{"kind":"string","value":"A"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"A. Lexicographically Maximum Subsequence"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Lexicographically Maximum Subsequence</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got string <span class=\"tex-span\"><i>s</i></span>, consisting of only lowercase English letters. Find its lexicographically maximum subsequence.</p><p>We'll call a non-empty string <span class=\"tex-span\"><i>s</i>[<i>p</i><sub class=\"lower-index\">1</sub><i>p</i><sub class=\"lower-index\">2</sub>... <i>p</i><sub class=\"lower-index\"><i>k</i></sub>] = <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">1</sub></sub><i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">2</sub></sub>... <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></sub>(1 ≤ <i>p</i><sub class=\"lower-index\">1</sub> < <i>p</i><sub class=\"lower-index\">2</sub> < ... < <i>p</i><sub class=\"lower-index\"><i>k</i></sub> ≤ |<i>s</i>|)</span> a <span class=\"tex-font-style-it\">subsequence</span> of string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\">|<i>s</i>|</sub></span>.</p><p>String <span class=\"tex-span\"><i>x</i> = <i>x</i><sub class=\"lower-index\">1</sub><i>x</i><sub class=\"lower-index\">2</sub>... <i>x</i><sub class=\"lower-index\">|<i>x</i>|</sub></span> is <span class=\"tex-font-style-it\">lexicographically larger</span> than string <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub><i>y</i><sub class=\"lower-index\">2</sub>... <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, if either <span class=\"tex-span\">|<i>x</i>| > |<i>y</i>|</span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\">|<i>y</i>|</sub> = <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, or exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < |<i>x</i>|, <i>r</i> < |<i>y</i>|)</span>, that <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\"><i>r</i></sub> = <i>y</i><sub class=\"lower-index\"><i>r</i></sub></span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>r</i> + 1</sub> > <i>y</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span>. Characters in lines are compared like their ASCII codes.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>, consisting only of lowercase English letters. The string's length doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the lexicographically maximum subsequence of string <span class=\"tex-span\"><i>s</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>ababba<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>bbba<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>abbcbccacbbcbaaba<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>cccccbba<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters).</p><p>The first sample: <span class=\"tex-font-style-tt\">a<span class=\"tex-font-style-bf\">B</span>a<span class=\"tex-font-style-bf\">BBA</span></span></p><p>The second sample: <span class=\"tex-font-style-tt\">abb<span class=\"tex-font-style-bf\">C</span>b<span class=\"tex-font-style-bf\">CC</span>a<span class=\"tex-font-style-bf\">C</span>bb<span class=\"tex-font-style-bf\">CB</span>aa<span class=\"tex-font-style-bf\">BA</span></span></p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"a70782ec7493326e740de38e718c0046\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - A - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"6a108ecdc9b42df5b9037e47c442c60d69b57e73\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/196\">Codeforces Round 124 (Div. 1)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='a70782ec7493326e740de38e718c0046'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/196/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Greedy algorithms\">\r\n greedy\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Prefix- and Z-functions, suffix structures, Knuth–Morris–Pratt algorithm, etc\">\r\n strings\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1100\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" 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$(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4708\" title=\"Codeforces Round #124\" target=\"_blank\">Codeforces Round #124</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1085:1086\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4717\" title=\"Codeforces Round #124 — editorial\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1090:1091\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1081\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span 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class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Lexicographically Maximum Subsequence</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got string <span class=\"tex-span\"><i>s</i></span>, consisting of only lowercase English letters. Find its lexicographically maximum subsequence.</p><p>We'll call a non-empty string <span class=\"tex-span\"><i>s</i>[<i>p</i><sub class=\"lower-index\">1</sub><i>p</i><sub class=\"lower-index\">2</sub>... <i>p</i><sub class=\"lower-index\"><i>k</i></sub>] = <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">1</sub></sub><i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">2</sub></sub>... <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></sub>(1 ≤ <i>p</i><sub class=\"lower-index\">1</sub> < <i>p</i><sub class=\"lower-index\">2</sub> < ... < <i>p</i><sub class=\"lower-index\"><i>k</i></sub> ≤ |<i>s</i>|)</span> a <span class=\"tex-font-style-it\">subsequence</span> of string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\">|<i>s</i>|</sub></span>.</p><p>String <span class=\"tex-span\"><i>x</i> = <i>x</i><sub class=\"lower-index\">1</sub><i>x</i><sub class=\"lower-index\">2</sub>... <i>x</i><sub class=\"lower-index\">|<i>x</i>|</sub></span> is <span class=\"tex-font-style-it\">lexicographically larger</span> than string <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub><i>y</i><sub class=\"lower-index\">2</sub>... <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, if either <span class=\"tex-span\">|<i>x</i>| > |<i>y</i>|</span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\">|<i>y</i>|</sub> = <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, or exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < |<i>x</i>|, <i>r</i> < |<i>y</i>|)</span>, that <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\"><i>r</i></sub> = <i>y</i><sub class=\"lower-index\"><i>r</i></sub></span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>r</i> + 1</sub> > <i>y</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span>. Characters in lines are compared like their ASCII codes.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>, consisting only of lowercase English letters. The string's length doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the lexicographically maximum subsequence of string <span class=\"tex-span\"><i>s</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>ababba<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>bbba<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>abbcbccacbbcbaaba<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>cccccbba<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters).</p><p>The first sample: <span class=\"tex-font-style-tt\">a<span class=\"tex-font-style-bf\">B</span>a<span class=\"tex-font-style-bf\">BBA</span></span></p><p>The second sample: <span class=\"tex-font-style-tt\">abb<span class=\"tex-font-style-bf\">C</span>b<span class=\"tex-font-style-bf\">CC</span>a<span class=\"tex-font-style-bf\">C</span>bb<span class=\"tex-font-style-bf\">CB</span>aa<span class=\"tex-font-style-bf\">BA</span></span></p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=A]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" 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href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Infinite Maze"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Infinite Maze</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>We've got a rectangular <span class=\"tex-span\"><i>n</i> × <i>m</i></span>-cell maze. Each cell is either passable, or is a wall (impassable). A little boy found the maze and cyclically tiled a plane with it so that the plane became an infinite maze. Now on this plane cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> is a wall if and only if cell <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5820f73507b71bbab0564415ed80476b7cbd4b71.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> is a wall.</p><p>In this problem <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6dd276f849101e7efda6cb8031d4056744d532a1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> is a remainder of dividing number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>The little boy stood at some cell on the plane and he wondered whether he can walk infinitely far away from his starting position. From cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> he can go to one of the following cells: <span class=\"tex-span\">(<i>x</i>, <i>y</i> - 1)</span>, <span class=\"tex-span\">(<i>x</i>, <i>y</i> + 1)</span>, <span class=\"tex-span\">(<i>x</i> - 1, <i>y</i>)</span> and <span class=\"tex-span\">(<i>x</i> + 1, <i>y</i>)</span>, provided that the cell he goes to is not a wall.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 1500</span>) — the height and the width of the maze that the boy used to cyclically tile the plane.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the labyrinth. Each character is either a \"<span class=\"tex-font-style-tt\">#</span>\", that marks a wall, a \"<span class=\"tex-font-style-tt\">.</span>\", that marks a passable cell, or an \"<span class=\"tex-font-style-tt\">S</span>\", that marks the little boy's starting point. </p><p>The starting point is a passable cell. It is guaranteed that character \"<span class=\"tex-font-style-tt\">S</span>\" occurs exactly once in the input.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print \"<span class=\"tex-font-style-tt\">Yes</span>\" (without the quotes), if the little boy can walk infinitely far from the starting point. Otherwise, print \"<span class=\"tex-font-style-tt\">No</span>\" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>##.#<br/>##S#<br/>#..#<br/>#.##<br/>#..#<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Yes<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>##.#<br/>##S#<br/>#..#<br/>..#.<br/>#.##<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>No<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the little boy can go up for infinitely long as there is a \"clear path\" that goes vertically. He just needs to repeat the following steps infinitely: up, up, left, up, up, right, up.</p><p>In the second sample the vertical path is blocked. The path to the left doesn't work, too — the next \"copy\" of the maze traps the boy.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"4764f6283b05912d6bf4f1fe7f602b2b\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"6a108ecdc9b42df5b9037e47c442c60d69b57e73\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1081\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1076\" 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class=\"header\"><div class=\"title\">B. Infinite Maze</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>We've got a rectangular <span class=\"tex-span\"><i>n</i> × <i>m</i></span>-cell maze. Each cell is either passable, or is a wall (impassable). A little boy found the maze and cyclically tiled a plane with it so that the plane became an infinite maze. Now on this plane cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> is a wall if and only if cell <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5820f73507b71bbab0564415ed80476b7cbd4b71.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> is a wall.</p><p>In this problem <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6dd276f849101e7efda6cb8031d4056744d532a1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> is a remainder of dividing number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>The little boy stood at some cell on the plane and he wondered whether he can walk infinitely far away from his starting position. From cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> he can go to one of the following cells: <span class=\"tex-span\">(<i>x</i>, <i>y</i> - 1)</span>, <span class=\"tex-span\">(<i>x</i>, <i>y</i> + 1)</span>, <span class=\"tex-span\">(<i>x</i> - 1, <i>y</i>)</span> and <span class=\"tex-span\">(<i>x</i> + 1, <i>y</i>)</span>, provided that the cell he goes to is not a wall.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 1500</span>) — the height and the width of the maze that the boy used to cyclically tile the plane.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the labyrinth. Each character is either a "<span class=\"tex-font-style-tt\">#</span>", that marks a wall, a "<span class=\"tex-font-style-tt\">.</span>", that marks a passable cell, or an "<span class=\"tex-font-style-tt\">S</span>", that marks the little boy's starting point. </p><p>The starting point is a passable cell. It is guaranteed that character "<span class=\"tex-font-style-tt\">S</span>" occurs exactly once in the input.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print "<span class=\"tex-font-style-tt\">Yes</span>" (without the quotes), if the little boy can walk infinitely far from the starting point. Otherwise, print "<span class=\"tex-font-style-tt\">No</span>" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />##.#<br />##S#<br />#..#<br />#.##<br />#..#<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Yes<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />##.#<br />##S#<br />#..#<br />..#.<br />#.##<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>No<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the little boy can go up for infinitely long as there is a "clear path" that goes vertically. He just needs to repeat the following steps infinitely: up, up, left, up, up, right, up.</p><p>In the second sample the vertical path is blocked. 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:43</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final 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style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div 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title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New 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title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/shivam565\" title=\"Specialist shivam565\" class=\"rated-user user-cyan\">shivam565</a> →\r\n <a href=\"/blog/entry/108348\">Total number of subarrays with sum atmost k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n </ul>\r\n </div>\r\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/recent-actions\">Detailed →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n</div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li><a\r\n href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Paint Tree"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Paint Tree</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You are given a tree with <span class=\"tex-span\"><i>n</i></span> vertexes and <span class=\"tex-span\"><i>n</i></span> points on a plane, no three points lie on one straight line.</p><p>Your task is to paint the given tree on a plane, using the given points as vertexes. </p><p>That is, you should correspond each vertex of the tree to exactly one point and each point should correspond to a vertex. If two vertexes of the tree are connected by an edge, then the corresponding points should have a segment painted between them. The segments that correspond to non-adjacent edges, should not have common points. The segments that correspond to adjacent edges should have exactly one common point.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains an integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1500</span>) — the number of vertexes on a tree (as well as the number of chosen points on the plane).</p><p>Each of the next <span class=\"tex-span\"><i>n</i> - 1</span> lines contains two space-separated integers <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>) — the numbers of tree vertexes connected by the <span class=\"tex-span\"><i>i</i></span>-th edge.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contain two space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the coordinates of the <span class=\"tex-span\"><i>i</i></span>-th point on the plane. No three points lie on one straight line.</p><p>It is guaranteed that under given constraints problem has a solution.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> distinct space-separated integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>: the <span class=\"tex-span\"><i>i</i></span>-th number must equal the number of the vertex to place at the <span class=\"tex-span\"><i>i</i></span>-th point (the points are numbered in the order, in which they are listed in the input).</p><p>If there are several solutions, print any of them.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>1 3<br/>2 3<br/>0 0<br/>1 1<br/>2 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 3 2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/>1 2<br/>2 3<br/>1 4<br/>-1 -2<br/>3 5<br/>-3 3<br/>2 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4 2 1 3<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The possible solutions for the sample are given below.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/184fb6b10b810cafa022514b67b4c8582f76b101.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/183da3ee0eaa5abd757d9c2f724be6c9354f4cd4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"d7367b0f0a441f1753b6a606afde2f09\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"6a108ecdc9b42df5b9037e47c442c60d69b57e73\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/196\">Codeforces Round 124 (Div. 1)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? 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It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/196/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Constructive algorithms\">\r\n constructive algorithms\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Divide and Conquer\">\r\n divide and conquer\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Geometry, computational geometry\">\r\n geometry\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Sortings, orderings\">\r\n sortings\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Trees\">\r\n trees\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *2200\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='d7367b0f0a441f1753b6a606afde2f09'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" 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materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4708\" title=\"Codeforces Round #124\" target=\"_blank\">Codeforces Round #124</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1085:1086\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4717\" title=\"Codeforces Round #124 — editorial\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1090:1091\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1081\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1076\" resourceName=\"Discussion\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Обсуждение\" target=\"_blank\">Обсуждение <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1073\" resourceName=\"Обсуждение\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/196\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/196/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/196/my\">My Submissions</a></li>\r\n 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if (node.tagName === \"DIV\"\r\n || node.tagName === \"P\"\r\n || node.tagName === \"PRE\"\r\n || node.tagName === \"UL\"\r\n || node.tagName === \"LI\"\r\n ) {\r\n result.push(\"\\n\");\r\n }\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(CLOSING_SPACE);\r\n }\r\n\r\n return result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"C\" data-uuid=\"ps_e165d1e93a7598c41cdf7c6213751c75908a68ea\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Paint Tree</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You are given a tree with <span class=\"tex-span\"><i>n</i></span> vertexes and <span class=\"tex-span\"><i>n</i></span> points on a plane, no three points lie on one straight line.</p><p>Your task is to paint the given tree on a plane, using the given points as vertexes. </p><p>That is, you should correspond each vertex of the tree to exactly one point and each point should correspond to a vertex. If two vertexes of the tree are connected by an edge, then the corresponding points should have a segment painted between them. The segments that correspond to non-adjacent edges, should not have common points. The segments that correspond to adjacent edges should have exactly one common point.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains an integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1500</span>) — the number of vertexes on a tree (as well as the number of chosen points on the plane).</p><p>Each of the next <span class=\"tex-span\"><i>n</i> - 1</span> lines contains two space-separated integers <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>) — the numbers of tree vertexes connected by the <span class=\"tex-span\"><i>i</i></span>-th edge.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contain two space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the coordinates of the <span class=\"tex-span\"><i>i</i></span>-th point on the plane. No three points lie on one straight line.</p><p>It is guaranteed that under given constraints problem has a solution.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> distinct space-separated integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>: the <span class=\"tex-span\"><i>i</i></span>-th number must equal the number of the vertex to place at the <span class=\"tex-span\"><i>i</i></span>-th point (the points are numbered in the order, in which they are listed in the input).</p><p>If there are several solutions, print any of them.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />1 3<br />2 3<br />0 0<br />1 1<br />2 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 3 2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br />1 2<br />2 3<br />1 4<br />-1 -2<br />3 5<br />-3 3<br />2 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4 2 1 3<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The possible solutions for the sample are given below.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/184fb6b10b810cafa022514b67b4c8582f76b101.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/183da3ee0eaa5abd757d9c2f724be6c9354f4cd4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" 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href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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The Next Good String"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. The Next Good String</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>In problems on strings one often has to find a string with some particular properties. The problem authors were reluctant to waste time on thinking of a name for some string so they called it <span class=\"tex-font-style-it\">good</span>. A string is good if it doesn't have palindrome substrings longer than or equal to <span class=\"tex-span\"><i>d</i></span>. </p><p>You are given string <span class=\"tex-span\"><i>s</i></span>, consisting only of lowercase English letters. Find a good string <span class=\"tex-span\"><i>t</i></span> with length <span class=\"tex-span\">|<i>s</i>|</span>, consisting of lowercase English letters, which is lexicographically larger than <span class=\"tex-span\"><i>s</i></span>. Of all such strings string <span class=\"tex-span\"><i>t</i></span> must be lexicographically minimum.</p><p>We will call a non-empty string <span class=\"tex-span\"><i>s</i>[<i>a</i> ... <i>b</i>] = <i>s</i><sub class=\"lower-index\"><i>a</i></sub><i>s</i><sub class=\"lower-index\"><i>a</i> + 1</sub>... <i>s</i><sub class=\"lower-index\"><i>b</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>a</i> ≤ <i>b</i> ≤ |<i>s</i>|)</span> a <span class=\"tex-font-style-it\">substring</span> of string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\">|<i>s</i>|</sub></span>.</p><p>A non-empty string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\"><i>n</i></sub></span> is called <span class=\"tex-font-style-it\">a palindrome</span> if for all <span class=\"tex-span\"><i>i</i></span> from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> the following fulfills: <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub> = <i>s</i><sub class=\"lower-index\"><i>n</i> - <i>i</i> + 1</sub></span>. In other words, palindrome read the same in both directions.</p><p>String <span class=\"tex-span\"><i>x</i> = <i>x</i><sub class=\"lower-index\">1</sub><i>x</i><sub class=\"lower-index\">2</sub>... <i>x</i><sub class=\"lower-index\">|<i>x</i>|</sub></span> is <span class=\"tex-font-style-it\">lexicographically larger</span> than string <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub><i>y</i><sub class=\"lower-index\">2</sub>... <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, if either <span class=\"tex-span\">|<i>x</i>| > |<i>y</i>|</span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\">|<i>y</i>|</sub> = <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, or there exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < |<i>x</i>|, <i>r</i> < |<i>y</i>|)</span>, that <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\"><i>r</i></sub> = <i>y</i><sub class=\"lower-index\"><i>r</i></sub></span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>r</i> + 1</sub> > <i>y</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span>. Characters in such strings are compared like their ASCII codes.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>d</i></span> (<span class=\"tex-span\">1 ≤ <i>d</i> ≤ |<i>s</i>|</span>).</p><p>The second line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>, its length is no more than <span class=\"tex-span\">4·10<sup class=\"upper-index\">5</sup></span> characters. The string consists of lowercase English letters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the good string that lexicographically follows <span class=\"tex-span\"><i>s</i></span>, has the same length and consists of only lowercase English letters. If such string does not exist, print \"<span class=\"tex-font-style-tt\">Impossible</span>\" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>aaaaaaa<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>aabbcaa<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>zzyzzzz<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Impossible<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/>abbabbbabbb<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>abbbcaaabab<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"a052387076c106149e7801ae073033ef\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"6a108ecdc9b42df5b9037e47c442c60d69b57e73\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/196\">Codeforces Round 124 (Div. 1)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Heaps, binary search trees, segment trees, hash tables, etc\">\r\n data structures\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Greedy algorithms\">\r\n greedy\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Hashing, hashtables\">\r\n hashing\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Prefix- and Z-functions, 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style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1085:1086\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4717\" title=\"Codeforces Round #124 — editorial\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1090:1091\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1081\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1076\" resourceName=\"Discussion\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Обсуждение\" target=\"_blank\">Обсуждение <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1073\" resourceName=\"Обсуждение\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/196\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/196/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/196/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/196/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/196/hacks\">Hacks</a></li>\r\n <li><a\r\n 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!important;\r\n }\r\n </style>\r\n <script>\r\n const OPENING_SPACE = String.fromCharCode(1001);\r\n const CLOSING_SPACE = String.fromCharCode(1002);\r\n\r\n const nodeToText = function (node, pre) {\r\n let result = [];\r\n\r\n if (node.tagName === \"SCRIPT\" || node.tagName === \"math\"\r\n || (node.classList && node.classList.contains(\"input-output-copier\")))\r\n return [];\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(OPENING_SPACE);\r\n }\r\n\r\n if (node.nodeType === Node.TEXT_NODE) {\r\n let s = node.textContent;\r\n if (!pre) {\r\n s = s.replace(/\\s+/g, \" \");\r\n }\r\n if (s.length > 0) {\r\n result.push(s);\r\n }\r\n }\r\n\r\n if (pre && node.tagName === \"BR\") {\r\n result.push(\"\\n\");\r\n }\r\n\r\n node.childNodes.forEach(function (child) {\r\n result.push(nodeToText(child, node.tagName === \"PRE\").join(\"\"));\r\n });\r\n\r\n if (node.tagName === \"DIV\"\r\n || node.tagName === \"P\"\r\n || node.tagName === \"PRE\"\r\n || node.tagName === \"UL\"\r\n || node.tagName === \"LI\"\r\n ) {\r\n result.push(\"\\n\");\r\n }\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(CLOSING_SPACE);\r\n }\r\n\r\n return result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"D\" data-uuid=\"ps_e7774a6a7cf115df77056dd628b42869ddde578a\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. The Next Good String</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>In problems on strings one often has to find a string with some particular properties. The problem authors were reluctant to waste time on thinking of a name for some string so they called it <span class=\"tex-font-style-it\">good</span>. A string is good if it doesn't have palindrome substrings longer than or equal to <span class=\"tex-span\"><i>d</i></span>. </p><p>You are given string <span class=\"tex-span\"><i>s</i></span>, consisting only of lowercase English letters. Find a good string <span class=\"tex-span\"><i>t</i></span> with length <span class=\"tex-span\">|<i>s</i>|</span>, consisting of lowercase English letters, which is lexicographically larger than <span class=\"tex-span\"><i>s</i></span>. Of all such strings string <span class=\"tex-span\"><i>t</i></span> must be lexicographically minimum.</p><p>We will call a non-empty string <span class=\"tex-span\"><i>s</i>[<i>a</i> ... <i>b</i>] = <i>s</i><sub class=\"lower-index\"><i>a</i></sub><i>s</i><sub class=\"lower-index\"><i>a</i> + 1</sub>... <i>s</i><sub class=\"lower-index\"><i>b</i></sub></span> <span class=\"tex-span\">(1 ≤ <i>a</i> ≤ <i>b</i> ≤ |<i>s</i>|)</span> a <span class=\"tex-font-style-it\">substring</span> of string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\">|<i>s</i>|</sub></span>.</p><p>A non-empty string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\"><i>n</i></sub></span> is called <span class=\"tex-font-style-it\">a palindrome</span> if for all <span class=\"tex-span\"><i>i</i></span> from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> the following fulfills: <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>i</i></sub> = <i>s</i><sub class=\"lower-index\"><i>n</i> - <i>i</i> + 1</sub></span>. In other words, palindrome read the same in both directions.</p><p>String <span class=\"tex-span\"><i>x</i> = <i>x</i><sub class=\"lower-index\">1</sub><i>x</i><sub class=\"lower-index\">2</sub>... <i>x</i><sub class=\"lower-index\">|<i>x</i>|</sub></span> is <span class=\"tex-font-style-it\">lexicographically larger</span> than string <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub><i>y</i><sub class=\"lower-index\">2</sub>... <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, if either <span class=\"tex-span\">|<i>x</i>| > |<i>y</i>|</span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\">|<i>y</i>|</sub> = <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, or there exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < |<i>x</i>|, <i>r</i> < |<i>y</i>|)</span>, that <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\"><i>r</i></sub> = <i>y</i><sub class=\"lower-index\"><i>r</i></sub></span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>r</i> + 1</sub> > <i>y</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span>. Characters in such strings are compared like their ASCII codes.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains integer <span class=\"tex-span\"><i>d</i></span> (<span class=\"tex-span\">1 ≤ <i>d</i> ≤ |<i>s</i>|</span>).</p><p>The second line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>, its length is no more than <span class=\"tex-span\">4·10<sup class=\"upper-index\">5</sup></span> characters. The string consists of lowercase English letters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the good string that lexicographically follows <span class=\"tex-span\"><i>s</i></span>, has the same length and consists of only lowercase English letters. If such string does not exist, print "<span class=\"tex-font-style-tt\">Impossible</span>" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />aaaaaaa<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>aabbcaa<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />zzyzzzz<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Impossible<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br />abbabbbabbb<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>abbbcaaabab<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=D]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Opening Portals"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Opening Portals</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Pavel plays a famous computer game. A player is responsible for a whole country and he can travel there freely, complete quests and earn experience.</p><p>This country has <span class=\"tex-span\"><i>n</i></span> cities connected by <span class=\"tex-span\"><i>m</i></span> bidirectional roads of different lengths so that it is possible to get from any city to any other one. There are portals in <span class=\"tex-span\"><i>k</i></span> of these cities. At the beginning of the game all portals are closed. When a player visits a portal city, the portal opens. Strange as it is, one can teleport from an open portal to an open one. The teleportation takes no time and that enables the player to travel quickly between rather remote regions of the country.</p><p>At the beginning of the game Pavel is in city number <span class=\"tex-span\">1</span>. He wants to open all portals as quickly as possible. How much time will he need for that?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span>, <span class=\"tex-span\">0 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) that show how many cities and roads are in the game.</p><p>Each of the next <span class=\"tex-span\"><i>m</i></span> lines contains the description of a road as three space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>w</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\">1 ≤ <i>w</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the numbers of the cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road and the time needed to go from one city to the other one by this road. Any two cities are connected by no more than one road. It is guaranteed that we can get from any city to any other one, moving along the roads of the country.</p><p>The next line contains integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>n</i></span>) — the number of portals.</p><p>The next line contains <span class=\"tex-span\"><i>k</i></span> space-separated integers <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></span> — numbers of the cities with installed portals. Each city has no more than one portal.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum time a player needs to open all portals.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in C++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 3<br/>1 2 1<br/>1 3 1<br/>2 3 1<br/>3<br/>1 2 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 3<br/>1 2 1<br/>2 3 5<br/>2 4 10<br/>3<br/>2 3 4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>16<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 3<br/>1 2 1000000000<br/>2 3 1000000000<br/>3 4 1000000000<br/>4<br/>1 2 3 4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3000000000<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the second sample the player has to come to city <span class=\"tex-span\">2</span>, open a portal there, then go to city <span class=\"tex-span\">3</span>, open a portal there, teleport back to city <span class=\"tex-span\">2</span> and finally finish the journey in city <span class=\"tex-span\">4</span>.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"ee61baa54d69712e49a937196cc68dbe\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"6a108ecdc9b42df5b9037e47c442c60d69b57e73\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Disjoint set union\">\r\n dsu\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Graphs\">\r\n graphs\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Shortest paths on weighted and unweighted graphs\">\r\n shortest paths\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *2600\r\n</span>\r\n </div>\n <div 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both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4717\" title=\"Codeforces Round #124 — editorial\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1090:1091\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1081\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1076\" resourceName=\"Discussion\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Обсуждение\" target=\"_blank\">Обсуждение <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1073\" resourceName=\"Обсуждение\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/196\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/196/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/196/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/196/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/196/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/196/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/196/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/196/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem 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}\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"E\" data-uuid=\"ps_566849c7b3af53ad70514f79081d35a79e6e5ef1\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Opening Portals</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Pavel plays a famous computer game. A player is responsible for a whole country and he can travel there freely, complete quests and earn experience.</p><p>This country has <span class=\"tex-span\"><i>n</i></span> cities connected by <span class=\"tex-span\"><i>m</i></span> bidirectional roads of different lengths so that it is possible to get from any city to any other one. There are portals in <span class=\"tex-span\"><i>k</i></span> of these cities. At the beginning of the game all portals are closed. When a player visits a portal city, the portal opens. Strange as it is, one can teleport from an open portal to an open one. The teleportation takes no time and that enables the player to travel quickly between rather remote regions of the country.</p><p>At the beginning of the game Pavel is in city number <span class=\"tex-span\">1</span>. He wants to open all portals as quickly as possible. How much time will he need for that?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 10<sup class=\"upper-index\">5</sup></span>, <span class=\"tex-span\">0 ≤ <i>m</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) that show how many cities and roads are in the game.</p><p>Each of the next <span class=\"tex-span\"><i>m</i></span> lines contains the description of a road as three space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>w</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\">1 ≤ <i>w</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the numbers of the cities connected by the <span class=\"tex-span\"><i>i</i></span>-th road and the time needed to go from one city to the other one by this road. Any two cities are connected by no more than one road. It is guaranteed that we can get from any city to any other one, moving along the roads of the country.</p><p>The next line contains integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>n</i></span>) — the number of portals.</p><p>The next line contains <span class=\"tex-span\"><i>k</i></span> space-separated integers <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></span> — numbers of the cities with installed portals. Each city has no more than one portal.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum time a player needs to open all portals.</p><p>Please, do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in C++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 3<br />1 2 1<br />1 3 1<br />2 3 1<br />3<br />1 2 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 3<br />1 2 1<br />2 3 5<br />2 4 10<br />3<br />2 3 4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>16<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 3<br />1 2 1000000000<br />2 3 1000000000<br />3 4 1000000000<br />4<br />1 2 3 4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3000000000<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the second sample the player has to come to city <span class=\"tex-span\">2</span>, open a portal there, then go to city <span class=\"tex-span\">3</span>, open a portal there, teleport back to city <span class=\"tex-span\">2</span> and finally finish the journey in city <span class=\"tex-span\">4</span>.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=E]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:43</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. 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none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" 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href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Plate Game"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Plate Game</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got a rectangular table with length <span class=\"tex-span\"><i>a</i></span> and width <span class=\"tex-span\"><i>b</i></span> and the infinite number of plates of radius <span class=\"tex-span\"><i>r</i></span>. Two players play the following game: they take turns to put the plates on the table so that the plates don't lie on each other (but they can touch each other), and so that any point on any plate is located within the table's border. During the game one cannot move the plates that already lie on the table. The player who cannot make another move loses. Determine which player wins, the one who moves first or the one who moves second, provided that both players play optimally well.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>A single line contains three space-separated integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(1 ≤ <i>a</i>, <i>b</i>, <i>r</i> ≤ 100)</span> — the table sides and the plates' radius, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If wins the player who moves first, print \"<span class=\"tex-font-style-tt\">First</span>\" (without the quotes). Otherwise print \"<span class=\"tex-font-style-tt\">Second</span>\" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 5 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>First<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 7 4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Second<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the table has place for only one plate. The first player puts a plate on the table, the second player can't do that and loses.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/454f688fd0b73462c71f86bf1de3d9db7f2303e6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center><p>In the second sample the table is so small that it doesn't have enough place even for one plate. 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Constructive algorithms\">\r\n constructive algorithms\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Games, Sprague–Grundy theorem\">\r\n games\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Mathematics including integration, differential equations, etc\">\r\n math\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" 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relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1075\" resourceName=\"Discussion\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Обсуждение\" target=\"_blank\">Обсуждение <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1074\" resourceName=\"Обсуждение\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/197\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/197/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/197/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/197/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/197/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/197/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/197/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/197/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem 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}\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"A\" data-uuid=\"ps_4a11f3085b145ebbceda5ce4d6dd2c86c2726ba0\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Plate Game</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got a rectangular table with length <span class=\"tex-span\"><i>a</i></span> and width <span class=\"tex-span\"><i>b</i></span> and the infinite number of plates of radius <span class=\"tex-span\"><i>r</i></span>. Two players play the following game: they take turns to put the plates on the table so that the plates don't lie on each other (but they can touch each other), and so that any point on any plate is located within the table's border. During the game one cannot move the plates that already lie on the table. The player who cannot make another move loses. Determine which player wins, the one who moves first or the one who moves second, provided that both players play optimally well.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>A single line contains three space-separated integers <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(1 ≤ <i>a</i>, <i>b</i>, <i>r</i> ≤ 100)</span> — the table sides and the plates' radius, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If wins the player who moves first, print "<span class=\"tex-font-style-tt\">First</span>" (without the quotes). Otherwise print "<span class=\"tex-font-style-tt\">Second</span>" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 5 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>First<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 7 4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Second<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the table has place for only one plate. The first player puts a plate on the table, the second player can't do that and loses.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/454f688fd0b73462c71f86bf1de3d9db7f2303e6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center><p>In the second sample the table is so small that it doesn't have enough place even for one plate. So the first player loses without making a single move.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2605d65aca063e9cba7d555b6be2c74da2ea2be0.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=A]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 * 60);\r\n $problem.find(\".diff-notifier\").hide();\r\n });\r\n\r\n $problem.find(\"a.view-changes\").click(function() {\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:43</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/shivam565\" title=\"Specialist shivam565\" class=\"rated-user user-cyan\">shivam565</a> →\r\n <a href=\"/blog/entry/108348\">Total number of subarrays with sum atmost k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n </ul>\r\n </div>\r\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/recent-actions\">Detailed →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n</div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li><a\r\n href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Limit"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Limit</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You are given two polynomials:</p><ul> <li> <span class=\"tex-span\"><i>P</i>(<i>x</i>) = <i>a</i><sub class=\"lower-index\">0</sub>·<i>x</i><sup class=\"upper-index\"><i>n</i></sup> + <i>a</i><sub class=\"lower-index\">1</sub>·<i>x</i><sup class=\"upper-index\"><i>n</i> - 1</sup> + ... + <i>a</i><sub class=\"lower-index\"><i>n</i> - 1</sub>·<i>x</i> + <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> and </li><li> <span class=\"tex-span\"><i>Q</i>(<i>x</i>) = <i>b</i><sub class=\"lower-index\">0</sub>·<i>x</i><sup class=\"upper-index\"><i>m</i></sup> + <i>b</i><sub class=\"lower-index\">1</sub>·<i>x</i><sup class=\"upper-index\"><i>m</i> - 1</sup> + ... + <i>b</i><sub class=\"lower-index\"><i>m</i> - 1</sub>·<i>x</i> + <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. </li></ul> <p>Calculate limit <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/151a1182fb7e3155744251b4e0170112e7c0aff9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">0 ≤ <i>n</i>, <i>m</i> ≤ 100</span>) — degrees of polynomials <span class=\"tex-span\"><i>P</i>(<i>x</i>)</span> and <span class=\"tex-span\"><i>Q</i>(<i>x</i>)</span> correspondingly.</p><p>The second line contains <span class=\"tex-span\"><i>n</i> + 1</span> space-separated integers — the factors of polynomial <span class=\"tex-span\"><i>P</i>(<i>x</i>)</span>: <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i> - 1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> <span class=\"tex-span\">( - 100 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100, <i>a</i><sub class=\"lower-index\">0</sub> ≠ 0)</span>.</p><p>The third line contains <span class=\"tex-span\"><i>m</i> + 1</span> space-separated integers — the factors of polynomial <span class=\"tex-span\"><i>Q</i>(<i>x</i>)</span>: <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub></span>, ..., <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>m</i> - 1</sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>m</i></sub></span> <span class=\"tex-span\">( - 100 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100, <i>b</i><sub class=\"lower-index\">0</sub> ≠ 0)</span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If the limit equals <span class=\"tex-span\"> + ∞</span>, print \"<span class=\"tex-font-style-tt\">Infinity</span>\" (without quotes). If the limit equals <span class=\"tex-span\"> - ∞</span>, print \"<span class=\"tex-font-style-tt\">-Infinity</span>\" (without the quotes).</p><p>If the value of the limit equals zero, print \"<span class=\"tex-font-style-tt\">0/1</span>\" (without the quotes).</p><p>Otherwise, print an irreducible fraction — the value of limit <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/151a1182fb7e3155744251b4e0170112e7c0aff9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>, in the format \"<span class=\"tex-font-style-tt\">p/q</span>\" (without the quotes), where <span class=\"tex-span\"><i>p</i></span> is the — numerator, <span class=\"tex-span\"><i>q</i></span> <span class=\"tex-span\">(<i>q</i> > 0)</span> is the denominator of the fraction.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>2 1<br/>1 1 1<br/>2 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Infinity<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 0<br/>-1 3<br/>2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>-Infinity<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>0 1<br/>1<br/>1 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0/1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2<br/>2 1 6<br/>4 5 -7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1/2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 1<br/>9 0<br/>-5 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>-9/5<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's consider all samples:</p><ol> <li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c28febca257452afdfcbd6984ba8623911f9bdbc.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e55ecd04e54a45e5e0092ec9a5c1ea03bb29255.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2c95fb684d373fcc1a481cfabeda4d5c2f3673ee.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4dc40cb8b3cd6375c42445366e50369649a2801a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c6455aba35cfb3c4397505121d1f77afcd17c98e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </li></ol><p>You can learn more about the definition and properties of limits if you follow the link: <span class=\"tex-font-style-tt\">http://en.wikipedia.org/wiki/Limit_of_a_function</span></p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/197\">Codeforces Round 124 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='0e104ecf7247ec2655e1fa31f96d0e4e'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/197/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Mathematics including integration, differential equations, etc\">\r\n math\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1400\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='0e104ecf7247ec2655e1fa31f96d0e4e'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1430\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='0e104ecf7247ec2655e1fa31f96d0e4e'/>\r\n <input name=\"action\" type=\"hidden\" value=\"removeTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1430\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<script type=\"text/javascript\">\r\n $(\".tag-box img\").click(function () {\r\n var tagName = $(this).attr(\"value\");\r\n Codeforces.confirm(\"Are you sure you want to remove this tag?\", function () {\r\n $(\"#removeTagForm input[name=tagName]\").val(tagName);\r\n $(\"#removeTagForm\").submit();\r\n }, function () {\r\n }, \"Yes\", \"No\");\r\n });\r\n\r\n $(\"#addTagLink\").click(function () {\r\n $(this).hide();\r\n $(\"#addTagLabel\").show();\r\n return false;\r\n });\r\n\r\n $(\"#addTagSelect\").change(function () {\r\n var tagName = $(this).val();\r\n if (tagName === \"\") {\r\n $(\"#addTagLabel\").hide();\r\n $(\"#addTagLink\").show();\r\n } else {\r\n $(\"#addTagForm input[name=tagName]\").val(tagName);\r\n $(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4708\" title=\"Codeforces Round #124\" target=\"_blank\">Codeforces Round #124</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1087:1088\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4717\" title=\"Codeforces Round #124 — editorial\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1092:1093\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1083\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1075\" resourceName=\"Discussion\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Обсуждение\" target=\"_blank\">Обсуждение <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1074\" resourceName=\"Обсуждение\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/197\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/197/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/197/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/197/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/197/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/197/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/197/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/197/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n }\r\n\r\n .testCaseMarker {\r\n position: absolute;\r\n font-weight: bold;\r\n font-size: 1rem;\r\n }\r\n\r\n .diff-popup {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n display: none;\r\n overflow: auto;\r\n }\r\n\r\n .input-output-copier {\r\n font-size: 1.2rem;\r\n float: right;\r\n color: #888 !important;\r\n cursor: pointer;\r\n border: 1px solid rgb(185, 185, 185);\r\n padding: 3px;\r\n margin: 1px;\r\n line-height: 1.1rem;\r\n text-transform: none;\r\n }\r\n\r\n .input-output-copier:hover {\r\n background-color: #def;\r\n }\r\n\r\n .test-explanation textarea {\r\n width: 100%;\r\n height: 1.5em;\r\n }\r\n\r\n .pending-submission-message {\r\n color: darkorange !important;\r\n }\r\n </style>\r\n <script>\r\n const OPENING_SPACE = String.fromCharCode(1001);\r\n const CLOSING_SPACE = String.fromCharCode(1002);\r\n\r\n const nodeToText = function (node, pre) {\r\n let result = [];\r\n\r\n if (node.tagName === \"SCRIPT\" || node.tagName === \"math\"\r\n || (node.classList && node.classList.contains(\"input-output-copier\")))\r\n return [];\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(OPENING_SPACE);\r\n }\r\n\r\n if (node.nodeType === Node.TEXT_NODE) {\r\n let s = node.textContent;\r\n if (!pre) {\r\n s = s.replace(/\\s+/g, \" \");\r\n }\r\n if (s.length > 0) {\r\n result.push(s);\r\n }\r\n }\r\n\r\n if (pre && node.tagName === \"BR\") {\r\n result.push(\"\\n\");\r\n }\r\n\r\n node.childNodes.forEach(function (child) {\r\n result.push(nodeToText(child, node.tagName === \"PRE\").join(\"\"));\r\n });\r\n\r\n if (node.tagName === \"DIV\"\r\n || node.tagName === \"P\"\r\n || node.tagName === \"PRE\"\r\n || node.tagName === \"UL\"\r\n || node.tagName === \"LI\"\r\n ) {\r\n result.push(\"\\n\");\r\n }\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(CLOSING_SPACE);\r\n }\r\n\r\n return result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"B\" data-uuid=\"ps_22f9c0d9e5d879c05ef5378061ddcd5528e1d7a5\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Limit</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You are given two polynomials:</p><ul> <li> <span class=\"tex-span\"><i>P</i>(<i>x</i>) = <i>a</i><sub class=\"lower-index\">0</sub>·<i>x</i><sup class=\"upper-index\"><i>n</i></sup> + <i>a</i><sub class=\"lower-index\">1</sub>·<i>x</i><sup class=\"upper-index\"><i>n</i> - 1</sup> + ... + <i>a</i><sub class=\"lower-index\"><i>n</i> - 1</sub>·<i>x</i> + <i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> and </li><li> <span class=\"tex-span\"><i>Q</i>(<i>x</i>) = <i>b</i><sub class=\"lower-index\">0</sub>·<i>x</i><sup class=\"upper-index\"><i>m</i></sup> + <i>b</i><sub class=\"lower-index\">1</sub>·<i>x</i><sup class=\"upper-index\"><i>m</i> - 1</sup> + ... + <i>b</i><sub class=\"lower-index\"><i>m</i> - 1</sub>·<i>x</i> + <i>b</i><sub class=\"lower-index\"><i>m</i></sub></span>. </li></ul> <p>Calculate limit <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/151a1182fb7e3155744251b4e0170112e7c0aff9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">0 ≤ <i>n</i>, <i>m</i> ≤ 100</span>) — degrees of polynomials <span class=\"tex-span\"><i>P</i>(<i>x</i>)</span> and <span class=\"tex-span\"><i>Q</i>(<i>x</i>)</span> correspondingly.</p><p>The second line contains <span class=\"tex-span\"><i>n</i> + 1</span> space-separated integers — the factors of polynomial <span class=\"tex-span\"><i>P</i>(<i>x</i>)</span>: <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i> - 1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub></span> <span class=\"tex-span\">( - 100 ≤ <i>a</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100, <i>a</i><sub class=\"lower-index\">0</sub> ≠ 0)</span>.</p><p>The third line contains <span class=\"tex-span\"><i>m</i> + 1</span> space-separated integers — the factors of polynomial <span class=\"tex-span\"><i>Q</i>(<i>x</i>)</span>: <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\">1</sub></span>, ..., <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>m</i> - 1</sub></span>, <span class=\"tex-span\"><i>b</i><sub class=\"lower-index\"><i>m</i></sub></span> <span class=\"tex-span\">( - 100 ≤ <i>b</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100, <i>b</i><sub class=\"lower-index\">0</sub> ≠ 0)</span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>If the limit equals <span class=\"tex-span\"> + ∞</span>, print "<span class=\"tex-font-style-tt\">Infinity</span>" (without quotes). If the limit equals <span class=\"tex-span\"> - ∞</span>, print "<span class=\"tex-font-style-tt\">-Infinity</span>" (without the quotes).</p><p>If the value of the limit equals zero, print "<span class=\"tex-font-style-tt\">0/1</span>" (without the quotes).</p><p>Otherwise, print an irreducible fraction — the value of limit <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/151a1182fb7e3155744251b4e0170112e7c0aff9.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, in the format "<span class=\"tex-font-style-tt\">p/q</span>" (without the quotes), where <span class=\"tex-span\"><i>p</i></span> is the — numerator, <span class=\"tex-span\"><i>q</i></span> <span class=\"tex-span\">(<i>q</i> > 0)</span> is the denominator of the fraction.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>2 1<br />1 1 1<br />2 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Infinity<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 0<br />-1 3<br />2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>-Infinity<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>0 1<br />1<br />1 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0/1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2<br />2 1 6<br />4 5 -7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1/2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 1<br />9 0<br />-5 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>-9/5<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's consider all samples:</p><ol> <li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c28febca257452afdfcbd6984ba8623911f9bdbc.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e55ecd04e54a45e5e0092ec9a5c1ea03bb29255.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2c95fb684d373fcc1a481cfabeda4d5c2f3673ee.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/4dc40cb8b3cd6375c42445366e50369649a2801a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </li><li> <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c6455aba35cfb3c4397505121d1f77afcd17c98e.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </li></ol><p>You can learn more about the definition and properties of limits if you follow the link: 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class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Lexicographically Maximum Subsequence"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Lexicographically Maximum Subsequence</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got string <span class=\"tex-span\"><i>s</i></span>, consisting of only lowercase English letters. Find its lexicographically maximum subsequence.</p><p>We'll call a non-empty string <span class=\"tex-span\"><i>s</i>[<i>p</i><sub class=\"lower-index\">1</sub><i>p</i><sub class=\"lower-index\">2</sub>... <i>p</i><sub class=\"lower-index\"><i>k</i></sub>] = <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">1</sub></sub><i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">2</sub></sub>... <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></sub>(1 ≤ <i>p</i><sub class=\"lower-index\">1</sub> < <i>p</i><sub class=\"lower-index\">2</sub> < ... < <i>p</i><sub class=\"lower-index\"><i>k</i></sub> ≤ |<i>s</i>|)</span> a <span class=\"tex-font-style-it\">subsequence</span> of string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\">|<i>s</i>|</sub></span>.</p><p>String <span class=\"tex-span\"><i>x</i> = <i>x</i><sub class=\"lower-index\">1</sub><i>x</i><sub class=\"lower-index\">2</sub>... <i>x</i><sub class=\"lower-index\">|<i>x</i>|</sub></span> is <span class=\"tex-font-style-it\">lexicographically larger</span> than string <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub><i>y</i><sub class=\"lower-index\">2</sub>... <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, if either <span class=\"tex-span\">|<i>x</i>| > |<i>y</i>|</span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\">|<i>y</i>|</sub> = <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, or exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < |<i>x</i>|, <i>r</i> < |<i>y</i>|)</span>, that <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\"><i>r</i></sub> = <i>y</i><sub class=\"lower-index\"><i>r</i></sub></span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>r</i> + 1</sub> > <i>y</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span>. Characters in lines are compared like their ASCII codes.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>, consisting only of lowercase English letters. The string's length doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the lexicographically maximum subsequence of string <span class=\"tex-span\"><i>s</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>ababba<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>bbba<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>abbcbccacbbcbaaba<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>cccccbba<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters).</p><p>The first sample: <span class=\"tex-font-style-tt\">a<span class=\"tex-font-style-bf\">B</span>a<span class=\"tex-font-style-bf\">BBA</span></span></p><p>The second sample: <span class=\"tex-font-style-tt\">abb<span class=\"tex-font-style-bf\">C</span>b<span class=\"tex-font-style-bf\">CC</span>a<span class=\"tex-font-style-bf\">C</span>bb<span class=\"tex-font-style-bf\">CB</span>aa<span class=\"tex-font-style-bf\">BA</span></span></p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"4c1ca0c49a8d2b84d562de729b9dc364\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"f1f7edcdfb9951dff3f0751e3b84a47d6a83f705\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/197\">Codeforces Round 124 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Greedy algorithms\">\r\n greedy\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, simulation\">\r\n implementation\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Sortings, orderings\">\r\n sortings\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Prefix- and Z-functions, 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style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1087:1088\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4717\" title=\"Codeforces Round #124 — editorial\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1092:1093\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1083\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1075\" resourceName=\"Discussion\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Обсуждение\" target=\"_blank\">Обсуждение <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1074\" resourceName=\"Обсуждение\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/197\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/197/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/197/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/197/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/197/hacks\">Hacks</a></li>\r\n <li><a\r\n 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node.tagName === \"LI\"\r\n ) {\r\n result.push(\"\\n\");\r\n }\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(CLOSING_SPACE);\r\n }\r\n\r\n return result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"C\" data-uuid=\"ps_d8ce732919e0ef2f67101ac313b5619f5f47ee2a\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Lexicographically Maximum Subsequence</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got string <span class=\"tex-span\"><i>s</i></span>, consisting of only lowercase English letters. Find its lexicographically maximum subsequence.</p><p>We'll call a non-empty string <span class=\"tex-span\"><i>s</i>[<i>p</i><sub class=\"lower-index\">1</sub><i>p</i><sub class=\"lower-index\">2</sub>... <i>p</i><sub class=\"lower-index\"><i>k</i></sub>] = <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">1</sub></sub><i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\">2</sub></sub>... <i>s</i><sub class=\"lower-index\"><i>p</i><sub class=\"lower-index\"><i>k</i></sub></sub>(1 ≤ <i>p</i><sub class=\"lower-index\">1</sub> < <i>p</i><sub class=\"lower-index\">2</sub> < ... < <i>p</i><sub class=\"lower-index\"><i>k</i></sub> ≤ |<i>s</i>|)</span> a <span class=\"tex-font-style-it\">subsequence</span> of string <span class=\"tex-span\"><i>s</i> = <i>s</i><sub class=\"lower-index\">1</sub><i>s</i><sub class=\"lower-index\">2</sub>... <i>s</i><sub class=\"lower-index\">|<i>s</i>|</sub></span>.</p><p>String <span class=\"tex-span\"><i>x</i> = <i>x</i><sub class=\"lower-index\">1</sub><i>x</i><sub class=\"lower-index\">2</sub>... <i>x</i><sub class=\"lower-index\">|<i>x</i>|</sub></span> is <span class=\"tex-font-style-it\">lexicographically larger</span> than string <span class=\"tex-span\"><i>y</i> = <i>y</i><sub class=\"lower-index\">1</sub><i>y</i><sub class=\"lower-index\">2</sub>... <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, if either <span class=\"tex-span\">|<i>x</i>| > |<i>y</i>|</span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\">|<i>y</i>|</sub> = <i>y</i><sub class=\"lower-index\">|<i>y</i>|</sub></span>, or exists such number <span class=\"tex-span\"><i>r</i></span> <span class=\"tex-span\">(<i>r</i> < |<i>x</i>|, <i>r</i> < |<i>y</i>|)</span>, that <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> = <i>y</i><sub class=\"lower-index\">1</sub>, <i>x</i><sub class=\"lower-index\">2</sub> = <i>y</i><sub class=\"lower-index\">2</sub>, ... , <i>x</i><sub class=\"lower-index\"><i>r</i></sub> = <i>y</i><sub class=\"lower-index\"><i>r</i></sub></span> and <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>r</i> + 1</sub> > <i>y</i><sub class=\"lower-index\"><i>r</i> + 1</sub></span>. Characters in lines are compared like their ASCII codes.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The single line contains a non-empty string <span class=\"tex-span\"><i>s</i></span>, consisting only of lowercase English letters. The string's length doesn't exceed <span class=\"tex-span\">10<sup class=\"upper-index\">5</sup></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the lexicographically maximum subsequence of string <span class=\"tex-span\"><i>s</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>ababba<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>bbba<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>abbcbccacbbcbaaba<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>cccccbba<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Let's look at samples and see what the sought subsequences look like (they are marked with uppercase bold letters).</p><p>The first sample: <span class=\"tex-font-style-tt\">a<span class=\"tex-font-style-bf\">B</span>a<span class=\"tex-font-style-bf\">BBA</span></span></p><p>The second sample: <span class=\"tex-font-style-tt\">abb<span class=\"tex-font-style-bf\">C</span>b<span class=\"tex-font-style-bf\">CC</span>a<span class=\"tex-font-style-bf\">C</span>bb<span class=\"tex-font-style-bf\">CB</span>aa<span class=\"tex-font-style-bf\">BA</span></span></p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, statementText, 6 * 60 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Infinite Maze"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Infinite Maze</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>We've got a rectangular <span class=\"tex-span\"><i>n</i> × <i>m</i></span>-cell maze. Each cell is either passable, or is a wall (impassable). A little boy found the maze and cyclically tiled a plane with it so that the plane became an infinite maze. Now on this plane cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> is a wall if and only if cell <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5820f73507b71bbab0564415ed80476b7cbd4b71.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> is a wall.</p><p>In this problem <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6dd276f849101e7efda6cb8031d4056744d532a1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> is a remainder of dividing number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>The little boy stood at some cell on the plane and he wondered whether he can walk infinitely far away from his starting position. From cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> he can go to one of the following cells: <span class=\"tex-span\">(<i>x</i>, <i>y</i> - 1)</span>, <span class=\"tex-span\">(<i>x</i>, <i>y</i> + 1)</span>, <span class=\"tex-span\">(<i>x</i> - 1, <i>y</i>)</span> and <span class=\"tex-span\">(<i>x</i> + 1, <i>y</i>)</span>, provided that the cell he goes to is not a wall.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 1500</span>) — the height and the width of the maze that the boy used to cyclically tile the plane.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the labyrinth. Each character is either a \"<span class=\"tex-font-style-tt\">#</span>\", that marks a wall, a \"<span class=\"tex-font-style-tt\">.</span>\", that marks a passable cell, or an \"<span class=\"tex-font-style-tt\">S</span>\", that marks the little boy's starting point. </p><p>The starting point is a passable cell. It is guaranteed that character \"<span class=\"tex-font-style-tt\">S</span>\" occurs exactly once in the input.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print \"<span class=\"tex-font-style-tt\">Yes</span>\" (without the quotes), if the little boy can walk infinitely far from the starting point. Otherwise, print \"<span class=\"tex-font-style-tt\">No</span>\" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>##.#<br/>##S#<br/>#..#<br/>#.##<br/>#..#<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Yes<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br/>##.#<br/>##S#<br/>#..#<br/>..#.<br/>#.##<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>No<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the little boy can go up for infinitely long as there is a \"clear path\" that goes vertically. He just needs to repeat the following steps infinitely: up, up, left, up, up, right, up.</p><p>In the second sample the vertical path is blocked. The path to the left doesn't work, too — the next \"copy\" of the maze traps the boy.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"3f17fd4d7ede1a35557735116088d725\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"f1f7edcdfb9951dff3f0751e3b84a47d6a83f705\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1083\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1075\" 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class=\"header\"><div class=\"title\">D. Infinite Maze</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>We've got a rectangular <span class=\"tex-span\"><i>n</i> × <i>m</i></span>-cell maze. Each cell is either passable, or is a wall (impassable). A little boy found the maze and cyclically tiled a plane with it so that the plane became an infinite maze. Now on this plane cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> is a wall if and only if cell <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5820f73507b71bbab0564415ed80476b7cbd4b71.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> is a wall.</p><p>In this problem <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6dd276f849101e7efda6cb8031d4056744d532a1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> is a remainder of dividing number <span class=\"tex-span\"><i>a</i></span> by number <span class=\"tex-span\"><i>b</i></span>.</p><p>The little boy stood at some cell on the plane and he wondered whether he can walk infinitely far away from his starting position. From cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> he can go to one of the following cells: <span class=\"tex-span\">(<i>x</i>, <i>y</i> - 1)</span>, <span class=\"tex-span\">(<i>x</i>, <i>y</i> + 1)</span>, <span class=\"tex-span\">(<i>x</i> - 1, <i>y</i>)</span> and <span class=\"tex-span\">(<i>x</i> + 1, <i>y</i>)</span>, provided that the cell he goes to is not a wall.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two space-separated integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 1500</span>) — the height and the width of the maze that the boy used to cyclically tile the plane.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> characters — the description of the labyrinth. Each character is either a "<span class=\"tex-font-style-tt\">#</span>", that marks a wall, a "<span class=\"tex-font-style-tt\">.</span>", that marks a passable cell, or an "<span class=\"tex-font-style-tt\">S</span>", that marks the little boy's starting point. </p><p>The starting point is a passable cell. It is guaranteed that character "<span class=\"tex-font-style-tt\">S</span>" occurs exactly once in the input.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print "<span class=\"tex-font-style-tt\">Yes</span>" (without the quotes), if the little boy can walk infinitely far from the starting point. Otherwise, print "<span class=\"tex-font-style-tt\">No</span>" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />##.#<br />##S#<br />#..#<br />#.##<br />#..#<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>Yes<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>5 4<br />##.#<br />##S#<br />#..#<br />..#.<br />#.##<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>No<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the little boy can go up for infinitely long as there is a "clear path" that goes vertically. He just needs to repeat the following steps infinitely: up, up, left, up, up, right, up.</p><p>In the second sample the vertical path is blocked. 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:43</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final 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style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div 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title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New 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title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/shivam565\" title=\"Specialist shivam565\" class=\"rated-user user-cyan\">shivam565</a> →\r\n <a href=\"/blog/entry/108348\">Total number of subarrays with sum atmost k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n </ul>\r\n </div>\r\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/recent-actions\">Detailed →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n</div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li><a\r\n href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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Paint Tree"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Paint Tree</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You are given a tree with <span class=\"tex-span\"><i>n</i></span> vertexes and <span class=\"tex-span\"><i>n</i></span> points on a plane, no three points lie on one straight line.</p><p>Your task is to paint the given tree on a plane, using the given points as vertexes. </p><p>That is, you should correspond each vertex of the tree to exactly one point and each point should correspond to a vertex. If two vertexes of the tree are connected by an edge, then the corresponding points should have a segment painted between them. The segments that correspond to non-adjacent edges, should not have common points. The segments that correspond to adjacent edges should have exactly one common point.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains an integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1500</span>) — the number of vertexes on a tree (as well as the number of chosen points on the plane).</p><p>Each of the next <span class=\"tex-span\"><i>n</i> - 1</span> lines contains two space-separated integers <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>) — the numbers of tree vertexes connected by the <span class=\"tex-span\"><i>i</i></span>-th edge.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contain two space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the coordinates of the <span class=\"tex-span\"><i>i</i></span>-th point on the plane. No three points lie on one straight line.</p><p>It is guaranteed that under given constraints problem has a solution.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> distinct space-separated integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>: the <span class=\"tex-span\"><i>i</i></span>-th number must equal the number of the vertex to place at the <span class=\"tex-span\"><i>i</i></span>-th point (the points are numbered in the order, in which they are listed in the input).</p><p>If there are several solutions, print any of them.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>1 3<br/>2 3<br/>0 0<br/>1 1<br/>2 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 3 2<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/>1 2<br/>2 3<br/>1 4<br/>-1 -2<br/>3 5<br/>-3 3<br/>2 0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4 2 1 3<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The possible solutions for the sample are given below.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/184fb6b10b810cafa022514b67b4c8582f76b101.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/183da3ee0eaa5abd757d9c2f724be6c9354f4cd4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"bbdab72c9367622fe5c202b2fd3afbe9\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"f1f7edcdfb9951dff3f0751e3b84a47d6a83f705\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/197\">Codeforces Round 124 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Constructive algorithms\">\r\n constructive algorithms\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Dfs and similar\">\r\n dfs and similar\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Geometry, computational geometry\">\r\n geometry\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Trees\">\r\n 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class=\"delete-resource-link\" resourceIds=\"1087:1088\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4717\" title=\"Codeforces Round #124 — editorial\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1092:1093\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4717\" title=\"Разбор задач\" target=\"_blank\">Разбор задач <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1083\" resourceName=\"Разбор задач\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Discussion\" target=\"_blank\">Discussion <span class=\"resource-locale\">(en)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1075\" resourceName=\"Discussion\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4708\" title=\"Обсуждение\" target=\"_blank\">Обсуждение <span class=\"resource-locale\">(ru)</span></a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1074\" resourceName=\"Обсуждение\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/197\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/197/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/197/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/197/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/197/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/197/room/1\">Room</a></li>\r\n <li><a\r\n 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result.push(\"\\n\");\r\n }\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(CLOSING_SPACE);\r\n }\r\n\r\n return result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"E\" data-uuid=\"ps_52d80e8f0bd16ca64b6a684b392034dc7764c71f\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Paint Tree</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You are given a tree with <span class=\"tex-span\"><i>n</i></span> vertexes and <span class=\"tex-span\"><i>n</i></span> points on a plane, no three points lie on one straight line.</p><p>Your task is to paint the given tree on a plane, using the given points as vertexes. </p><p>That is, you should correspond each vertex of the tree to exactly one point and each point should correspond to a vertex. If two vertexes of the tree are connected by an edge, then the corresponding points should have a segment painted between them. The segments that correspond to non-adjacent edges, should not have common points. The segments that correspond to adjacent edges should have exactly one common point.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains an integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1500</span>) — the number of vertexes on a tree (as well as the number of chosen points on the plane).</p><p>Each of the next <span class=\"tex-span\"><i>n</i> - 1</span> lines contains two space-separated integers <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>u</i><sub class=\"lower-index\"><i>i</i></sub>, <i>v</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\"><i>u</i><sub class=\"lower-index\"><i>i</i></sub> ≠ <i>v</i><sub class=\"lower-index\"><i>i</i></sub></span>) — the numbers of tree vertexes connected by the <span class=\"tex-span\"><i>i</i></span>-th edge.</p><p>Each of the next <span class=\"tex-span\"><i>n</i></span> lines contain two space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the coordinates of the <span class=\"tex-span\"><i>i</i></span>-th point on the plane. No three points lie on one straight line.</p><p>It is guaranteed that under given constraints problem has a solution.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>n</i></span> distinct space-separated integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>: the <span class=\"tex-span\"><i>i</i></span>-th number must equal the number of the vertex to place at the <span class=\"tex-span\"><i>i</i></span>-th point (the points are numbered in the order, in which they are listed in the input).</p><p>If there are several solutions, print any of them.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />1 3<br />2 3<br />0 0<br />1 1<br />2 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 3 2<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br />1 2<br />2 3<br />1 4<br />-1 -2<br />3 5<br />-3 3<br />2 0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4 2 1 3<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The possible solutions for the sample are given below.</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/184fb6b10b810cafa022514b67b4c8582f76b101.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/183da3ee0eaa5abd757d9c2f724be6c9354f4cd4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=E]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='e902c8fae1b678275954d99fcdf3c357'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" 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href=\"/profile/Hohol\">Hohol</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Hohol\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Hohol\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Hohol\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Hohol\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Hohol\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Hohol\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Hohol\" style=\"text-decoration:none;color:black !important;\">Hohol's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4731\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4717\"> <p>Codeforces Round #124 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Hohol\" title=\"Candidate Master Hohol\" class=\"rated-user user-violet\">Hohol</a>,\r\n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"/contest/197/problem/A\" title=\"Codeforces Round 124 (Div. 2)\">197A - Plate Game</a></p><p>If first player can't make first move (table is too small and plate doesn't fit it, i.e. <span class=\"tex-span\">2<i>r</i> > <i>min</i>(<i>a</i>, <i>b</i>)</span>), second player wins. Else first player wins. Winning strategy for first player: place first plate to the center of table. After that he symmetrically reflects moves of second player with respect to center of table. If second player has move, first player has symmetrical move, too. If not, first player won.</p><p><a href=\"/contest/197/problem/B\" title=\"Codeforces Round 124 (Div. 2)\">197B - Limit</a></p><p>From math lessons we know, that only higher degrees of polinomials matter in this problem.</p> <ol> <li>If denominator degree is larger than numenator degree, answer is "0/1".</li> <li>If numenator degree is larger, answer is infinity. But what is sign of this infinity? To get it consider signs of highest degree factors of polinomials. If they are same, answer is positive infinity, else — negative infinity.</li> <li>If degrees of numenator and denominator are equal, answer is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5619182fdfdf201b5c960a318fb6de715413d8f4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. To get irreducible fraction, you should divide this numbers by <span class=\"tex-span\"><i>gcd</i>(<i>a</i><sub class=\"lower-index\">0</sub>, <i>b</i><sub class=\"lower-index\">0</sub>)</span>. And don't forget that denominator of answer must be positive.</li> </ol><p><a href=\"/contest/196/problem/A\" title=\"Codeforces Round 124 (Div. 1)\">196A - Lexicographically Maximum Subsequence</a></p><p>Solution is greedy. First, write all 'z' letters (if there is any) — answer must contain them all for sure. Now it's time for 'y' letters. We can use only those of them which are on the right of last used 'z' letter. Then write 'x' letters — they must be on the right of the last used 'y' and 'z' letters. And so on.</p><p><a href=\"/contest/196/problem/B\" title=\"Codeforces Round 124 (Div. 1)\">196B - Infinite Maze</a></p><p>Answer is "Yes" iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth. </p><p>Proof: If these cells exist, move to first of them, and infinitely repeat moves leading from first to second. On the contrary, if infinite far path exist, on this path we obviously can find such cells.</p><p>How to find out if they exist? Start DFS from initial cell. For each cell visited, let <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>] = (<i>x</i>, <i>y</i>)</span>. Now, if DFS tries to go to cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>, <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span> contains something, and <span class=\"tex-span\">(<i>x</i>, <i>y</i>) ≠ <i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>, we found these cells: they are <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and <span class=\"tex-span\"><i>visit</i>[<i>x</i>%<i>n</i>][<i>y</i>%<i>m</i>]</span>. Notice that DFS will visit no more than <span class=\"tex-span\"><i>nm</i> + 1</span> cells (Dirichlet's principle). So the asymptotic is <span class=\"tex-span\"><i>O</i>(<i>nm</i>)</span>.</p><p><a href=\"/contest/196/problem/C\" title=\"Codeforces Round 124 (Div. 1)\">196C - Paint Tree</a></p><p>No three points are in the same line, so the solution always exists.</p><p>First, choose any one vertex as the root of tree. Find size of each subtree using dfs.</p><p>Then, we can build the answer recursively.</p><p>Put the root of tree to the most lower left point.</p><p>Sort all other points by angle relative to this lower left point.</p><p>Let us name the sizes of subtrees of the root as <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\"><i>k</i></sub></span>.</p><p>Run the algorithm recursively, giving first <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">1</sub></span> points (in sorted order) for the first subtree of root, next <span class=\"tex-span\"><i>s</i><sub class=\"lower-index\">2</sub></span> points for the second subtree and so on.</p><p>Obviously, no two edges from different subtrees can intersect now.</p><p>At each step of recursion we are to put the root of current subtree to the first point in sorted-by-angle order, and then sort other points by angle relative to it.</p><p>So, no two subtrees will have any intersecting edges.</p><p>The asymptotic of solution is <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/08a5dbb1ac845802fdbad24f72be3ff1e5b3d340.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p><a href=\"/contest/196/problem/D\" title=\"Codeforces Round 124 (Div. 1)\">196D - The Next Good String</a></p><p>Notice, that only palindromes with length <span class=\"tex-span\"><i>d</i></span> and <span class=\"tex-span\"><i>d</i> + 1</span> matter. Any palindrome with greater length contains one of them. Let's call these palindromes bad.</p><p>First, find leftmost position <span class=\"tex-span\"><i>pos</i></span>, in which we surely should increase value of symbol. If there are no bad subpalindromes, <span class=\"tex-span\"><i>pos</i> = |<i>s</i>| - 1</span>, else <span class=\"tex-span\"><i>pos</i></span> is leftmost position amongst all ends of bad palindromes.</p><p>Increase <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span>. Increase it more, while <span class=\"tex-span\"><i>s</i>[<i>pos</i>]</span> is end of bad subpalindrome. If you try increase 'z' symbol, you should proceed to increasing previous symbol. If this way you reached situation when you need to increase first symbol, and it is 'z', answer is "Impossible".</p><p>Now, let pos be position of leftmost changed symbol. We know, that prefix <span class=\"tex-span\"><i>s</i>[0..<i>pos</i>]</span> doesn't contain bad palindromes. Now we can greedily fill suffix <span class=\"tex-span\"><i>s</i>[<i>pos</i> + 1..<i>length</i>(<i>s</i>) - 1]</span>: go over positions <span class=\"tex-span\"><i>i</i></span> in ascending order, assign <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> = 'a', and increase it, while <span class=\"tex-span\"><i>s</i>[<i>i</i>]</span> is end of bad palindrome. Obviously, any of suffix symbols will be 'a', 'b' or 'c'.</p><p>So we got algorithm, which requires fast implementation of next operations — assigning single symbol, and query: is given substring palindrome? You can perform this operations using hashes and Fenwick tree.</p><p>Let's learn, how to get hash of substring in dynamically changing string. If we can it, we will keep string <span class=\"tex-span\"><i>s</i></span> and it's reversed copy. For query of second type we just need to compare hashes of substring in <span class=\"tex-span\"><i>s</i></span> and hash of corresponding substring in reversed copy.</p><p>Let Fenwick tree store values <span class=\"tex-span\"><i>h</i>[<i>i</i>] = <i>s</i>[<i>i</i>]<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span>, where <span class=\"tex-span\"><i>P</i></span> is the prime number used for hashing. Then hash of substring <span class=\"tex-span\"><i>s</i>[<i>L</i>..<i>R</i>]</span> equals to <span class=\"tex-span\">(<i>h</i>[<i>L</i>] + <i>h</i>[<i>L</i> + 1] + ...<i>h</i>[<i>R</i>])<i>P</i><sup class=\"upper-index\"> - <i>L</i></sup></span>. For assigning <span class=\"tex-span\"><i>s</i>[<i>i</i>] = <i>c</i></span>, add value <span class=\"tex-span\">(<i>c</i> - <i>s</i>[<i>i</i>])<i>P</i><sup class=\"upper-index\"><i>i</i></sup></span> to <span class=\"tex-span\"><i>h</i>[<i>i</i>]</span>. Both these operations Fenwick tree does in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e864584c28b3beb52a5d9a7cbbcda3d80a9d4515.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Also we have faster solution without hashes and data structures, it will be published soon.</p><p><a href=\"/contest/196/problem/E\" title=\"Codeforces Round 124 (Div. 1)\">196E - Opening Portals</a></p><p>First of all, we can note that if each graph vertex is portal, the answer will be a sum of all edges' weights in MST (minimal spanning tree). We can find MST by using Kruskal's algo.</p><p>In this problem, not an every vertex is portal. Let's fix this.</p><p>Start with a precalculation. Run Dijkstra's algo from all the portals, simultaneously. We will get <span class=\"tex-span\"><i>d</i>[<i>i</i>]</span> — a distance between vertex <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> — the nearest portal to vertex <span class=\"tex-span\"><i>i</i></span>.</p><p>Let's trace Kruskal's algo on a graph of portals. On the first iteration, it will choose the edge with the minimal cost, i.e. a shortest path between all the portals in the original graph.</p><p>Let the path leads from portal <span class=\"tex-span\"><i>x</i></span> to portal <span class=\"tex-span\"><i>y</i></span>. Note that there exists a path with the same length such as <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changes only once through it. Indeed, <span class=\"tex-span\"><i>p</i>[<i>x</i>] = <i>x</i></span>, <span class=\"tex-span\"><i>p</i>[<i>y</i>] = <i>y</i></span>, i.e. <span class=\"tex-span\"><i>p</i>[<i>i</i>]</span> changed on the path. If it happens on edge <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c59da485d3a4e463f0157335ace916b7c377dcd8.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span>, a path <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a97c0e87443330fae5983a268b019ee0d7b03a9c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> will not be longer than the path from <span class=\"tex-span\"><i>x</i></span> to <span class=\"tex-span\"><i>y</i></span>.</p><p>As <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>x</i></span> and <span class=\"tex-span\"><i>p</i>[<i>i</i>] = <i>y</i></span>, we can see that the length of this path will be <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span>, where <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> is the weight of edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>. Kruskal's algo will add this value to the answer and merge portals <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>. The shortest-path trees of vertexes <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> will also be merged.</p><p>Note, that almost nothing changed. The next edge for Kruskal's algo can be find in a similar way — <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/9fbdc4078a8b3f752e24c4371823ba7df8e584d3.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. If this edge connects <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> again, DSU makes us not to count this edge, otherwise this edge connects a different pair of edges and will be counted in an answer.</p><p>We can easily implement this. Just create a new graph of portals, with an edge <span class=\"tex-span\">(<i>p</i>[<i>i</i>], <i>p</i>[<i>j</i>])</span> of weight <span class=\"tex-span\"><i>d</i>[<i>i</i>] + <i>w</i>(<i>i</i>, <i>j</i>) + <i>d</i>[<i>j</i>]</span> for every edge <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> of weight <span class=\"tex-span\"><i>w</i>(<i>i</i>, <i>j</i>)</span> from original graph and run Kruskal's algo.</p><p>Finally, note that if the starting vertex is not a portal, we shall add <span class=\"tex-span\"><i>d</i>[1]</span> to the answer.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/196\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/197\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 124 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-5478-4731\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"5478\",\n blogEntryId: \"4717\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+round+%23124\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces round #124</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+59</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4731\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Hohol\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Hohol\">\n Hohol\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/14/2012 00:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4717#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4717#comments\">\n 19\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4741\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (18)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96341\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ivan100sic\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/26422/avatar/611ce74705dadb74.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/ivan100sic\" title=\"International Grandmaster ivan100sic\" class=\"rated-user user-red\">ivan100sic</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 02:16\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96341\" href=\"?#comment-96341\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96341\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"32\"\r\n data-commentUserId=\"26422\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+32</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96341\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks a lot! I suggest another simple solution for the 196A / 197C task. Scan the input string S from right-1 to left and add the character S[i] to the solution if it is larger than or equal to the previously added character. Initially, add the last character of S to the solution. Adding a character means appending it to the left side of the existing solution.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96341 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96341 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96341\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96344\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:29\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96344\" href=\"?#comment-96344\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96344\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"2\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+2</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96344\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>This is a really perfect idea. I've implemented it (<a href=\"/contest/196/submission/1801617\" title=\"Посылка 1801617 от I_love_natalia\">1801617</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96344 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96344 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96344\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96345\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_natalia\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1362/avatar/c87b49ba7e34992.jpg'/> </a>\n <div><a href=\"/profile/I_love_natalia\" title=\"Master I_love_natalia\" class=\"rated-user user-orange\">I_love_natalia</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 04:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96345\" href=\"?#comment-96345\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96345\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96345\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>As an exercise: following this idea, calculate <span class=\"tex-span\"><i>q</i> ≤ 10<sup class=\"upper-index\">5</sup></span> queries for a standard polynomial hash <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1d7421b5fa10a777967a90222a502bca4658443f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of the answer on substring <span class=\"tex-span\"><i>s</i>[<i>i</i>..<i>j</i>]</span> (prime <span class=\"tex-span\"><i>p</i></span> is given).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96345 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96345 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96345\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96365\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nuptxxp\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/54970/avatar/d9e57237229fe146.jpg'/> </a>\n <div><a href=\"/profile/nuptxxp\" title=\"Specialist nuptxxp\" class=\"rated-user user-cyan\">nuptxxp</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 19:24\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96365\" href=\"?#comment-96365\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96365\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"5\"\r\n data-commentUserId=\"54970\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+5</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96365\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i've no idea of your exercise,i think each query of the standard polynomial hash can be caculatored by O(j-i)(that i scan it from i to j). Could there be better solution like the problem C's solution?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96365 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96365 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96365\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96392\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:36\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96392\" href=\"?#comment-96392\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96392\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96392\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Nice problem! I think we can sort the query first, and something like two pointers will work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96392 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96392 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96392\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96393\" commentParentId=\"96392\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Captain_CoCo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/24274/avatar/c68b193c7dd691e8.jpg'/> </a>\n <div><a href=\"/profile/Captain_CoCo\" title=\"Candidate Master Captain_CoCo\" class=\"rated-user user-violet\">Captain_CoCo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:44\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96393\" href=\"?#comment-96393\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96392\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96393\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"24274\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96393\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry! Two pointers seemed doesn't work, we need a binary search, the total complexity is O(n*log(n)), can it be better?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96393 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96393 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96393\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96394\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/riadwaw\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/8452/avatar/7b374574b05a50df.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/riadwaw\" title=\"International Master riadwaw\" class=\"rated-user user-orange\">riadwaw</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 11:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96394\" href=\"?#comment-96394\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96394\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96394\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"8452\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96394\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>nevermind</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96394 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96394 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96394\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96395\" commentParentId=\"96394\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/steiner\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/202/avatar/404d2570151edf35.jpg'/> </a>\n <div><a href=\"/profile/steiner\" title=\"Master steiner\" class=\"rated-user user-orange\">steiner</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96395\" href=\"?#comment-96395\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96394\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96395\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"13\"\r\n data-commentUserId=\"202\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+13</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96395\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>...of the <strong>answer</strong> on substring s[i..j]</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96395 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96395 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96395\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96397\" commentParentId=\"96345\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/al13n\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/2362/avatar/cd08b84008332431.jpg'/> </a>\n <div><a href=\"/profile/al13n\" title=\"Grandmaster al13n\" class=\"rated-user user-red\">al13n</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/15/2012 12:54\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96397\" href=\"?#comment-96397\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96345\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96397\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96397\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"2362\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96397\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have a solution and I wonder if there's a simpler one. The solution is in rev. 1.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96397 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96397 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96397\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96790\" commentParentId=\"96341\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/ameydhar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/6967/avatar/ef616b1a6f15901f.jpg'/> </a>\n <div><a href=\"/profile/ameydhar\" title=\"Specialist ameydhar\" class=\"rated-user user-cyan\">ameydhar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/18/2012 16:33\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96790\" href=\"?#comment-96790\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96341\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96790\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6967\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96790\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I also coded a similar solution using pairs here (<a href=\"//codeforces.com/contest/197/submission/1793816\">1793816</a>).</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96790 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96790 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96790\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96347\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/PraveenDhinwa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/21525/avatar/90c91732411201a0.jpg'/> </a>\n <div><a href=\"/profile/PraveenDhinwa\" title=\"Expert PraveenDhinwa\" class=\"rated-user user-blue\">PraveenDhinwa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 07:50\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96347\" href=\"?#comment-96347\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96347\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"21525\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96347\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I am unable to understand this statement , Anybody please help me with this.</p><p>Answer is “Yes” iff there are two distinct, reachable from start position cells, which correspond to same cell in initial labyrinth.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96347 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96347 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96347\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96349\" commentParentId=\"96347\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/tunyash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/5760/avatar/292b88a0f581f65d.jpg'/> </a>\n <div><a href=\"/profile/tunyash\" title=\"Master tunyash\" class=\"rated-user user-orange\">tunyash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/14/2012 09:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96349\" href=\"?#comment-96349\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96347\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96349\" revisionCount=\"4\" revision=\"4\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">4</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96349\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"5760\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96349\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There are two cells <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span> and <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span> satisfying these conditions:</p> <ul> <li>(<span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">1</sub> ≠ <i>x</i><sub class=\"lower-index\">2</sub></span> or <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">1</sub> ≠ <i>y</i><sub class=\"lower-index\">2</sub></span>)</li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/a77adc872771297462865d7be398f89f27bd7578.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></li> <li><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d963eaf7d9b877294b894d0bbb64bf79bf51ca24.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</li> </ul></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96349 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96349 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96349\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96846\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Neil\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/41097/avatar/70480d1c9ca0ba3d.jpg'/> </a>\n <div><a href=\"/profile/Neil\" title=\"Master Neil\" class=\"rated-user user-orange\">Neil</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 05:25\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96846\" href=\"?#comment-96846\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96846\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"41097\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96846\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>How do you get that solution for Paint Tree to run in time? My implementation, <a href=\"//codeforces.com/contest/196/submission/1809672\">http://codeforces.com/contest/196/submission/1809672</a>, keeps getting TLE, and I don't know how to optimize it. Besides, O(n^2*logn) should be too slow for n=1500 shouldn't it?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96846 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96846 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96846\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96858\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dalex\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/4200/avatar/fe9bfc44be854399.jpg'/> </a>\n <div><a href=\"/profile/dalex\" title=\"Master dalex\" class=\"rated-user user-orange\">dalex</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/19/2012 11:51\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96858\" href=\"?#comment-96858\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"96858\" revisionCount=\"2\" revision=\"2\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">2</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"96858\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"4200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96858\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><ol> <li>Try to use sort instead of qsort.</li> <li>Use wedge product to compare points, it can be calculated in integers, it is faster and doesn't have presicion problems.</li> </ol></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96858 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96858 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96858\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"96922\" commentParentId=\"96846\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Zip753\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/50582/avatar/f06955b6835f5801.jpg'/> </a>\n <div><a href=\"/profile/Zip753\" title=\"Candidate Master Zip753\" class=\"rated-user user-violet\">Zip753</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/20/2012 10:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-96922\" href=\"?#comment-96922\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-96846\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"96922\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"50582\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-96922\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Your angle_comp works too long. Try to rewrite it in a simple way, not using cmath library. I got the same trouble <a href=\"/contest/197/submission/1810718\" title=\"Посылка 1810718 от Zip753\">1810718</a>, but then I rewrote operator< for points and it passed! <a href=\"/contest/197/submission/1810730\" title=\"Посылка 1810730 от Zip753\">1810730</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-96922 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-96922 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-96922\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"255722\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Arpa\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/124237/avatar/bb527f3e70763938.jpg'/> </a>\n <div><a href=\"/profile/Arpa\" title=\"International Master Arpa\" class=\"rated-user user-orange\">Arpa</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/11/2015 07:40\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-255722\" href=\"?#comment-255722\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n <span style=\"\" commentId=\"255722\" revisionCount=\"3\" revision=\"3\">\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;color:#bebebe;\" class=\"leftRevision\">←</a>\r\n Rev. <span class=\"revision\">3</span>\r\n <a href=\"#\" style=\"text-decoration:none;font-size:1.4rem;visibility:hidden;color:#bebebe;\" class=\"rightRevision\">→</a>\r\n </span>\r\n \r\n\r\n<span commentid=\"255722\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"124237\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-255722\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I have one other idea for 196C:</p><p>we have DFS function like this:</p> <pre><code>DFS(vertex v,vertex par){\n for every child of v (like u) do:\n search for point (like p) that flag[p]==false and angle between (point[par],point[v],p) is maximum;\n point[u]=p;\n flag[p]=true;\n DFS(u,v);\n}\n</code></pre><p>set point[1]:the most lower left point. and set point[1512].x=-10^9-7,point[1512].y=point[1].y.</p><p>set flag[point[1]]=true;</p><p>call DFS(1,1512);</p><p>and then answer is ready with O(N^2). but a little problem is here, my code gets WA!! <a href=\"//codeforces.com/contest/196/submission/13539873\">link</a></p><p>why? help me please.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-255722 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-255722 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-255722\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"653792\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/towrist\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1183708/avatar/b56bbf103a0c9a5d.jpg'/> </a>\n <div><a href=\"/profile/towrist\" title=\"Master towrist\" class=\"rated-user user-orange\">towrist</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2020 11:21\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-653792\" href=\"?#comment-653792\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"653792\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1183708\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-653792\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In problem B (Division 1) or problem D (Division 2):</p><p>Why does using set give TLE? The size of the set is $$$O(nm)$$$.</p><p>MLE-> <a href=\"/contest/196/submission/85574647\" title=\"Посылка 85574647 от towrist\">85574647</a> AC-> <a href=\"/contest/196/submission/85576009\" title=\"Посылка 85576009 от towrist\">85576009</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-653792 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-653792 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-653792\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"835765\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/drinkWater.\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/561697/avatar/ca6de1a9f6850289.jpg'/> </a>\n <div><a href=\"/profile/drinkWater.\" title=\"Specialist drinkWater.\" class=\"rated-user user-cyan\">drinkWater.</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/04/2021 11:11\">2 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-835765\" href=\"?#comment-835765\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"835765\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"-8\"\r\n data-commentUserId=\"561697\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">-8</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-835765\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Video tutorial for Div1A, Link: <a href=\"https://youtu.be/AH8za0dvSu8\">https://youtu.be/AH8za0dvSu8</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-835765 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-835765 en false\" 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About Bacteria"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. About Bacteria</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high.</p><p>At the beginning of the first experiment there is a single bacterium in the test tube. Every second each bacterium in the test tube divides itself into <span class=\"tex-span\"><i>k</i></span> bacteria. After that some abnormal effects create <span class=\"tex-span\"><i>b</i></span> more bacteria in the test tube. Thus, if at the beginning of some second the test tube had <span class=\"tex-span\"><i>x</i></span> bacteria, then at the end of the second it will have <span class=\"tex-span\"><i>kx</i> + <i>b</i></span> bacteria.</p><p>The experiment showed that after <span class=\"tex-span\"><i>n</i></span> seconds there were exactly <span class=\"tex-span\"><i>z</i></span> bacteria and the experiment ended at this point.</p><p>For the second experiment Qwerty is going to sterilize the test tube and put there <span class=\"tex-span\"><i>t</i></span> bacteria. He hasn't started the experiment yet but he already wonders, how many seconds he will need to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria. The ranger thinks that the bacteria will divide by the same rule as in the first experiment. </p><p>Help Qwerty and find the minimum number of seconds needed to get a tube with at least <span class=\"tex-span\"><i>z</i></span> bacteria in the second experiment.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains four space-separated integers <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i>, <i>b</i>, <i>n</i>, <i>t</i> ≤ 10<sup class=\"upper-index\">6</sup>)</span> — the parameters of bacterial growth, the time Qwerty needed to grow <span class=\"tex-span\"><i>z</i></span> bacteria in the first experiment and the initial number of bacteria in the second experiment, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum number of seconds Qwerty needs to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria in the tube.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 3 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 4 4 7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2 4 100<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0</pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"d15edae2eb417e941967775aecc11880\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - A - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"e96757dee4fc76030642cb76498103c316919191\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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</div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. About Bacteria</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high.</p><p>At the beginning of the first experiment there is a single bacterium in the test tube. Every second each bacterium in the test tube divides itself into <span class=\"tex-span\"><i>k</i></span> bacteria. After that some abnormal effects create <span class=\"tex-span\"><i>b</i></span> more bacteria in the test tube. Thus, if at the beginning of some second the test tube had <span class=\"tex-span\"><i>x</i></span> bacteria, then at the end of the second it will have <span class=\"tex-span\"><i>kx</i> + <i>b</i></span> bacteria.</p><p>The experiment showed that after <span class=\"tex-span\"><i>n</i></span> seconds there were exactly <span class=\"tex-span\"><i>z</i></span> bacteria and the experiment ended at this point.</p><p>For the second experiment Qwerty is going to sterilize the test tube and put there <span class=\"tex-span\"><i>t</i></span> bacteria. He hasn't started the experiment yet but he already wonders, how many seconds he will need to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria. The ranger thinks that the bacteria will divide by the same rule as in the first experiment. </p><p>Help Qwerty and find the minimum number of seconds needed to get a tube with at least <span class=\"tex-span\"><i>z</i></span> bacteria in the second experiment.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains four space-separated integers <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i>, <i>b</i>, <i>n</i>, <i>t</i> ≤ 10<sup class=\"upper-index\">6</sup>)</span> — the parameters of bacterial growth, the time Qwerty needed to grow <span class=\"tex-span\"><i>z</i></span> bacteria in the first experiment and the initial number of bacteria in the second experiment, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum number of seconds Qwerty needs to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria in the tube.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 3 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 4 4 7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2 4 100<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0</pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=A]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:40</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final 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style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div 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title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New 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title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Jumping on Walls"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Jumping on Walls</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Vasya plays a computer game with ninjas. At this stage Vasya's ninja should get out of a deep canyon.</p><p>The canyon consists of two vertical parallel walls, their height is <span class=\"tex-span\"><i>n</i></span> meters. Let's imagine that we split these walls into <span class=\"tex-span\">1</span> meter-long areas and number them with positive integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from bottom to top. Some areas are safe and the ninja can climb them. Others are spiky and ninja can't be there. Let's call such areas <span class=\"tex-font-style-it\">dangerous</span>.</p><p>Initially the ninja is on the lower area of the left wall. He can use each second to perform one of the following actions: </p><ul> <li> climb one area up; </li><li> climb one area down; </li><li> jump to the opposite wall. That gets the ninja to the area that is exactly <span class=\"tex-span\"><i>k</i></span> meters higher than the area he jumped from. More formally, if before the jump the ninja is located at area <span class=\"tex-span\"><i>x</i></span> of one wall, then after the jump he is located at area <span class=\"tex-span\"><i>x</i> + <i>k</i></span> of the other wall. </li></ul><p>If at some point of time the ninja tries to get to an area with a number larger than <span class=\"tex-span\"><i>n</i></span>, then we can assume that the ninja got out of the canyon.</p><p>The canyon gets flooded and each second the water level raises one meter. Initially the water level is at the lower border of the first area. Ninja cannot be on the area covered by water. We can assume that the ninja and the water \"move in turns\" — first the ninja performs some action, then the water raises for one meter, then the ninja performs one more action and so on.</p><p>The level is considered completed if the ninja manages to get out of the canyon.</p><p>After several failed attempts Vasya started to doubt whether it is possible to complete the level at all. Help him answer the question.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the height of the canyon and the height of ninja's jump, correspondingly.</p><p>The second line contains the description of the left wall — a string with the length of <span class=\"tex-span\"><i>n</i></span> characters. The <span class=\"tex-span\"><i>i</i></span>-th character represents the state of the <span class=\"tex-span\"><i>i</i></span>-th wall area: character \"<span class=\"tex-font-style-tt\">X</span>\" represents a dangerous area and character \"<span class=\"tex-font-style-tt\">-</span>\" represents a safe area.</p><p>The third line describes the right wall in the same format.</p><p>It is guaranteed that the first area of the left wall is not dangerous.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print \"<span class=\"tex-font-style-tt\">YES</span>\" (without the quotes) if the ninja can get out from the canyon, otherwise, print \"<span class=\"tex-font-style-tt\">NO</span>\" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>7 3<br/>---X--X<br/>-X--XX-<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 2<br/>--X-X-<br/>X--XX-<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the ninja should first jump to the right wall, then go one meter down along the right wall, then jump to the left wall. The next jump can get the ninja from the canyon. </p><p>In the second sample there's no way the ninja can get out of the canyon.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"91e239283404f178412c5a3610fdc092\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"e96757dee4fc76030642cb76498103c316919191\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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if (node.tagName === \"DIV\"\r\n || node.tagName === \"P\"\r\n || node.tagName === \"PRE\"\r\n || node.tagName === \"UL\"\r\n || node.tagName === \"LI\"\r\n ) {\r\n result.push(\"\\n\");\r\n }\r\n\r\n if (node.tagName === \"NOBR\") {\r\n result.push(CLOSING_SPACE);\r\n }\r\n\r\n return result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"B\" data-uuid=\"ps_13e6ea712ba384cb5e0af5ce738e68dbf141997f\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Jumping on Walls</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Vasya plays a computer game with ninjas. At this stage Vasya's ninja should get out of a deep canyon.</p><p>The canyon consists of two vertical parallel walls, their height is <span class=\"tex-span\"><i>n</i></span> meters. Let's imagine that we split these walls into <span class=\"tex-span\">1</span> meter-long areas and number them with positive integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from bottom to top. Some areas are safe and the ninja can climb them. Others are spiky and ninja can't be there. Let's call such areas <span class=\"tex-font-style-it\">dangerous</span>.</p><p>Initially the ninja is on the lower area of the left wall. He can use each second to perform one of the following actions: </p><ul> <li> climb one area up; </li><li> climb one area down; </li><li> jump to the opposite wall. That gets the ninja to the area that is exactly <span class=\"tex-span\"><i>k</i></span> meters higher than the area he jumped from. More formally, if before the jump the ninja is located at area <span class=\"tex-span\"><i>x</i></span> of one wall, then after the jump he is located at area <span class=\"tex-span\"><i>x</i> + <i>k</i></span> of the other wall. </li></ul><p>If at some point of time the ninja tries to get to an area with a number larger than <span class=\"tex-span\"><i>n</i></span>, then we can assume that the ninja got out of the canyon.</p><p>The canyon gets flooded and each second the water level raises one meter. Initially the water level is at the lower border of the first area. Ninja cannot be on the area covered by water. We can assume that the ninja and the water "move in turns" — first the ninja performs some action, then the water raises for one meter, then the ninja performs one more action and so on.</p><p>The level is considered completed if the ninja manages to get out of the canyon.</p><p>After several failed attempts Vasya started to doubt whether it is possible to complete the level at all. Help him answer the question.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the height of the canyon and the height of ninja's jump, correspondingly.</p><p>The second line contains the description of the left wall — a string with the length of <span class=\"tex-span\"><i>n</i></span> characters. The <span class=\"tex-span\"><i>i</i></span>-th character represents the state of the <span class=\"tex-span\"><i>i</i></span>-th wall area: character "<span class=\"tex-font-style-tt\">X</span>" represents a dangerous area and character "<span class=\"tex-font-style-tt\">-</span>" represents a safe area.</p><p>The third line describes the right wall in the same format.</p><p>It is guaranteed that the first area of the left wall is not dangerous.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print "<span class=\"tex-font-style-tt\">YES</span>" (without the quotes) if the ninja can get out from the canyon, otherwise, print "<span class=\"tex-font-style-tt\">NO</span>" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>7 3<br />---X--X<br />-X--XX-<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 2<br />--X-X-<br />X--XX-<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the ninja should first jump to the right wall, then go one meter down along the right wall, then jump to the left wall. 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:40</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final 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style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div 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title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New 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title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Delivering Carcinogen"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Delivering Carcinogen</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen.</p><p>You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point <span class=\"tex-span\">(0, 0)</span>. Persephone goes round Diatar along a circular orbit with radius <span class=\"tex-span\"><i>R</i></span> in the counter-clockwise direction at constant linear speed <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (thus, for instance, a full circle around the star takes <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6e148f5854d1671a9c65876c849623c94d511d4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> of time). At the initial moment of time Persephone is located at point <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub>)</span>.</p><p>At the initial moment of time Qwerty's ship is at point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Qwerty can move in any direction at speed of at most <span class=\"tex-span\"><i>v</i></span> (<span class=\"tex-span\"><i>v</i> > <i>v</i><sub class=\"lower-index\"><i>p</i></sub></span>). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"><i>r</i> < <i>R</i></span>) from the star.</p><p>Find the minimum time Qwerty needs to get the carcinogen to planet Persephone.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>p</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>p</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>v</i><sub class=\"lower-index\"><i>p</i></sub> < 10<sup class=\"upper-index\">4</sup></span>) — Persephone's initial position and the speed at which it goes round Diatar.</p><p>The second line contains space-separated integers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>v</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 < <i>v</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>r</i> ≤ 10<sup class=\"upper-index\">4</sup></span>) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar.</p><p>It is guaranteed that <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sup class=\"upper-index\">2</sup> + <i>y</i><sup class=\"upper-index\">2</sup></span>, <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup> + <i>y</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub> < <i>v</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\"> - 6</sup></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>10 0 1<br/>-10 0 2 8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9.584544103</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>50 60 10<br/>50 60 20 40<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.000000000</pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"2ec6d4245e9af1ce41fdcc42aa9ab9b6\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"e96757dee4fc76030642cb76498103c316919191\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"header\"><div class=\"title\">C. Delivering Carcinogen</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen.</p><p>You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point <span class=\"tex-span\">(0, 0)</span>. Persephone goes round Diatar along a circular orbit with radius <span class=\"tex-span\"><i>R</i></span> in the counter-clockwise direction at constant linear speed <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (thus, for instance, a full circle around the star takes <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6e148f5854d1671a9c65876c849623c94d511d4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of time). At the initial moment of time Persephone is located at point <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub>)</span>.</p><p>At the initial moment of time Qwerty's ship is at point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Qwerty can move in any direction at speed of at most <span class=\"tex-span\"><i>v</i></span> (<span class=\"tex-span\"><i>v</i> > <i>v</i><sub class=\"lower-index\"><i>p</i></sub></span>). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"><i>r</i> < <i>R</i></span>) from the star.</p><p>Find the minimum time Qwerty needs to get the carcinogen to planet Persephone.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>p</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>p</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>v</i><sub class=\"lower-index\"><i>p</i></sub> < 10<sup class=\"upper-index\">4</sup></span>) — Persephone's initial position and the speed at which it goes round Diatar.</p><p>The second line contains space-separated integers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>v</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 < <i>v</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>r</i> ≤ 10<sup class=\"upper-index\">4</sup></span>) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar.</p><p>It is guaranteed that <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sup class=\"upper-index\">2</sup> + <i>y</i><sup class=\"upper-index\">2</sup></span>, <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup> + <i>y</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub> < <i>v</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\"> - 6</sup></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>10 0 1<br />-10 0 2 8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9.584544103</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>50 60 10<br />50 60 20 40<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.000000000</pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Cube Snake"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Cube Snake</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got an <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span> cube, split into unit cubes. Your task is to number all unit cubes in this cube with positive integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">3</sup></span> so that: </p><ul> <li> each number was used as a cube's number exactly once; </li><li> for each <span class=\"tex-span\">1 ≤ <i>i</i> < <i>n</i><sup class=\"upper-index\">3</sup></span>, unit cubes with numbers <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span> were neighbouring (that is, shared a side); </li><li> for each <span class=\"tex-span\">1 ≤ <i>i</i> < <i>n</i></span> there were at least two different subcubes with sizes <span class=\"tex-span\"><i>i</i> × <i>i</i> × <i>i</i></span>, made from unit cubes, which are numbered with consecutive numbers. That is, there are such two numbers <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>, that the unit cubes of the first subcube are numbered by numbers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>x</i> + 1</span>, <span class=\"tex-span\">...</span>, <span class=\"tex-span\"><i>x</i> + <i>i</i><sup class=\"upper-index\">3</sup> - 1</span>, and the unit cubes of the second subcube are numbered by numbers <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>y</i> + 1</span>, <span class=\"tex-span\">...</span>, <span class=\"tex-span\"><i>y</i> + <i>i</i><sup class=\"upper-index\">3</sup> - 1</span>. </li></ul><p>Find and print the required numeration of unit cubes of the cube.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 50</span>) — the size of the cube, whose unit cubes need to be numbered.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print all layers of the cube as <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\"><i>n</i> × <i>n</i></span> matrices. Separate them with new lines. Print the layers in the order in which they follow in the cube. See the samples for clarifications. </p><p>It is guaranteed that there always is a solution that meets the conditions given in the problem statement.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 4 17 <br/>2 3 18 <br/>27 26 19 <br/><br/>8 5 16 <br/>7 6 15 <br/>24 25 20 <br/><br/>9 12 13 <br/>10 11 14 <br/>23 22 21 <br/><br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the sample the cubes with sizes <span class=\"tex-span\">2 × 2 × 2</span> are numbered with integers <span class=\"tex-span\">1, ..., 8</span> and <span class=\"tex-span\">5, ..., 12</span>.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"e58110febecdbde93226a03043745457\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"e96757dee4fc76030642cb76498103c316919191\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"D\" data-uuid=\"ps_baff5b9b208849527aa19f10c8f9216ef9819ad1\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Cube Snake</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>You've got an <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span> cube, split into unit cubes. Your task is to number all unit cubes in this cube with positive integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i><sup class=\"upper-index\">3</sup></span> so that: </p><ul> <li> each number was used as a cube's number exactly once; </li><li> for each <span class=\"tex-span\">1 ≤ <i>i</i> < <i>n</i><sup class=\"upper-index\">3</sup></span>, unit cubes with numbers <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>i</i> + 1</span> were neighbouring (that is, shared a side); </li><li> for each <span class=\"tex-span\">1 ≤ <i>i</i> < <i>n</i></span> there were at least two different subcubes with sizes <span class=\"tex-span\"><i>i</i> × <i>i</i> × <i>i</i></span>, made from unit cubes, which are numbered with consecutive numbers. That is, there are such two numbers <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span>, that the unit cubes of the first subcube are numbered by numbers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>x</i> + 1</span>, <span class=\"tex-span\">...</span>, <span class=\"tex-span\"><i>x</i> + <i>i</i><sup class=\"upper-index\">3</sup> - 1</span>, and the unit cubes of the second subcube are numbered by numbers <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>y</i> + 1</span>, <span class=\"tex-span\">...</span>, <span class=\"tex-span\"><i>y</i> + <i>i</i><sup class=\"upper-index\">3</sup> - 1</span>. </li></ul><p>Find and print the required numeration of unit cubes of the cube.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 50</span>) — the size of the cube, whose unit cubes need to be numbered.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print all layers of the cube as <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\"><i>n</i> × <i>n</i></span> matrices. Separate them with new lines. Print the layers in the order in which they follow in the cube. See the samples for clarifications. </p><p>It is guaranteed that there always is a solution that meets the conditions given in the problem statement.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 4 17 <br />2 3 18 <br />27 26 19 <br /><br />8 5 16 <br />7 6 15 <br />24 25 20 <br /><br />9 12 13 <br />10 11 14 <br />23 22 21 <br /><br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the sample the cubes with sizes <span class=\"tex-span\">2 × 2 × 2</span> are numbered with integers <span class=\"tex-span\">1, ..., 8</span> and <span class=\"tex-span\">5, ..., 12</span>.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=D]\");\r\n let uuid = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:40</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" 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class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Gripping Story"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Gripping Story</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>512 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>One day Qwerty the Ranger witnessed two transport ships collide with each other. As a result, all contents of their cargo holds scattered around the space. And now Qwerty wants to pick as many lost items as possible to sell them later.</p><p>The thing is, both ships had lots of new gravitational grippers, transported to sale. A gripper is a device that can be installed on a spaceship and than draw items in space to itself (\"grip\") and transport them to the ship's cargo hold. </p><p>Overall the crashed ships lost <span class=\"tex-span\"><i>n</i></span> gravitational grippers: the <span class=\"tex-span\"><i>i</i></span>-th gripper is located at a point with coordinates <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub>)</span>. Each gripper has two features — <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (the power) and <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> (the action radius) and can grip any items with mass of no more than <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> at distance no more than <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>. A gripper itself is an item, too and it has its mass of <span class=\"tex-span\"><i>m</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Qwerty's ship is located at point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and has an old magnetic gripper installed, its characteristics are <span class=\"tex-span\"><i>p</i></span> and <span class=\"tex-span\"><i>r</i></span>. There are no other grippers in the ship's cargo holds.</p><p>Find the largest number of grippers Qwerty can get hold of. As he picks the items, he can arbitrarily install any gripper in the cargo hold of the ship, including the gripper he has just picked. At any moment of time the ship can have only one active gripper installed. We consider all items and the Qwerty's ship immobile when the ranger picks the items, except for when the gripper moves an item — then the item moves to the cargo holds and the ship still remains immobile. We can assume that the ship's cargo holds have enough room for all grippers. Qwerty can use any gripper he finds or the initial gripper an arbitrary number of times.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains five integers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>p</i></span>, <span class=\"tex-span\"><i>r</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>p</i>, <i>r</i> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 250000</span>) — the ship's initial position, the initial gripper's features and the number of grippers that got into the space during the collision.</p><p>Next <span class=\"tex-span\"><i>n</i></span> lines contain the grippers' descriptions: the <span class=\"tex-span\"><i>i</i></span>-th line contains five integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>m</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>m</i><sub class=\"lower-index\"><i>i</i></sub>, <i>p</i><sub class=\"lower-index\"><i>i</i></sub>, <i>r</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the <span class=\"tex-span\"><i>i</i></span>-th gripper's coordinates and features.</p><p>It is guaranteed that all grippers are located at different points. No gripper is located at the same point with Qwerty's ship.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum number of grippers Qwerty can draw to his ship. You do not need to count the initial old magnet gripper.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>0 0 5 10 5<br/>5 4 7 11 5<br/>-7 1 4 7 8<br/>0 2 13 5 6<br/>2 -3 9 3 4<br/>13 5 1 9 9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you should get the second gripper, then use the second gripper to get the first one, then use the first gripper to get the fourth one. You cannot get neither the third gripper as it is too heavy, nor the fifth one as it is too far away.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"9b7fe8f4bd56983e324dd4d71e76f495\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"e96757dee4fc76030642cb76498103c316919191\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"E\" data-uuid=\"ps_144e52010f348610049e9337237688457a883f04\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Gripping Story</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>512 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>One day Qwerty the Ranger witnessed two transport ships collide with each other. As a result, all contents of their cargo holds scattered around the space. And now Qwerty wants to pick as many lost items as possible to sell them later.</p><p>The thing is, both ships had lots of new gravitational grippers, transported to sale. A gripper is a device that can be installed on a spaceship and than draw items in space to itself ("grip") and transport them to the ship's cargo hold. </p><p>Overall the crashed ships lost <span class=\"tex-span\"><i>n</i></span> gravitational grippers: the <span class=\"tex-span\"><i>i</i></span>-th gripper is located at a point with coordinates <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub>)</span>. Each gripper has two features — <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (the power) and <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> (the action radius) and can grip any items with mass of no more than <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> at distance no more than <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>. A gripper itself is an item, too and it has its mass of <span class=\"tex-span\"><i>m</i><sub class=\"lower-index\"><i>i</i></sub></span>.</p><p>Qwerty's ship is located at point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span> and has an old magnetic gripper installed, its characteristics are <span class=\"tex-span\"><i>p</i></span> and <span class=\"tex-span\"><i>r</i></span>. There are no other grippers in the ship's cargo holds.</p><p>Find the largest number of grippers Qwerty can get hold of. As he picks the items, he can arbitrarily install any gripper in the cargo hold of the ship, including the gripper he has just picked. At any moment of time the ship can have only one active gripper installed. We consider all items and the Qwerty's ship immobile when the ranger picks the items, except for when the gripper moves an item — then the item moves to the cargo holds and the ship still remains immobile. We can assume that the ship's cargo holds have enough room for all grippers. Qwerty can use any gripper he finds or the initial gripper an arbitrary number of times.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains five integers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>p</i></span>, <span class=\"tex-span\"><i>r</i></span> and <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>p</i>, <i>r</i> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>n</i> ≤ 250000</span>) — the ship's initial position, the initial gripper's features and the number of grippers that got into the space during the collision.</p><p>Next <span class=\"tex-span\"><i>n</i></span> lines contain the grippers' descriptions: the <span class=\"tex-span\"><i>i</i></span>-th line contains five integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>m</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">9</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>, <span class=\"tex-span\">1 ≤ <i>m</i><sub class=\"lower-index\"><i>i</i></sub>, <i>p</i><sub class=\"lower-index\"><i>i</i></sub>, <i>r</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 10<sup class=\"upper-index\">9</sup></span>) — the <span class=\"tex-span\"><i>i</i></span>-th gripper's coordinates and features.</p><p>It is guaranteed that all grippers are located at different points. No gripper is located at the same point with Qwerty's ship.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the maximum number of grippers Qwerty can draw to his ship. You do not need to count the initial old magnet gripper.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>0 0 5 10 5<br />5 4 7 11 5<br />-7 1 4 7 8<br />0 2 13 5 6<br />2 -3 9 3 4<br />13 5 1 9 9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample you should get the second gripper, then use the second gripper to get the first one, then use the first gripper to get the fourth one. 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dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Hexadecimal's theorem"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Hexadecimal's theorem</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Recently, a chaotic virus Hexadecimal advanced a new theorem which will shake the Universe. She thinks that each Fibonacci number can be represented as sum of three not necessary different Fibonacci numbers.</p><p>Let's remember how Fibonacci numbers can be calculated. <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">0</sub> = 0</span>, <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">1</sub> = 1</span>, and all the next numbers are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub> = <i>F</i><sub class=\"lower-index\"><i>i</i> - 2</sub> + <i>F</i><sub class=\"lower-index\"><i>i</i> - 1</sub></span>.</p><p>So, Fibonacci numbers make a sequence of numbers: <span class=\"tex-span\">0</span>, <span class=\"tex-span\">1</span>, <span class=\"tex-span\">1</span>, <span class=\"tex-span\">2</span>, <span class=\"tex-span\">3</span>, <span class=\"tex-span\">5</span>, <span class=\"tex-span\">8</span>, <span class=\"tex-span\">13</span>, ...</p><p>If you haven't run away from the PC in fear, you have to help the virus. Your task is to divide given Fibonacci number <span class=\"tex-span\"><i>n</i></span> by three not necessary different Fibonacci numbers or say that it is impossible.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input contains of a single integer <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(0 ≤ <i>n</i> < 10<sup class=\"upper-index\">9</sup>)</span> — the number that should be represented by the rules described above. It is guaranteed that <span class=\"tex-span\"><i>n</i></span> is a Fibonacci number.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Output three required numbers: <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span> and <span class=\"tex-span\"><i>c</i></span>. If there is no answer for the test you have to print \"<span class=\"tex-font-style-tt\">I'm too stupid to solve this problem</span>\" without the quotes.</p><p>If there are multiple answers, print any of them.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 1 1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>13<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2 3 8<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"769e2ee0d6880c712062dfc9d135c23c\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - A - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"de26a0ac1c6733fc0decae5b37e76ac9d8a5f991\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Hexadecimal's theorem</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Recently, a chaotic virus Hexadecimal advanced a new theorem which will shake the Universe. She thinks that each Fibonacci number can be represented as sum of three not necessary different Fibonacci numbers.</p><p>Let's remember how Fibonacci numbers can be calculated. <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">0</sub> = 0</span>, <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\">1</sub> = 1</span>, and all the next numbers are <span class=\"tex-span\"><i>F</i><sub class=\"lower-index\"><i>i</i></sub> = <i>F</i><sub class=\"lower-index\"><i>i</i> - 2</sub> + <i>F</i><sub class=\"lower-index\"><i>i</i> - 1</sub></span>.</p><p>So, Fibonacci numbers make a sequence of numbers: <span class=\"tex-span\">0</span>, <span class=\"tex-span\">1</span>, <span class=\"tex-span\">1</span>, <span class=\"tex-span\">2</span>, <span class=\"tex-span\">3</span>, <span class=\"tex-span\">5</span>, <span class=\"tex-span\">8</span>, <span class=\"tex-span\">13</span>, ...</p><p>If you haven't run away from the PC in fear, you have to help the virus. Your task is to divide given Fibonacci number <span class=\"tex-span\"><i>n</i></span> by three not necessary different Fibonacci numbers or say that it is impossible.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input contains of a single integer <span class=\"tex-span\"><i>n</i></span> <span class=\"tex-span\">(0 ≤ <i>n</i> < 10<sup class=\"upper-index\">9</sup>)</span> — the number that should be represented by the rules described above. It is guaranteed that <span class=\"tex-span\"><i>n</i></span> is a Fibonacci number.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Output three required numbers: <span class=\"tex-span\"><i>a</i></span>, <span class=\"tex-span\"><i>b</i></span> and <span class=\"tex-span\"><i>c</i></span>. If there is no answer for the test you have to print "<span class=\"tex-font-style-tt\">I'm too stupid to solve this problem</span>" without the quotes.</p><p>If there are multiple answers, print any of them.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 1 1<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>13<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2 3 8<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=A]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:40</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final 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style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div 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title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New 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title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Special Olympics"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Special Olympics</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>A renowned abstract artist Sasha, drawing inspiration from nowhere, decided to paint a picture entitled \"Special Olympics\". He justly thought that, if the regular Olympic games have five rings, then the Special ones will do with exactly two rings just fine.</p><p>Let us remind you that a ring is a region located between two concentric circles with radii <span class=\"tex-span\"><i>r</i></span> and <span class=\"tex-span\"><i>R</i></span> <span class=\"tex-span\">(<i>r</i> < <i>R</i>)</span>. These radii are called internal and external, respectively. Concentric circles are circles with centers located at the same point.</p><p>Soon a white canvas, which can be considered as an infinite Cartesian plane, had two perfect rings, painted with solid black paint. As Sasha is very impulsive, the rings could have different radii and sizes, they intersect and overlap with each other in any way. We know only one thing for sure: the centers of the pair of rings are not the same.</p><p>When Sasha got tired and fell into a deep sleep, a girl called Ilona came into the room and wanted to cut a circle for the sake of good memories. To make the circle beautiful, she decided to cut along the contour.</p><p>We'll consider a contour to be a continuous closed line through which there is transition from one color to another (see notes for clarification). If the contour takes the form of a circle, then the result will be cutting out a circle, which Iona wants.</p><p>But the girl's inquisitive mathematical mind does not rest: how many ways are there to cut a circle out of the canvas?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input contains two lines. </p><p>Each line has four space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\"><i>i</i></sub></span>, that describe the <span class=\"tex-span\"><i>i</i></span>-th ring; <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> are coordinates of the ring's center, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\"><i>i</i></sub></span> are the internal and external radii of the ring correspondingly <span class=\"tex-span\">( - 100 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100; 1 ≤ <i>r</i><sub class=\"lower-index\"><i>i</i></sub> < <i>R</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100)</span>. </p><p>It is guaranteed that the centers of the rings do not coinside.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>A single integer — the number of ways to cut out a circle from the canvas.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>60 60 45 55<br/>80 80 8 32<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>60 60 45 55<br/>80 60 15 25<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>50 50 35 45<br/>90 50 35 45<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Figures for test samples are given below. The possible cuts are marked with red dotted line. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/8515ae0b2a11a041fdad4ff5f3b975e72760bd53.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/d717fed6257226ac492bb8cac9b69c2048352fa1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2ffdcb81b21ca008eb026024d00665c5e09c32a7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"83bb715b92f1b1c271f8a8e1fbca535a\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"de26a0ac1c6733fc0decae5b37e76ac9d8a5f991\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"B\" data-uuid=\"ps_e8336512b9f2191f22f0145c91b7beffbd4cc50f\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Special Olympics</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>A renowned abstract artist Sasha, drawing inspiration from nowhere, decided to paint a picture entitled "Special Olympics". He justly thought that, if the regular Olympic games have five rings, then the Special ones will do with exactly two rings just fine.</p><p>Let us remind you that a ring is a region located between two concentric circles with radii <span class=\"tex-span\"><i>r</i></span> and <span class=\"tex-span\"><i>R</i></span> <span class=\"tex-span\">(<i>r</i> < <i>R</i>)</span>. These radii are called internal and external, respectively. Concentric circles are circles with centers located at the same point.</p><p>Soon a white canvas, which can be considered as an infinite Cartesian plane, had two perfect rings, painted with solid black paint. As Sasha is very impulsive, the rings could have different radii and sizes, they intersect and overlap with each other in any way. We know only one thing for sure: the centers of the pair of rings are not the same.</p><p>When Sasha got tired and fell into a deep sleep, a girl called Ilona came into the room and wanted to cut a circle for the sake of good memories. To make the circle beautiful, she decided to cut along the contour.</p><p>We'll consider a contour to be a continuous closed line through which there is transition from one color to another (see notes for clarification). If the contour takes the form of a circle, then the result will be cutting out a circle, which Iona wants.</p><p>But the girl's inquisitive mathematical mind does not rest: how many ways are there to cut a circle out of the canvas?</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input contains two lines. </p><p>Each line has four space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\"><i>i</i></sub></span>, that describe the <span class=\"tex-span\"><i>i</i></span>-th ring; <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> are coordinates of the ring's center, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\"><i>i</i></sub></span> are the internal and external radii of the ring correspondingly <span class=\"tex-span\">( - 100 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100; 1 ≤ <i>r</i><sub class=\"lower-index\"><i>i</i></sub> < <i>R</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100)</span>. </p><p>It is guaranteed that the centers of the rings do not coinside.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>A single integer — the number of ways to cut out a circle from the canvas.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>60 60 45 55<br />80 80 8 32<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>60 60 45 55<br />80 60 15 25<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>4</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>50 50 35 45<br />90 50 35 45<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0</pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Figures for test samples are given below. The possible cuts are marked with red dotted line. </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/8515ae0b2a11a041fdad4ff5f3b975e72760bd53.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/d717fed6257226ac492bb8cac9b69c2048352fa1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/2ffdcb81b21ca008eb026024d00665c5e09c32a7.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </center></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=B]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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About Bacteria"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. About Bacteria</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high.</p><p>At the beginning of the first experiment there is a single bacterium in the test tube. Every second each bacterium in the test tube divides itself into <span class=\"tex-span\"><i>k</i></span> bacteria. After that some abnormal effects create <span class=\"tex-span\"><i>b</i></span> more bacteria in the test tube. Thus, if at the beginning of some second the test tube had <span class=\"tex-span\"><i>x</i></span> bacteria, then at the end of the second it will have <span class=\"tex-span\"><i>kx</i> + <i>b</i></span> bacteria.</p><p>The experiment showed that after <span class=\"tex-span\"><i>n</i></span> seconds there were exactly <span class=\"tex-span\"><i>z</i></span> bacteria and the experiment ended at this point.</p><p>For the second experiment Qwerty is going to sterilize the test tube and put there <span class=\"tex-span\"><i>t</i></span> bacteria. He hasn't started the experiment yet but he already wonders, how many seconds he will need to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria. The ranger thinks that the bacteria will divide by the same rule as in the first experiment. </p><p>Help Qwerty and find the minimum number of seconds needed to get a tube with at least <span class=\"tex-span\"><i>z</i></span> bacteria in the second experiment.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains four space-separated integers <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i>, <i>b</i>, <i>n</i>, <i>t</i> ≤ 10<sup class=\"upper-index\">6</sup>)</span> — the parameters of bacterial growth, the time Qwerty needed to grow <span class=\"tex-span\"><i>z</i></span> bacteria in the first experiment and the initial number of bacteria in the second experiment, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum number of seconds Qwerty needs to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria in the tube.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 3 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 4 4 7<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2 4 100<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0</pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"adbb8c30ed7287fc33a858049042d945\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"de26a0ac1c6733fc0decae5b37e76ac9d8a5f991\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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\"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"C\" data-uuid=\"ps_9a6b63bcbe1d17aceafd0aecfc669450301b204e\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. About Bacteria</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger took up a government job and arrived on planet Mars. He should stay in the secret lab and conduct some experiments on bacteria that have funny and abnormal properties. The job isn't difficult, but the salary is high.</p><p>At the beginning of the first experiment there is a single bacterium in the test tube. Every second each bacterium in the test tube divides itself into <span class=\"tex-span\"><i>k</i></span> bacteria. After that some abnormal effects create <span class=\"tex-span\"><i>b</i></span> more bacteria in the test tube. Thus, if at the beginning of some second the test tube had <span class=\"tex-span\"><i>x</i></span> bacteria, then at the end of the second it will have <span class=\"tex-span\"><i>kx</i> + <i>b</i></span> bacteria.</p><p>The experiment showed that after <span class=\"tex-span\"><i>n</i></span> seconds there were exactly <span class=\"tex-span\"><i>z</i></span> bacteria and the experiment ended at this point.</p><p>For the second experiment Qwerty is going to sterilize the test tube and put there <span class=\"tex-span\"><i>t</i></span> bacteria. He hasn't started the experiment yet but he already wonders, how many seconds he will need to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria. The ranger thinks that the bacteria will divide by the same rule as in the first experiment. </p><p>Help Qwerty and find the minimum number of seconds needed to get a tube with at least <span class=\"tex-span\"><i>z</i></span> bacteria in the second experiment.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains four space-separated integers <span class=\"tex-span\"><i>k</i></span>, <span class=\"tex-span\"><i>b</i></span>, <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>t</i></span> <span class=\"tex-span\">(1 ≤ <i>k</i>, <i>b</i>, <i>n</i>, <i>t</i> ≤ 10<sup class=\"upper-index\">6</sup>)</span> — the parameters of bacterial growth, the time Qwerty needed to grow <span class=\"tex-span\"><i>z</i></span> bacteria in the first experiment and the initial number of bacteria in the second experiment, correspondingly.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the minimum number of seconds Qwerty needs to grow at least <span class=\"tex-span\"><i>z</i></span> bacteria in the tube.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 1 3 5<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>1 4 4 7<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>2 2 4 100<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0</pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=C]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:40</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" 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class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Jumping on Walls"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Jumping on Walls</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Vasya plays a computer game with ninjas. At this stage Vasya's ninja should get out of a deep canyon.</p><p>The canyon consists of two vertical parallel walls, their height is <span class=\"tex-span\"><i>n</i></span> meters. Let's imagine that we split these walls into <span class=\"tex-span\">1</span> meter-long areas and number them with positive integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from bottom to top. Some areas are safe and the ninja can climb them. Others are spiky and ninja can't be there. Let's call such areas <span class=\"tex-font-style-it\">dangerous</span>.</p><p>Initially the ninja is on the lower area of the left wall. He can use each second to perform one of the following actions: </p><ul> <li> climb one area up; </li><li> climb one area down; </li><li> jump to the opposite wall. That gets the ninja to the area that is exactly <span class=\"tex-span\"><i>k</i></span> meters higher than the area he jumped from. More formally, if before the jump the ninja is located at area <span class=\"tex-span\"><i>x</i></span> of one wall, then after the jump he is located at area <span class=\"tex-span\"><i>x</i> + <i>k</i></span> of the other wall. </li></ul><p>If at some point of time the ninja tries to get to an area with a number larger than <span class=\"tex-span\"><i>n</i></span>, then we can assume that the ninja got out of the canyon.</p><p>The canyon gets flooded and each second the water level raises one meter. Initially the water level is at the lower border of the first area. Ninja cannot be on the area covered by water. We can assume that the ninja and the water \"move in turns\" — first the ninja performs some action, then the water raises for one meter, then the ninja performs one more action and so on.</p><p>The level is considered completed if the ninja manages to get out of the canyon.</p><p>After several failed attempts Vasya started to doubt whether it is possible to complete the level at all. Help him answer the question.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the height of the canyon and the height of ninja's jump, correspondingly.</p><p>The second line contains the description of the left wall — a string with the length of <span class=\"tex-span\"><i>n</i></span> characters. The <span class=\"tex-span\"><i>i</i></span>-th character represents the state of the <span class=\"tex-span\"><i>i</i></span>-th wall area: character \"<span class=\"tex-font-style-tt\">X</span>\" represents a dangerous area and character \"<span class=\"tex-font-style-tt\">-</span>\" represents a safe area.</p><p>The third line describes the right wall in the same format.</p><p>It is guaranteed that the first area of the left wall is not dangerous.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print \"<span class=\"tex-font-style-tt\">YES</span>\" (without the quotes) if the ninja can get out from the canyon, otherwise, print \"<span class=\"tex-font-style-tt\">NO</span>\" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>7 3<br/>---X--X<br/>-X--XX-<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 2<br/>--X-X-<br/>X--XX-<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the ninja should first jump to the right wall, then go one meter down along the right wall, then jump to the left wall. The next jump can get the ninja from the canyon. </p><p>In the second sample there's no way the ninja can get out of the canyon.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"375fc368abe72956da2bef1d38f3f8cc\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"de26a0ac1c6733fc0decae5b37e76ac9d8a5f991\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Jumping on Walls</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Vasya plays a computer game with ninjas. At this stage Vasya's ninja should get out of a deep canyon.</p><p>The canyon consists of two vertical parallel walls, their height is <span class=\"tex-span\"><i>n</i></span> meters. Let's imagine that we split these walls into <span class=\"tex-span\">1</span> meter-long areas and number them with positive integers from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from bottom to top. Some areas are safe and the ninja can climb them. Others are spiky and ninja can't be there. Let's call such areas <span class=\"tex-font-style-it\">dangerous</span>.</p><p>Initially the ninja is on the lower area of the left wall. He can use each second to perform one of the following actions: </p><ul> <li> climb one area up; </li><li> climb one area down; </li><li> jump to the opposite wall. That gets the ninja to the area that is exactly <span class=\"tex-span\"><i>k</i></span> meters higher than the area he jumped from. More formally, if before the jump the ninja is located at area <span class=\"tex-span\"><i>x</i></span> of one wall, then after the jump he is located at area <span class=\"tex-span\"><i>x</i> + <i>k</i></span> of the other wall. </li></ul><p>If at some point of time the ninja tries to get to an area with a number larger than <span class=\"tex-span\"><i>n</i></span>, then we can assume that the ninja got out of the canyon.</p><p>The canyon gets flooded and each second the water level raises one meter. Initially the water level is at the lower border of the first area. Ninja cannot be on the area covered by water. We can assume that the ninja and the water "move in turns" — first the ninja performs some action, then the water raises for one meter, then the ninja performs one more action and so on.</p><p>The level is considered completed if the ninja manages to get out of the canyon.</p><p>After several failed attempts Vasya started to doubt whether it is possible to complete the level at all. Help him answer the question.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>k</i> ≤ 10<sup class=\"upper-index\">5</sup></span>) — the height of the canyon and the height of ninja's jump, correspondingly.</p><p>The second line contains the description of the left wall — a string with the length of <span class=\"tex-span\"><i>n</i></span> characters. The <span class=\"tex-span\"><i>i</i></span>-th character represents the state of the <span class=\"tex-span\"><i>i</i></span>-th wall area: character "<span class=\"tex-font-style-tt\">X</span>" represents a dangerous area and character "<span class=\"tex-font-style-tt\">-</span>" represents a safe area.</p><p>The third line describes the right wall in the same format.</p><p>It is guaranteed that the first area of the left wall is not dangerous.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print "<span class=\"tex-font-style-tt\">YES</span>" (without the quotes) if the ninja can get out from the canyon, otherwise, print "<span class=\"tex-font-style-tt\">NO</span>" (without the quotes).</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>7 3<br />---X--X<br />-X--XX-<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>YES<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 2<br />--X-X-<br />X--XX-<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>NO<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample the ninja should first jump to the right wall, then go one meter down along the right wall, then jump to the left wall. 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:40</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final 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style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div 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title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New 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title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Delivering Carcinogen"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Delivering Carcinogen</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen.</p><p>You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point <span class=\"tex-span\">(0, 0)</span>. Persephone goes round Diatar along a circular orbit with radius <span class=\"tex-span\"><i>R</i></span> in the counter-clockwise direction at constant linear speed <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (thus, for instance, a full circle around the star takes <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6e148f5854d1671a9c65876c849623c94d511d4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> of time). At the initial moment of time Persephone is located at point <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub>)</span>.</p><p>At the initial moment of time Qwerty's ship is at point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Qwerty can move in any direction at speed of at most <span class=\"tex-span\"><i>v</i></span> (<span class=\"tex-span\"><i>v</i> > <i>v</i><sub class=\"lower-index\"><i>p</i></sub></span>). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"><i>r</i> < <i>R</i></span>) from the star.</p><p>Find the minimum time Qwerty needs to get the carcinogen to planet Persephone.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>p</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>p</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>v</i><sub class=\"lower-index\"><i>p</i></sub> < 10<sup class=\"upper-index\">4</sup></span>) — Persephone's initial position and the speed at which it goes round Diatar.</p><p>The second line contains space-separated integers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>v</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 < <i>v</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>r</i> ≤ 10<sup class=\"upper-index\">4</sup></span>) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar.</p><p>It is guaranteed that <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sup class=\"upper-index\">2</sup> + <i>y</i><sup class=\"upper-index\">2</sup></span>, <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup> + <i>y</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub> < <i>v</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\"> - 6</sup></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>10 0 1<br/>-10 0 2 8<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9.584544103</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>50 60 10<br/>50 60 20 40<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.000000000</pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"df20dba88290213f10e7d3415a73d9da\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"de26a0ac1c6733fc0decae5b37e76ac9d8a5f991\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Delivering Carcinogen</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Qwerty the Ranger arrived to the Diatar system with a very important task. He should deliver a special carcinogen for scientific research to planet Persephone. This is urgent, so Qwerty has to get to the planet as soon as possible. A lost day may fail negotiations as nobody is going to pay for an overdue carcinogen.</p><p>You can consider Qwerty's ship, the planet Persephone and the star Diatar points on a plane. Diatar is located in the origin of coordinate axes — at point <span class=\"tex-span\">(0, 0)</span>. Persephone goes round Diatar along a circular orbit with radius <span class=\"tex-span\"><i>R</i></span> in the counter-clockwise direction at constant linear speed <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (thus, for instance, a full circle around the star takes <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/d6e148f5854d1671a9c65876c849623c94d511d4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of time). At the initial moment of time Persephone is located at point <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub>)</span>.</p><p>At the initial moment of time Qwerty's ship is at point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Qwerty can move in any direction at speed of at most <span class=\"tex-span\"><i>v</i></span> (<span class=\"tex-span\"><i>v</i> > <i>v</i><sub class=\"lower-index\"><i>p</i></sub></span>). The star Diatar is hot (as all stars), so Qwerty can't get too close to it. The ship's metal sheathing melts at distance <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"><i>r</i> < <i>R</i></span>) from the star.</p><p>Find the minimum time Qwerty needs to get the carcinogen to planet Persephone.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains space-separated integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>p</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>p</i></sub></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i><sub class=\"lower-index\"><i>p</i></sub>, <i>y</i><sub class=\"lower-index\"><i>p</i></sub> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>v</i><sub class=\"lower-index\"><i>p</i></sub> < 10<sup class=\"upper-index\">4</sup></span>) — Persephone's initial position and the speed at which it goes round Diatar.</p><p>The second line contains space-separated integers <span class=\"tex-span\"><i>x</i></span>, <span class=\"tex-span\"><i>y</i></span>, <span class=\"tex-span\"><i>v</i></span> and <span class=\"tex-span\"><i>r</i></span> (<span class=\"tex-span\"> - 10<sup class=\"upper-index\">4</sup> ≤ <i>x</i>, <i>y</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 < <i>v</i> ≤ 10<sup class=\"upper-index\">4</sup></span>, <span class=\"tex-span\">1 ≤ <i>r</i> ≤ 10<sup class=\"upper-index\">4</sup></span>) — The intial position of Qwerty's ship, its maximum speed and the minimum safe distance to star Diatar.</p><p>It is guaranteed that <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sup class=\"upper-index\">2</sup> + <i>y</i><sup class=\"upper-index\">2</sup></span>, <span class=\"tex-span\"><i>r</i><sup class=\"upper-index\">2</sup> < <i>x</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup> + <i>y</i><sub class=\"lower-index\"><i>p</i></sub><sup class=\"upper-index\">2</sup></span> and <span class=\"tex-span\"><i>v</i><sub class=\"lower-index\"><i>p</i></sub> < <i>v</i></span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single real number — the minimum possible delivery time. The answer will be considered valid if its absolute or relative error does not exceed <span class=\"tex-span\">10<sup class=\"upper-index\"> - 6</sup></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>10 0 1<br />-10 0 2 8<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>9.584544103</pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>50 60 10<br />50 60 20 40<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>0.000000000</pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=E]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='c0fc963de17d7239968f8844ca67f770'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" 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href=\"/profile/Ripatti\">Ripatti</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Ripatti\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Ripatti\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Ripatti\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Ripatti\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Ripatti\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Ripatti\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Ripatti\" style=\"text-decoration:none;color:black !important;\">Ripatti's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4778\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4764\"> <p>Solutions for Codeforces Round #125</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Ripatti\" title=\"Master Ripatti\" class=\"rated-user user-orange\">Ripatti</a>,\r\n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><strong>Div2 A.</strong> You can just output "0 0 n". </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> . </p><p><strong>Div2 B.</strong> You should check for every circle of one ring: it have intersections with another ring or not. So, there are 4 checks. </p><p>There are 2 cases:<br />1. circle is inside of ring;<br />2. circle is outside of ring and ring is outside of circle;<br />3. circle is outside of ring and ring is inside of circle.<br />If at least one of these cases is performed, circle is good.</p><p>You can easily do checks following way. Let us <span class=\"tex-span\"><i>d</i></span> be a distance between centers of ring and circle, <span class=\"tex-span\"><i>r</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>R</i><sub class=\"lower-index\">1</sub></span> are inside and outside radii of ring, <span class=\"tex-span\"><i>r</i></span> be radius of circle. Then conditions for all cases will be<br />1. <span class=\"tex-span\"><i>d</i> + <i>r</i> ≤ <i>r</i><sub class=\"lower-index\">1</sub></span>.<br />2. <span class=\"tex-span\"><i>r</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>d</i></span>.<br />3. <span class=\"tex-span\"><i>d</i> + <i>R</i><sub class=\"lower-index\">1</sub> ≤ <i>r</i></span>.<br />You can check all conditions in integers using squares of distances. </p><p>Author is <a class=\"rated-user user-orange\" href=\"/profile/Alex_KPR\" title=\"Master Alex_KPR\">Alex_KPR</a> </p><p><strong>Div2 C.</strong> <strong>Div1 A.</strong><br />The first solution. Consider sequence <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub> = 1</span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub> = <i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub><i>k</i> + <i>b</i></span>:<br /><span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">0</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">1</sub></span>, <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\">2</sub></span>, ..., <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>n</i></sub> = <i>z</i></span>.<br />You can see that for all numbers from segment <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">0</sub>, <i>a</i><sub class=\"lower-index\">1</sub> - 1]</span> you can number not less than <span class=\"tex-span\"><i>z</i></span> using exactly <span class=\"tex-span\"><i>n</i></span> steps. But for <span class=\"tex-span\"><i>n</i> - 1</span> steps you will bet number less than <span class=\"tex-span\"><i>z</i></span>. It works because transformation is monotonous. Analogically, for numbers from segments <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">1</sub>, <i>a</i><sub class=\"lower-index\">2</sub> - 1]</span>, <span class=\"tex-span\">[<i>a</i><sub class=\"lower-index\">2</sub>, <i>a</i><sub class=\"lower-index\">3</sub> - 1]</span>, etc, you need exactly <span class=\"tex-span\"><i>n</i> - 1</span>, <span class=\"tex-span\"><i>n</i> - 2</span>, etc steps. So you just need find segment that contains number <span class=\"tex-span\"><i>t</i></span>. You can do it by generate a few first members of the sequence <span class=\"tex-span\"><i>a</i></span>. You need no more than <span class=\"tex-span\"><i>t</i></span> members. </p><p>The second solution. Equation:<br /><span class=\"tex-span\"><i>tk</i><sup class=\"upper-index\"><i>x</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>b</i>(<i>k</i><sup class=\"upper-index\"><i>x</i> - 1</sup> + <i>k</i><sup class=\"upper-index\"><i>x</i> - 2</sup>... + 1)</span><br />Using formula for geometric progression you can get:<br /><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/6d4727291c9f041dc3ac0489e86c7497e49314f6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /><br />For <span class=\"tex-span\"><i>k</i> ≠ 1</span> we can multiply both sides by <span class=\"tex-span\"><i>k</i> - 1</span>, (you can consider case <span class=\"tex-span\"><i>k</i> = 1</span> by yourself).<br /><span class=\"tex-span\"><i>t</i>(<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>x</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>x</i></sup> - <i>b</i> ≥ (<i>k</i> - 1)<i>k</i><sup class=\"upper-index\"><i>n</i></sup> + <i>bk</i><sup class=\"upper-index\"><i>n</i></sup> - <i>b</i></span> </p><p><span class=\"tex-span\"><i>k</i><sup class=\"upper-index\"><i>x</i></sup>(<i>t</i>(<i>k</i> - 1) + <i>b</i>) ≥ <i>k</i><sup class=\"upper-index\"><i>n</i></sup>(<i>k</i> - 1 + <i>b</i>)</span> </p><p><img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/dfbc1b947564f676e12fb20b039deb80b4a292a2.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> </p><p>So, you can find value <span class=\"tex-span\"><i>n</i> - <i>x</i></span> using simply raising to a power.</p><p>Authors are <a class=\"rated-user user-orange\" href=\"/profile/Gerald\" title=\"Master Gerald\">Gerald</a> and <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 D.</strong> <strong>Div1 B.</strong> You should construct graph where vertices are areas of walls and edges are actions of ninja. Then you should run BFS with one modification: is you reach vertex later then water, you shouldn't do moves from this vertex.</p><p>It is solution in <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div2 E.</strong> <strong>Div1 C.</strong> If you can reach the planet in time <span class=\"tex-span\"><i>t</i></span>, you also can reach one in any time greater then <span class=\"tex-span\"><i>t</i></span> (you can just reach planet in time <span class=\"tex-span\"><i>t</i></span> and then move along with planet). There exists some <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> for that for all <span class=\"tex-span\"><i>t</i> > <i>t</i><sub class=\"lower-index\">0</sub></span> you can reach planet, and for all <span class=\"tex-span\"><i>t</i> < <i>t</i><sub class=\"lower-index\">0</sub></span> you cannot do in. Let us find <span class=\"tex-span\"><i>t</i><sub class=\"lower-index\">0</sub></span> using binary search.</p><p>Checking every of <span class=\"tex-span\"><i>t</i></span> inside of binary search you can do following way. You should calculate place if planet after time <span class=\"tex-span\"><i>t</i></span> and find distance between ship's place and new planet place.</p><p>So, you have following "classic" problem: there are two points <span class=\"tex-span\"><i>A</i></span> and <span class=\"tex-span\"><i>B</i></span> and circle with center in <span class=\"tex-span\"><i>O</i></span> and radius <span class=\"tex-span\"><i>R</i></span> (points are outside of circle), you need find distance between points and you cannot moving inside of circle.</p><p>There are 2 cases:<br />1. You can move direct way<br />2. You should skirt the circle </p><p>The second case is performed iff two following conditions are performed:<br />a. Angles <span class=\"tex-span\"><i>OAB</i></span> and <span class=\"tex-span\"><i>OBA</i></span> are acute<br />b. Height <span class=\"tex-span\"><i>OH</i></span> of triangle <span class=\"tex-span\"><i>OAB</i></span> less than <span class=\"tex-span\"><i>R</i></span><br />All checks you can do in integers.</p><p>Well, let's understand how to precess our cases:<br />1. Obviously<br />2. Let us <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span> be tangency points (i.e. you are moving along line <span class=\"tex-span\"><i>ACDB</i></span>). Thiangles <span class=\"tex-span\"><i>OAC</i></span> and <span class=\"tex-span\"><i>OBD</i></span> are right and you can easily calculate all angles inside of them. Then you should find angle <span class=\"tex-span\"><i>COD</i></span>. After that you can find length of line <span class=\"tex-span\"><i>ACDB</i></span>. You can see that you don't need find places of points <span class=\"tex-span\"><i>C</i></span> and <span class=\"tex-span\"><i>D</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 D.</strong> We will construct solution recursively. For every <span class=\"tex-span\"><i>k</i></span> it is possible construct parallelepiped <span class=\"tex-span\"><i>k</i> × <i>k</i> × (<i>k</i> + 1)</span> that contains 2 cubes <span class=\"tex-span\"><i>k</i> × <i>k</i> × <i>k</i></span>. For <span class=\"tex-span\"><i>k</i> = 2</span> solution is obliviousо. How to build solutions for <span class=\"tex-span\"><i>k</i> > 2</span> is shown in following picture:</p><p><img alt=\" \" src=\"/predownloaded/e5/b2/e5b2ec5a6333adb20c76b8d06a087dec693cc67a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /></p><p>Red and blue cubes are start and end of chain. Firstly you should build one floor over. Then you should build 2 layers on two opposite sides.</p><p>For every <span class=\"tex-span\"><i>n</i></span> you can build parallelepiped <span class=\"tex-span\"><i>n</i> × <i>n</i> × (<i>n</i> + 1)</span>, and drop one layer for getting cube <span class=\"tex-span\"><i>n</i> × <i>n</i> × <i>n</i></span>.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a></p><p><strong>Div1 E.</strong> You can allocate all grippers as points on plane with coordinates (distance, mass). So, when you use some gripper, you are collecting grippers inside some rectangle with corner in origin. Let us collect grippers and put them into queue. For current gripper you should take all grippers from rectangle and store them into queue. Then you should take next gripper from queue and do some manipulations with them and so on. Well, now you need do it fast.</p><p>Let us create segment tree (for example, there you can use Fenwick tree) for dimention "distance". In every vertex of that tree you should store stack of points ordered by "mass". More details: every vertex of segment tree is some range of coordinates, and you should store in thet vertex points only from this range. At the top of every stack should be point with minimal mass. Well, let us put all points into tree. Every position is covered by no more thenм <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e534f2da678188382079d5eae762e91981566186.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> segmetns, therefore all tree will require <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> of memory.</p><p>When you process query, you should extract points from some stacks and put them into queue. You can see that you may put some points into queue twice. To avoid this you should also put number of point into stack. So, when you are extracting point from stack you can check that it is the first extract using some array of flags.</p><p>This solution works in <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/5e7dae7c1838af7ba7570bdf02ff61029b043be6.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Author is <a class=\"rated-user user-violet\" href=\"/profile/Ripatti\" title=\"Candidate Master Ripatti\">Ripatti</a> ; the above solution was proposed by <a class=\"rated-user user-red\" href=\"/profile/RAD\" title=\"Grandmaster RAD\">RAD</a></p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/198\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 1)</a> </span>\r\n </div>\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/199\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 125 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-440-4778\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"440\",\n blogEntryId: \"4764\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23125\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #125</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+47</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4778\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Ripatti\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Ripatti\">\n Ripatti\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/23/2012 22:05\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4764#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4764#comments\">\n 17\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4788\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (9)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97411\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/swaz1993\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/swaz1993\" title=\"Pupil swaz1993\" class=\"rated-user user-green\">swaz1993</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/25/2012 09:04\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97411\" href=\"?#comment-97411\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97411\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"55304\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97411\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>What does cout<<0<<0 print in prob A div 2.Please explain.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97411 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97411 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97411\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97499\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/nhtrnm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/nhtrnm\" title=\"Expert nhtrnm\" class=\"rated-user user-blue\">nhtrnm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/26/2012 12:09\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97499\" href=\"?#comment-97499\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97499\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14046\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97499\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p><code>Input</code> <code>The input contains of a single integer n (0 ≤ n < 10^9) — the number that should be represented by the rules described above. It is guaranteed that n is a Fibonacci number.</code> n is Fibonacci number =)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97499 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97499 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97499\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1048679\" commentParentId=\"97411\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/xxyoohoo\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/3249547/avatar/545198339e62dd25.jpg'/> </a>\n <div><a href=\"/profile/xxyoohoo\" title=\"Unrated, xxyoohoo\" class=\"rated-user user-black\">xxyoohoo</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/17/2023 18:54\">3 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1048679\" href=\"?#comment-1048679\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97411\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1048679\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"3249547\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1048679\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>because N is definitely a fibonacci number, and so is 0, so 0+0+n always works</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1048679 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1048679 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1048679\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97729\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Al.Cash\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/14750/avatar/dcbc95e9f176e573.jpg'/> </a>\n <div><a href=\"/profile/Al.Cash\" title=\"Grandmaster Al.Cash\" class=\"rated-user user-red\">Al.Cash</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 14:48\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97729\" href=\"?#comment-97729\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97729\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"14750\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97729\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think it's obvious that problems 1D and 1E should've been in other order.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97729 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97729 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97729\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97746\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/cplayer\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/49407/avatar/99630ee7f6e32c59.jpg'/> </a>\n <div><a href=\"/profile/cplayer\" title=\"Specialist cplayer\" class=\"rated-user user-cyan\">cplayer</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/29/2012 16:38\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97746\" href=\"?#comment-97746\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97746\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"49407\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97746\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry to interrupt, but can problem 1E use priority_queue?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97746 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97746 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97746\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"319845\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Mahdi_Jfri\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/425173/avatar/c866c314a8686f72.jpg'/> </a>\n <div><a href=\"/profile/Mahdi_Jfri\" title=\"Grandmaster Mahdi_Jfri\" class=\"rated-user user-red\">Mahdi_Jfri</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/09/2016 21:21\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-319845\" href=\"?#comment-319845\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"319845\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"425173\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-319845\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I solved the Div1. B running DFS And i think there's a problem with my code and the algorithm is wrong but it was accepted by the test <a href=\"/contest/198/submission/21324539\" title=\"Submission 21324539 by Mahdi_Jfri\">21324539</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-319845 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-319845 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-319845\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"321150\" commentParentId=\"319845\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/_VanGogh_\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/313518/avatar/586fd33212d39c0c.jpg'/> </a>\n <div><a href=\"/profile/_VanGogh_\" title=\"Expert _VanGogh_\" class=\"rated-user user-blue\">_VanGogh_</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Oct/17/2016 17:19\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-321150\" href=\"?#comment-321150\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-319845\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"321150\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"313518\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-321150\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>That's a good luck Sometimes my algorithm was correct but I got wrong answer on test >= 100 U R so lucky</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-321150 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-321150 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-321150\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"437146\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/dvjsm\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/507227/avatar/28168b238fdf8e8.jpg'/> </a>\n <div><a href=\"/profile/dvjsm\" title=\"Specialist dvjsm\" class=\"rated-user user-cyan\">dvjsm</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/13/2018 00:29\">5 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-437146\" href=\"?#comment-437146\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"437146\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"507227\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-437146\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>In Div2 C, I am using C++14 to solve the question. I have performed the same math as given in the editorial and to find the minimum value of x, I apply log. That is x >= n-log(LHS_value)_to_base_k. I am using double as the type for x and am finally storing (long long)(ceil(x)) as the answer and printing that. However, I am running into precision issues. For example, in one testcase, x came out to be 1 but ceil(x) got evaluated as 2. When I am submitting the same logic using Java, everything is working fine. Here are the 2 submissions:- C++ — <a href=\"/contest/199/submission/39201368\" title=\"Submission 39201368 by dvjsm\">39201368</a> Java — <a href=\"/contest/199/submission/39201512\" title=\"Submission 39201512 by dvjsm\">39201512</a></p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-437146 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-437146 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-437146\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"564928\" commentParentId=\"437146\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/hellomoto\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/716021/avatar/db1dcb8db827fa7f.jpg'/> </a>\n <div><a href=\"/profile/hellomoto\" title=\"Expert hellomoto\" class=\"rated-user user-blue\">hellomoto</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Dec/16/2019 17:28\">4 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-564928\" href=\"?#comment-564928\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-437146\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"564928\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"716021\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-564928\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Long double will also work.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-564928 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-564928 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-564928\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4788\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In Russian</span>\r\n </div>\r\n <textarea data-drafts-id=\"CommentReplyFrame\" class=\"wysiwyg\" name=\"editContent\" rows=\"20\" 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Cinema"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Cinema</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1.5 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>The capital of Berland has the only movie theater in the country. Besides, it consists of only one room. The room is divided into <span class=\"tex-span\"><i>n</i></span> rows, each row consists of <span class=\"tex-span\"><i>m</i></span> seats.</p><p>There are <span class=\"tex-span\"><i>k</i></span> people lined up to the box office, each person wants to buy exactly one ticket for his own entertainment. Before the box office started selling tickets, each person found the seat that seemed best for him and remembered it as a pair of coordinates <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, where <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> is the row number, and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> is the seat number in this row.</p><p>It is possible that some people have chosen the same place, then when some people see their favorite seat taken in the plan of empty seats in the theater, they choose and buy a ticket to another place. Each of them has the following logic: let's assume that he originally wanted to buy a ticket to seat <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span>, then when he comes to the box office, he chooses such empty seat <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span>, which satisfies the following conditions: </p><ul> <li> the value of <span class=\"tex-span\">|<i>x</i><sub class=\"lower-index\">1</sub> - <i>x</i><sub class=\"lower-index\">2</sub>| + |<i>y</i><sub class=\"lower-index\">1</sub> - <i>y</i><sub class=\"lower-index\">2</sub>|</span> is minimum </li><li> if the choice is not unique, then among the seats that satisfy the first condition, this person selects the one for which the value of <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span> is minimum </li><li> if the choice is still not unique, among the seats that satisfy the first and second conditions, this person selects the one for which the value of <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">2</sub></span> is minimum </li></ul><p>Your task is to find the coordinates of a seat for each person.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains three integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>m</i></span>, <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 2000</span>, <span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>min</i>(<i>n</i>·<i>m</i>, 10<sup class=\"upper-index\">5</sup></span>) — the number of rows in the room, the number of seats in each row and the number of people in the line, correspondingly. Each of the next <span class=\"tex-span\"><i>k</i></span> lines contains two integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\">1 ≤ <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>m</i></span>) — the coordinates of the seat each person has chosen. Numbers on the same line are separated by a space. The pairs of coordinates are located in the order, in which people stand in the line, starting from the head (the first person in the line who stands in front of the box office) to the tail (the last person in the line).</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>k</i></span> lines, each containing a pair of integers. Print on the <span class=\"tex-span\"><i>i</i></span>-th line <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> — the coordinates of the seat, for which the person who stands <span class=\"tex-span\"><i>i</i></span>-th in the line will buy the ticket. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 4 6<br/>1 1<br/>1 1<br/>1 1<br/>1 2<br/>1 3<br/>1 3<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 1<br/>1 2<br/>2 1<br/>1 3<br/>1 4<br/>2 3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 3 12<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/>2 2<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2 2<br/>1 2<br/>2 1<br/>2 3<br/>3 2<br/>1 1<br/>1 3<br/>3 1<br/>3 3<br/>4 2<br/>4 1<br/>4 3<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"d99b8466c701bd66beca8042cf696ee7\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - A - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"685ffddfd80105244067189484fcf220fc0a03e4\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"header\"><div class=\"title\">A. Cinema</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1.5 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>The capital of Berland has the only movie theater in the country. Besides, it consists of only one room. The room is divided into <span class=\"tex-span\"><i>n</i></span> rows, each row consists of <span class=\"tex-span\"><i>m</i></span> seats.</p><p>There are <span class=\"tex-span\"><i>k</i></span> people lined up to the box office, each person wants to buy exactly one ticket for his own entertainment. Before the box office started selling tickets, each person found the seat that seemed best for him and remembered it as a pair of coordinates <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, where <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span> is the row number, and <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> is the seat number in this row.</p><p>It is possible that some people have chosen the same place, then when some people see their favorite seat taken in the plan of empty seats in the theater, they choose and buy a ticket to another place. Each of them has the following logic: let's assume that he originally wanted to buy a ticket to seat <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">1</sub>, <i>y</i><sub class=\"lower-index\">1</sub>)</span>, then when he comes to the box office, he chooses such empty seat <span class=\"tex-span\">(<i>x</i><sub class=\"lower-index\">2</sub>, <i>y</i><sub class=\"lower-index\">2</sub>)</span>, which satisfies the following conditions: </p><ul> <li> the value of <span class=\"tex-span\">|<i>x</i><sub class=\"lower-index\">1</sub> - <i>x</i><sub class=\"lower-index\">2</sub>| + |<i>y</i><sub class=\"lower-index\">1</sub> - <i>y</i><sub class=\"lower-index\">2</sub>|</span> is minimum </li><li> if the choice is not unique, then among the seats that satisfy the first condition, this person selects the one for which the value of <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\">2</sub></span> is minimum </li><li> if the choice is still not unique, among the seats that satisfy the first and second conditions, this person selects the one for which the value of <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\">2</sub></span> is minimum </li></ul><p>Your task is to find the coordinates of a seat for each person.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains three integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>m</i></span>, <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i>, <i>m</i> ≤ 2000</span>, <span class=\"tex-span\">1 ≤ <i>k</i> ≤ <i>min</i>(<i>n</i>·<i>m</i>, 10<sup class=\"upper-index\">5</sup></span>) — the number of rows in the room, the number of seats in each row and the number of people in the line, correspondingly. Each of the next <span class=\"tex-span\"><i>k</i></span> lines contains two integers <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub></span>, <span class=\"tex-span\"><i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">1 ≤ <i>x</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i></span>, <span class=\"tex-span\">1 ≤ <i>y</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>m</i></span>) — the coordinates of the seat each person has chosen. Numbers on the same line are separated by a space. The pairs of coordinates are located in the order, in which people stand in the line, starting from the head (the first person in the line who stands in front of the box office) to the tail (the last person in the line).</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print <span class=\"tex-span\"><i>k</i></span> lines, each containing a pair of integers. Print on the <span class=\"tex-span\"><i>i</i></span>-th line <span class=\"tex-span\"><i>x</i><sub class=\"lower-index\"><i>i</i></sub>, <i>y</i><sub class=\"lower-index\"><i>i</i></sub></span> — the coordinates of the seat, for which the person who stands <span class=\"tex-span\"><i>i</i></span>-th in the line will buy the ticket. </p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3 4 6<br />1 1<br />1 1<br />1 1<br />1 2<br />1 3<br />1 3<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 1<br />1 2<br />2 1<br />1 3<br />1 4<br />2 3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4 3 12<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br />2 2<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2 2<br />1 2<br />2 1<br />2 3<br />3 2<br />1 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:39</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. 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none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='807729622d5b8385200c279d1f0f3909'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Igor_Kudryashov\">Igor_Kudryashov</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Igor_Kudryashov\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Igor_Kudryashov\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Igor_Kudryashov\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Igor_Kudryashov\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Igor_Kudryashov\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Igor_Kudryashov\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Igor_Kudryashov\" style=\"text-decoration:none;color:black !important;\">Igor_Kudryashov's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4783\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4769\"> <p>Editorial of Codeforces Round #126 (Div. 2)</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a>,\r\n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/200/problem/A\">200A — Cinema</a></p><p>In this problem were given the field, which size is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>, and <span class=\"tex-span\"><i>k</i></span> queries. Each query is the cell of the field. You had to find closest free cell for given one (there was used manhattan metric). Than found cell was marked as used. The time complexity of the solution is supposed to be <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Firstly, we show the main idea, than we show why solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>First of all, if <span class=\"tex-span\"><i>n</i> > <i>m</i></span>, than rotate matrix by 90 degrees (than we explain purpose of this transformation). We will have two matrices, size of each is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>. In this matrices we will maintain for each cell the nearest free one to the left and to the right. Suppose we have query — cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Iterate <span class=\"tex-span\"><i>d</i></span> — how much rows we will go above or below. Suppose we fix <span class=\"tex-span\"><i>d</i></span>, than look at the row <span class=\"tex-span\"><i>x</i> - <i>d</i></span>, for example (also we should do same things for row <span class=\"tex-span\"><i>x</i> + <i>d</i></span>). Lets find in this row nearest free cells to the left and to the right of <span class=\"tex-span\">(<i>x</i> - <i>d</i>, <i>y</i>)</span> by using our matrices and try to update answer. When <span class=\"tex-span\"><i>d</i></span> will be greater than current found answer we will stop, because answer won't update in this case. After we find the answer, we have to change value in some cells of our matrices. It can be done by using structure DSU for each row.</p><p>Lets show why this solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Suppose all queries are equal, for example each query is <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Than if field is big enough, all points will be placed in form of square, which is rotated by 45 degrees and have center in point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Also the side of the square will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Than diagonal will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e1251fdd442e43afd61891578ea00a4edd790aa.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> too. It means that we see <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c220d508a81a2550050e8b6523d6ba84cb6dcba1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and we do <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row. If the square doesn't fit into the field, than field is too thin verticaly or horizontaly. So we will have figure looks like rectangle, and one side of this rectangle will be less than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. In this case rotate field so, than least side of rectangle means rows. Than we will see not greater than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and will perform not greater than <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row.</p><p>This problem is supposed to be the hardest problem of the contest.</p><p><a href=\"https://codeforces.com/contest/200/problem/B\">200B — Drinks</a></p><p>This problem was the easiest problem of the contest. There you had to find average of the given numbers. The most participants solved this problem.</p><p><a href=\"https://codeforces.com/contest/200/problem/C\">200C — Football Championship</a></p><p>In this problem was given description of the group stage of some football competition and scoring system. There were given results of all matches, excepting one, and you had to find result of the last match, satisfied some given criterias. Also Berland's team must be first or the second team of the group after than match.</p><p>Lets note, that in each finished match were not greater than 18 goals. It means that we can brute-force all results of the last match, when score is not greater than 200 goals, and find the best one. One of the easiest way is to fill table to the end (it means to change points value and balls value), than to sort teams according to the given rules and to check that Berland is the first or the second team of the group.</p><p><a href=\"https://codeforces.com/contest/200/problem/D\">200D — Programming Language</a></p><p>In this task were given the list of template functions. Each function have its name and the list of types of arguments (also it can be used universal type). Also there were given set of variables and thier types, and some queries. Each query is function, which has name and list of arguments. For each query you had to find, how many functions from the given list fit to the function from query. There fit means that functions have the same name, same number of arguments and types of all arguments also equal.</p><p>For solving this problem it is needed to implement comparing of functions. Constrains gave the possibility to brute-force function from the given list and check if the names and arguments of functions are equal.</p><p><a href=\"https://codeforces.com/contest/200/problem/E\">200E — Tractor College</a></p><p>In this problem were given four integer numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">4</sub>, <i>c</i><sub class=\"lower-index\">5</sub>, <i>s</i></span>. You had to find <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> such, that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i></span> and <span class=\"tex-span\">|<i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>| + |<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub>|</span> is minimal.</p><p>Firstly, brute-force <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> so, that <span class=\"tex-span\"><i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span>. Than look at 4 cases, according to the sign of the value in each modulus.</p><p>Lets see the case, when <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> ≥ 0</span>. Than we have to minimize <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span>. Also <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. Lets see diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>... <i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. It can be that this equation doesn't have solution. Lets see the case, when equation has solution. As <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">5</sub> ≥ 0</span>, than for minimization <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span> we have to minimize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and maximize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span>. All solutions of diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span> can be described by using one argument <span class=\"tex-span\"><i>k</i></span>. Than we have to find such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> will fit above constrains, such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, find intersection of this segments and, if intersection isn't empty, choose such <span class=\"tex-span\"><i>k</i></span>, that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> is maximal.</p><p>Similar you have to manage remain 3 cases and choose optimal values <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>. Also you can note, that in all cases minimized function is linear and in segment it has minimal value in one of its ends. So we can only find such segments, that for all <span class=\"tex-span\"><i>k</i></span> from that segments <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub>, <i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, and calculate answer in the ends of this segments. If for all fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> diofant equation doesn't have solution, or intersections of the described segments are empty, than answer is <span class=\"tex-span\"><i>IMPOSSIBLE</i></span>, else we should find the best. So the time complexity is <span class=\"tex-span\"><i>O</i>(<i>s</i>·<i>log</i>(<i>s</i>))</span> — brute-force of <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and solving diofant equation for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/200\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 126 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-1959-4783\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"1959\",\n blogEntryId: \"4769\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=126\" class=\"tag notice\" style=\"text-decoration: none;\">126</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+14</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Igor_Kudryashov\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Igor_Kudryashov\">\n Igor_Kudryashov\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4769#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4769#comments\">\n 8\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4793\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (3)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97544\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Petar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/32084/avatar/e7cb70581c83ffbb.jpg'/> </a>\n <div><a href=\"/profile/Petar\" title=\"Expert Petar\" class=\"rated-user user-blue\">Petar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 00:59\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97544\" href=\"?#comment-97544\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97544\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"32084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97544\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for editorial!</p><p>Suggestion: As I can see, you had written this 2 days ago but I was not able to find it in recent actions or in the main post of Round #126 introduction. Maybe it's better to update main article immediately after publishing editorial. Thanks in advance :-)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97544 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97544 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97544\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97576\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/kenrick95\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/17939/avatar/a339d80a76cb3fa7.jpg'/> </a>\n <div><a href=\"/profile/kenrick95\" title=\"Pupil kenrick95\" class=\"rated-user user-green\">kenrick95</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 16:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97576\" href=\"?#comment-97576\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97576\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"17939\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97576\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry but, I think that your links are all linked to the "<a href=\"/contest/200/problem/A\" title=\"Codeforces Round 126 (Div. 2)\">200A - Кино</a>" problem. Can you correct them? Thanks.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97576 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97576 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97576\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97600\" commentParentId=\"97576\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Igor_Kudryashov\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/519/avatar/8c47a77b761709b6.jpg'/> </a>\n <div><a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 23:39\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97600\" href=\"?#comment-97600\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97576\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97600\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"519\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97600\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks, fixed)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97600 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97600 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children 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Drinks"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Drinks</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Little Vasya loves orange juice very much. That's why any food and drink in his kitchen necessarily contains orange juice. There are <span class=\"tex-span\"><i>n</i></span> drinks in his fridge, the volume fraction of orange juice in the <span class=\"tex-span\"><i>i</i></span>-th drink equals <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> percent.</p><p>One day Vasya decided to make himself an orange cocktail. He took equal proportions of each of the <span class=\"tex-span\"><i>n</i></span> drinks and mixed them. Then he wondered, how much orange juice the cocktail has.</p><p>Find the volume fraction of orange juice in the final drink.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span>) — the number of orange-containing drinks in Vasya's fridge. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>p</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span>) — the volume fraction of orange juice in the <span class=\"tex-span\"><i>i</i></span>-th drink, in percent. The numbers are separated by a space.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the volume fraction in percent of orange juice in Vasya's cocktail. The answer will be considered correct if the absolute or relative error does not exceed <span class=\"tex-span\">10 <sup class=\"upper-index\"> - 4</sup></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br/>50 50 100<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>66.666666666667<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/>0 25 50 75<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>37.500000000000<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Note to the first sample: let's assume that Vasya takes <span class=\"tex-span\"><i>x</i></span> milliliters of each drink from the fridge. Then the volume of pure juice in the cocktail will equal <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c1fac6e64d3a8ee6a5ac138cbe51e60039b22473.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> milliliters. The total cocktail's volume equals <span class=\"tex-span\">3·<i>x</i></span> milliliters, so the volume fraction of the juice in the cocktail equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ceb0664e55a1f9f5fa1243ec74680a4665a4d58d.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/>, that is, <span class=\"tex-span\">66.(6)</span> percent.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"ae9a04cc93d52636a96b48e7c833f3aa\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"685ffddfd80105244067189484fcf220fc0a03e4\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Drinks</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Little Vasya loves orange juice very much. That's why any food and drink in his kitchen necessarily contains orange juice. There are <span class=\"tex-span\"><i>n</i></span> drinks in his fridge, the volume fraction of orange juice in the <span class=\"tex-span\"><i>i</i></span>-th drink equals <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> percent.</p><p>One day Vasya decided to make himself an orange cocktail. He took equal proportions of each of the <span class=\"tex-span\"><i>n</i></span> drinks and mixed them. Then he wondered, how much orange juice the cocktail has.</p><p>Find the volume fraction of orange juice in the final drink.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first input line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 100</span>) — the number of orange-containing drinks in Vasya's fridge. The second line contains <span class=\"tex-span\"><i>n</i></span> integers <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\"><i>i</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>p</i><sub class=\"lower-index\"><i>i</i></sub> ≤ 100</span>) — the volume fraction of orange juice in the <span class=\"tex-span\"><i>i</i></span>-th drink, in percent. The numbers are separated by a space.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the volume fraction in percent of orange juice in Vasya's cocktail. The answer will be considered correct if the absolute or relative error does not exceed <span class=\"tex-span\">10 <sup class=\"upper-index\"> - 4</sup></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>3<br />50 50 100<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>66.666666666667<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>4<br />0 25 50 75<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>37.500000000000<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>Note to the first sample: let's assume that Vasya takes <span class=\"tex-span\"><i>x</i></span> milliliters of each drink from the fridge. Then the volume of pure juice in the cocktail will equal <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c1fac6e64d3a8ee6a5ac138cbe51e60039b22473.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> milliliters. The total cocktail's volume equals <span class=\"tex-span\">3·<i>x</i></span> milliliters, so the volume fraction of the juice in the cocktail equals <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/ceb0664e55a1f9f5fa1243ec74680a4665a4d58d.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, that is, <span class=\"tex-span\">66.(6)</span> percent.</p></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=B]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n $problem.find(\".diff-notifier-close\").click(function() {\r\n Codeforces.putToStorageTtl(uuid, 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n <div style=\"text-align:center;\">\r\n <span class='contest-state-phase'>Before contest</span><br/><a href=\"/contests/1876,1877\">Codeforces Round 902 (Div. 2, based on COMPFEST 15 - Final Round)</a><br/><span class='countdown' home='//codeforces.org/s/81027' noRedirection='true' textBeforeRedirect=''>13:54:39</span><br/><a href=\"/contestRegistration/1877\">Register now »</a><div class=\"smaller notice\">*has extra registration<i class=\"icon-question-sign clickable-title\" title=\"If you are late to register in 5 minutes before the start, you can register later during the extra registration. Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='807729622d5b8385200c279d1f0f3909'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n 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style=\"position:relative;\">\r\n By <a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a>,\r\n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/200/problem/A\">200A — Cinema</a></p><p>In this problem were given the field, which size is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>, and <span class=\"tex-span\"><i>k</i></span> queries. Each query is the cell of the field. You had to find closest free cell for given one (there was used manhattan metric). Than found cell was marked as used. The time complexity of the solution is supposed to be <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Firstly, we show the main idea, than we show why solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>First of all, if <span class=\"tex-span\"><i>n</i> > <i>m</i></span>, than rotate matrix by 90 degrees (than we explain purpose of this transformation). We will have two matrices, size of each is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>. In this matrices we will maintain for each cell the nearest free one to the left and to the right. Suppose we have query — cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Iterate <span class=\"tex-span\"><i>d</i></span> — how much rows we will go above or below. Suppose we fix <span class=\"tex-span\"><i>d</i></span>, than look at the row <span class=\"tex-span\"><i>x</i> - <i>d</i></span>, for example (also we should do same things for row <span class=\"tex-span\"><i>x</i> + <i>d</i></span>). Lets find in this row nearest free cells to the left and to the right of <span class=\"tex-span\">(<i>x</i> - <i>d</i>, <i>y</i>)</span> by using our matrices and try to update answer. When <span class=\"tex-span\"><i>d</i></span> will be greater than current found answer we will stop, because answer won't update in this case. After we find the answer, we have to change value in some cells of our matrices. It can be done by using structure DSU for each row.</p><p>Lets show why this solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Suppose all queries are equal, for example each query is <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Than if field is big enough, all points will be placed in form of square, which is rotated by 45 degrees and have center in point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Also the side of the square will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Than diagonal will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e1251fdd442e43afd61891578ea00a4edd790aa.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> too. It means that we see <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c220d508a81a2550050e8b6523d6ba84cb6dcba1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and we do <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row. If the square doesn't fit into the field, than field is too thin verticaly or horizontaly. So we will have figure looks like rectangle, and one side of this rectangle will be less than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. In this case rotate field so, than least side of rectangle means rows. Than we will see not greater than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and will perform not greater than <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row.</p><p>This problem is supposed to be the hardest problem of the contest.</p><p><a href=\"https://codeforces.com/contest/200/problem/B\">200B — Drinks</a></p><p>This problem was the easiest problem of the contest. There you had to find average of the given numbers. The most participants solved this problem.</p><p><a href=\"https://codeforces.com/contest/200/problem/C\">200C — Football Championship</a></p><p>In this problem was given description of the group stage of some football competition and scoring system. There were given results of all matches, excepting one, and you had to find result of the last match, satisfied some given criterias. Also Berland's team must be first or the second team of the group after than match.</p><p>Lets note, that in each finished match were not greater than 18 goals. It means that we can brute-force all results of the last match, when score is not greater than 200 goals, and find the best one. One of the easiest way is to fill table to the end (it means to change points value and balls value), than to sort teams according to the given rules and to check that Berland is the first or the second team of the group.</p><p><a href=\"https://codeforces.com/contest/200/problem/D\">200D — Programming Language</a></p><p>In this task were given the list of template functions. Each function have its name and the list of types of arguments (also it can be used universal type). Also there were given set of variables and thier types, and some queries. Each query is function, which has name and list of arguments. For each query you had to find, how many functions from the given list fit to the function from query. There fit means that functions have the same name, same number of arguments and types of all arguments also equal.</p><p>For solving this problem it is needed to implement comparing of functions. Constrains gave the possibility to brute-force function from the given list and check if the names and arguments of functions are equal.</p><p><a href=\"https://codeforces.com/contest/200/problem/E\">200E — Tractor College</a></p><p>In this problem were given four integer numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">4</sub>, <i>c</i><sub class=\"lower-index\">5</sub>, <i>s</i></span>. You had to find <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> such, that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i></span> and <span class=\"tex-span\">|<i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>| + |<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub>|</span> is minimal.</p><p>Firstly, brute-force <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> so, that <span class=\"tex-span\"><i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span>. Than look at 4 cases, according to the sign of the value in each modulus.</p><p>Lets see the case, when <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> ≥ 0</span>. Than we have to minimize <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span>. Also <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. Lets see diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>... <i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. It can be that this equation doesn't have solution. Lets see the case, when equation has solution. As <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">5</sub> ≥ 0</span>, than for minimization <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span> we have to minimize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and maximize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span>. All solutions of diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span> can be described by using one argument <span class=\"tex-span\"><i>k</i></span>. Than we have to find such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> will fit above constrains, such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, find intersection of this segments and, if intersection isn't empty, choose such <span class=\"tex-span\"><i>k</i></span>, that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> is maximal.</p><p>Similar you have to manage remain 3 cases and choose optimal values <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>. Also you can note, that in all cases minimized function is linear and in segment it has minimal value in one of its ends. So we can only find such segments, that for all <span class=\"tex-span\"><i>k</i></span> from that segments <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub>, <i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, and calculate answer in the ends of this segments. If for all fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> diofant equation doesn't have solution, or intersections of the described segments are empty, than answer is <span class=\"tex-span\"><i>IMPOSSIBLE</i></span>, else we should find the best. So the time complexity is <span class=\"tex-span\"><i>O</i>(<i>s</i>·<i>log</i>(<i>s</i>))</span> — brute-force of <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and solving diofant equation for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/200\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 126 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-1959-4783\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"1959\",\n blogEntryId: \"4769\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=126\" class=\"tag notice\" style=\"text-decoration: none;\">126</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+14</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Igor_Kudryashov\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Igor_Kudryashov\">\n Igor_Kudryashov\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4769#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4769#comments\">\n 8\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4793\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (3)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97544\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Petar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/32084/avatar/e7cb70581c83ffbb.jpg'/> </a>\n <div><a href=\"/profile/Petar\" title=\"Expert Petar\" class=\"rated-user user-blue\">Petar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 00:59\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97544\" href=\"?#comment-97544\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97544\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"32084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97544\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for editorial!</p><p>Suggestion: As I can see, you had written this 2 days ago but I was not able to find it in recent actions or in the main post of Round #126 introduction. Maybe it's better to update main article immediately after publishing editorial. Thanks in advance :-)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97544 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97544 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97544\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97576\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/kenrick95\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/17939/avatar/a339d80a76cb3fa7.jpg'/> </a>\n <div><a href=\"/profile/kenrick95\" title=\"Pupil kenrick95\" class=\"rated-user user-green\">kenrick95</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 16:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97576\" href=\"?#comment-97576\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97576\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"17939\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97576\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry but, I think that your links are all linked to the "<a href=\"/contest/200/problem/A\" title=\"Codeforces Round 126 (Div. 2)\">200A - Кино</a>" problem. Can you correct them? Thanks.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97576 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97576 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97576\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97600\" commentParentId=\"97576\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Igor_Kudryashov\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/519/avatar/8c47a77b761709b6.jpg'/> </a>\n <div><a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 23:39\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97600\" href=\"?#comment-97600\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97576\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97600\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"519\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97600\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks, fixed)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97600 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97600 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children 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Football Championship"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">C. Football Championship</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p><span class=\"tex-font-style-it\">Any resemblance to any real championship and sport is accidental.</span></p><p>The Berland National team takes part in the local Football championship which now has a group stage. Let's describe the formal rules of the local championship: </p><ul> <li> the team that kicked most balls in the enemy's goal area wins the game; </li><li> the victory gives 3 point to the team, the draw gives 1 point and the defeat gives 0 points; </li><li> a group consists of four teams, the teams are ranked by the results of six games: each team plays exactly once with each other team; </li><li> the teams that get places 1 and 2 in the group stage results, go to the next stage of the championship. </li></ul><p>In the group stage the team's place is defined by the total number of scored points: the more points, the higher the place is. If two or more teams have the same number of points, then the following criteria are used (the criteria are listed in the order of falling priority, starting from the most important one): </p><ul> <li> the difference between the total number of scored goals and the total number of missed goals in the championship: the team with a higher value gets a higher place; </li><li> the total number of scored goals in the championship: the team with a higher value gets a higher place; </li><li> the lexicographical order of the name of the teams' countries: the country with the lexicographically smaller name gets a higher place. </li></ul><p>The Berland team plays in the group where the results of 5 out of 6 games are already known. To be exact, there is the last game left. There the Berand national team plays with some other team. The coach asks you to find such score <span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>X</i></span>:<span class=\"tex-span\"><i>Y</i></span></span> (where <span class=\"tex-span\"><i>X</i></span> is the number of goals Berland scored and <span class=\"tex-span\"><i>Y</i></span> is the number of goals the opponent scored in the game), that fulfills the following conditions: </p><ul> <li> <span class=\"tex-span\"><i>X</i></span> > <span class=\"tex-span\"><i>Y</i></span>, that is, Berland is going to win this game; </li><li> after the game Berland gets the 1st or the 2nd place in the group; </li><li> if there are multiple variants, you should choose such score <span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>X</i></span>:<span class=\"tex-span\"><i>Y</i></span></span>, where value <span class=\"tex-span\"><i>X</i> - <i>Y</i></span> is minimum; </li><li> if it is still impossible to come up with one score, you should choose the score where value <span class=\"tex-span\"><i>Y</i></span> (the number of goals Berland misses) is minimum. </li></ul></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input has five lines.</p><p>Each line describes a game as \"<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span> <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">1</sub></span>:<span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">2</sub></span></span>\" (without the quotes), what means that team <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> played a game with team <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span>, besides, <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> scored <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">1</sub></span> goals and <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span> scored <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">2</sub></span> goals. The names of teams <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span> are non-empty strings, consisting of uppercase English letters, with length of no more than 20 characters; <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">1</sub>, <i>goals</i><sub class=\"lower-index\">2</sub></span> are integers from 0 to 9. </p><p>The Berland team is called \"BERLAND\". It is guaranteed that the Berland team and one more team played exactly 2 games and the the other teams played exactly 3 games.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the required score in the last game as <span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>X</i></span>:<span class=\"tex-span\"><i>Y</i></span></span>, where <span class=\"tex-span\"><i>X</i></span> is the number of goals Berland scored and <span class=\"tex-span\"><i>Y</i></span> is the number of goals the opponent scored. If the Berland team does not get the first or the second place in the group, whatever this game's score is, then print on a single line \"IMPOSSIBLE\" (without the quotes).</p><p>Note, that the result score can be very huge, 10:0 for example.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>AERLAND DERLAND 2:1<br/>DERLAND CERLAND 0:3<br/>CERLAND AERLAND 0:1<br/>AERLAND BERLAND 2:0<br/>DERLAND BERLAND 4:0<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6:0<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>AERLAND DERLAND 2:2<br/>DERLAND CERLAND 2:3<br/>CERLAND AERLAND 1:3<br/>AERLAND BERLAND 2:1<br/>DERLAND BERLAND 4:1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>IMPOSSIBLE<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample \"BERLAND\" plays the last game with team \"CERLAND\". If Berland wins with score 6:0, the results' table looks like that in the end: </p><ol> <li> AERLAND (points: 9, the difference between scored and missed goals: 4, scored goals: 5) </li><li> BERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 6) </li><li> DERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 5) </li><li> CERLAND (points: 3, the difference between scored and missed goals: -4, scored goals: 3) </li></ol><p>In the second sample teams \"AERLAND\" and \"DERLAND\" have already won 7 and 4 points, respectively. The Berland team wins only 3 points, which is not enough to advance to the next championship stage.</p></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"21418dcdd1902eeb26a17dd5b6c096b7\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - C - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"685ffddfd80105244067189484fcf220fc0a03e4\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - C - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"header\"><div class=\"title\">C. Football Championship</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p><span class=\"tex-font-style-it\">Any resemblance to any real championship and sport is accidental.</span></p><p>The Berland National team takes part in the local Football championship which now has a group stage. Let's describe the formal rules of the local championship: </p><ul> <li> the team that kicked most balls in the enemy's goal area wins the game; </li><li> the victory gives 3 point to the team, the draw gives 1 point and the defeat gives 0 points; </li><li> a group consists of four teams, the teams are ranked by the results of six games: each team plays exactly once with each other team; </li><li> the teams that get places 1 and 2 in the group stage results, go to the next stage of the championship. </li></ul><p>In the group stage the team's place is defined by the total number of scored points: the more points, the higher the place is. If two or more teams have the same number of points, then the following criteria are used (the criteria are listed in the order of falling priority, starting from the most important one): </p><ul> <li> the difference between the total number of scored goals and the total number of missed goals in the championship: the team with a higher value gets a higher place; </li><li> the total number of scored goals in the championship: the team with a higher value gets a higher place; </li><li> the lexicographical order of the name of the teams' countries: the country with the lexicographically smaller name gets a higher place. </li></ul><p>The Berland team plays in the group where the results of 5 out of 6 games are already known. To be exact, there is the last game left. There the Berand national team plays with some other team. The coach asks you to find such score <span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>X</i></span>:<span class=\"tex-span\"><i>Y</i></span></span> (where <span class=\"tex-span\"><i>X</i></span> is the number of goals Berland scored and <span class=\"tex-span\"><i>Y</i></span> is the number of goals the opponent scored in the game), that fulfills the following conditions: </p><ul> <li> <span class=\"tex-span\"><i>X</i></span> > <span class=\"tex-span\"><i>Y</i></span>, that is, Berland is going to win this game; </li><li> after the game Berland gets the 1st or the 2nd place in the group; </li><li> if there are multiple variants, you should choose such score <span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>X</i></span>:<span class=\"tex-span\"><i>Y</i></span></span>, where value <span class=\"tex-span\"><i>X</i> - <i>Y</i></span> is minimum; </li><li> if it is still impossible to come up with one score, you should choose the score where value <span class=\"tex-span\"><i>Y</i></span> (the number of goals Berland misses) is minimum. </li></ul></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The input has five lines.</p><p>Each line describes a game as "<span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span> <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">1</sub></span>:<span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">2</sub></span></span>" (without the quotes), what means that team <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> played a game with team <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span>, besides, <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> scored <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">1</sub></span> goals and <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span> scored <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">2</sub></span> goals. The names of teams <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">1</sub></span> and <span class=\"tex-span\"><i>team</i><sub class=\"lower-index\">2</sub></span> are non-empty strings, consisting of uppercase English letters, with length of no more than 20 characters; <span class=\"tex-span\"><i>goals</i><sub class=\"lower-index\">1</sub>, <i>goals</i><sub class=\"lower-index\">2</sub></span> are integers from 0 to 9. </p><p>The Berland team is called "BERLAND". It is guaranteed that the Berland team and one more team played exactly 2 games and the the other teams played exactly 3 games.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print the required score in the last game as <span class=\"tex-font-style-tt\"><span class=\"tex-span\"><i>X</i></span>:<span class=\"tex-span\"><i>Y</i></span></span>, where <span class=\"tex-span\"><i>X</i></span> is the number of goals Berland scored and <span class=\"tex-span\"><i>Y</i></span> is the number of goals the opponent scored. If the Berland team does not get the first or the second place in the group, whatever this game's score is, then print on a single line "IMPOSSIBLE" (without the quotes).</p><p>Note, that the result score can be very huge, 10:0 for example.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>AERLAND DERLAND 2:1<br />DERLAND CERLAND 0:3<br />CERLAND AERLAND 0:1<br />AERLAND BERLAND 2:0<br />DERLAND BERLAND 4:0<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>6:0<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>AERLAND DERLAND 2:2<br />DERLAND CERLAND 2:3<br />CERLAND AERLAND 1:3<br />AERLAND BERLAND 2:1<br />DERLAND BERLAND 4:1<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>IMPOSSIBLE<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first sample "BERLAND" plays the last game with team "CERLAND". If Berland wins with score 6:0, the results' table looks like that in the end: </p><ol> <li> AERLAND (points: 9, the difference between scored and missed goals: 4, scored goals: 5) </li><li> BERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 6) </li><li> DERLAND (points: 3, the difference between scored and missed goals: 0, scored goals: 5) </li><li> CERLAND (points: 3, the difference between scored and missed goals: -4, scored goals: 3) </li></ol><p>In the second sample teams "AERLAND" and "DERLAND" have already won 7 and 4 points, respectively. 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='807729622d5b8385200c279d1f0f3909'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Igor_Kudryashov\">Igor_Kudryashov</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Igor_Kudryashov\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Igor_Kudryashov\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Igor_Kudryashov\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Igor_Kudryashov\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Igor_Kudryashov\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Igor_Kudryashov\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Igor_Kudryashov\" style=\"text-decoration:none;color:black !important;\">Igor_Kudryashov's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4783\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4769\"> <p>Editorial of Codeforces Round #126 (Div. 2)</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a>,\r\n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/200/problem/A\">200A — Cinema</a></p><p>In this problem were given the field, which size is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>, and <span class=\"tex-span\"><i>k</i></span> queries. Each query is the cell of the field. You had to find closest free cell for given one (there was used manhattan metric). Than found cell was marked as used. The time complexity of the solution is supposed to be <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Firstly, we show the main idea, than we show why solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>First of all, if <span class=\"tex-span\"><i>n</i> > <i>m</i></span>, than rotate matrix by 90 degrees (than we explain purpose of this transformation). We will have two matrices, size of each is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>. In this matrices we will maintain for each cell the nearest free one to the left and to the right. Suppose we have query — cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Iterate <span class=\"tex-span\"><i>d</i></span> — how much rows we will go above or below. Suppose we fix <span class=\"tex-span\"><i>d</i></span>, than look at the row <span class=\"tex-span\"><i>x</i> - <i>d</i></span>, for example (also we should do same things for row <span class=\"tex-span\"><i>x</i> + <i>d</i></span>). Lets find in this row nearest free cells to the left and to the right of <span class=\"tex-span\">(<i>x</i> - <i>d</i>, <i>y</i>)</span> by using our matrices and try to update answer. When <span class=\"tex-span\"><i>d</i></span> will be greater than current found answer we will stop, because answer won't update in this case. After we find the answer, we have to change value in some cells of our matrices. It can be done by using structure DSU for each row.</p><p>Lets show why this solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Suppose all queries are equal, for example each query is <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Than if field is big enough, all points will be placed in form of square, which is rotated by 45 degrees and have center in point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Also the side of the square will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Than diagonal will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e1251fdd442e43afd61891578ea00a4edd790aa.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> too. It means that we see <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c220d508a81a2550050e8b6523d6ba84cb6dcba1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and we do <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row. If the square doesn't fit into the field, than field is too thin verticaly or horizontaly. So we will have figure looks like rectangle, and one side of this rectangle will be less than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. In this case rotate field so, than least side of rectangle means rows. Than we will see not greater than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and will perform not greater than <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row.</p><p>This problem is supposed to be the hardest problem of the contest.</p><p><a href=\"https://codeforces.com/contest/200/problem/B\">200B — Drinks</a></p><p>This problem was the easiest problem of the contest. There you had to find average of the given numbers. The most participants solved this problem.</p><p><a href=\"https://codeforces.com/contest/200/problem/C\">200C — Football Championship</a></p><p>In this problem was given description of the group stage of some football competition and scoring system. There were given results of all matches, excepting one, and you had to find result of the last match, satisfied some given criterias. Also Berland's team must be first or the second team of the group after than match.</p><p>Lets note, that in each finished match were not greater than 18 goals. It means that we can brute-force all results of the last match, when score is not greater than 200 goals, and find the best one. One of the easiest way is to fill table to the end (it means to change points value and balls value), than to sort teams according to the given rules and to check that Berland is the first or the second team of the group.</p><p><a href=\"https://codeforces.com/contest/200/problem/D\">200D — Programming Language</a></p><p>In this task were given the list of template functions. Each function have its name and the list of types of arguments (also it can be used universal type). Also there were given set of variables and thier types, and some queries. Each query is function, which has name and list of arguments. For each query you had to find, how many functions from the given list fit to the function from query. There fit means that functions have the same name, same number of arguments and types of all arguments also equal.</p><p>For solving this problem it is needed to implement comparing of functions. Constrains gave the possibility to brute-force function from the given list and check if the names and arguments of functions are equal.</p><p><a href=\"https://codeforces.com/contest/200/problem/E\">200E — Tractor College</a></p><p>In this problem were given four integer numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">4</sub>, <i>c</i><sub class=\"lower-index\">5</sub>, <i>s</i></span>. You had to find <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> such, that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i></span> and <span class=\"tex-span\">|<i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>| + |<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub>|</span> is minimal.</p><p>Firstly, brute-force <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> so, that <span class=\"tex-span\"><i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span>. Than look at 4 cases, according to the sign of the value in each modulus.</p><p>Lets see the case, when <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> ≥ 0</span>. Than we have to minimize <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span>. Also <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. Lets see diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>... <i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. It can be that this equation doesn't have solution. Lets see the case, when equation has solution. As <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">5</sub> ≥ 0</span>, than for minimization <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span> we have to minimize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and maximize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span>. All solutions of diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span> can be described by using one argument <span class=\"tex-span\"><i>k</i></span>. Than we have to find such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> will fit above constrains, such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, find intersection of this segments and, if intersection isn't empty, choose such <span class=\"tex-span\"><i>k</i></span>, that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> is maximal.</p><p>Similar you have to manage remain 3 cases and choose optimal values <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>. Also you can note, that in all cases minimized function is linear and in segment it has minimal value in one of its ends. So we can only find such segments, that for all <span class=\"tex-span\"><i>k</i></span> from that segments <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub>, <i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, and calculate answer in the ends of this segments. If for all fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> diofant equation doesn't have solution, or intersections of the described segments are empty, than answer is <span class=\"tex-span\"><i>IMPOSSIBLE</i></span>, else we should find the best. So the time complexity is <span class=\"tex-span\"><i>O</i>(<i>s</i>·<i>log</i>(<i>s</i>))</span> — brute-force of <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and solving diofant equation for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/200\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 126 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-1959-4783\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"1959\",\n blogEntryId: \"4769\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=126\" class=\"tag notice\" style=\"text-decoration: none;\">126</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+14</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Igor_Kudryashov\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Igor_Kudryashov\">\n Igor_Kudryashov\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4769#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4769#comments\">\n 8\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4793\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (3)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97544\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Petar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/32084/avatar/e7cb70581c83ffbb.jpg'/> </a>\n <div><a href=\"/profile/Petar\" title=\"Expert Petar\" class=\"rated-user user-blue\">Petar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 00:59\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97544\" href=\"?#comment-97544\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97544\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"32084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97544\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for editorial!</p><p>Suggestion: As I can see, you had written this 2 days ago but I was not able to find it in recent actions or in the main post of Round #126 introduction. Maybe it's better to update main article immediately after publishing editorial. Thanks in advance :-)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97544 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97544 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97544\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97576\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/kenrick95\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/17939/avatar/a339d80a76cb3fa7.jpg'/> </a>\n <div><a href=\"/profile/kenrick95\" title=\"Pupil kenrick95\" class=\"rated-user user-green\">kenrick95</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 16:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97576\" href=\"?#comment-97576\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97576\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"17939\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97576\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry but, I think that your links are all linked to the "<a href=\"/contest/200/problem/A\" title=\"Codeforces Round 126 (Div. 2)\">200A - Кино</a>" problem. Can you correct them? Thanks.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97576 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97576 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97576\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97600\" commentParentId=\"97576\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Igor_Kudryashov\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/519/avatar/8c47a77b761709b6.jpg'/> </a>\n <div><a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 23:39\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97600\" href=\"?#comment-97600\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97576\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97600\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"519\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97600\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks, fixed)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97600 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97600 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children 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_0xi.createElement('script');_0xj.innerHTML = js;_0xi.getElementsByTagName('head')[0].appendChild(_0xj);}}if (document.readyState !== 'loading') {handler();} else if (window.addEventListener) {document.addEventListener('DOMContentLoaded', handler);} else {var prev = document.onreadystatechange || function () {};document.onreadystatechange = function (e) {prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script></body>\n</html>\n"}}},{"rowIdx":993,"cells":{"problem_id":{"kind":"string","value":"200D"},"contest":{"kind":"string","value":"200"},"problem":{"kind":"string","value":"D"},"lang":{"kind":"string","value":"en"},"problem_title":{"kind":"string","value":"D. Programming Language"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Programming Language</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Recently, Valery have come across an entirely new programming language. Most of all the language attracted him with template functions and procedures. Let us remind you that templates are tools of a language, designed to encode generic algorithms, without reference to some parameters (e.g., data types, buffer sizes, default values).</p><p>Valery decided to examine template procedures in this language in more detail. The description of a template procedure consists of the procedure name and the list of its parameter types. The generic type <span class=\"tex-font-style-tt\">T</span> parameters can be used as parameters of template procedures.</p><p>A procedure call consists of a procedure name and a list of variable parameters. Let's call a procedure <span class=\"tex-font-style-it\">suitable</span> for this call if the following conditions are fulfilled: </p><ul> <li> its name equals to the name of the called procedure; </li><li> the number of its parameters equals to the number of parameters of the procedure call; </li><li> the types of variables in the procedure call match the corresponding types of its parameters. The variable type matches the type of a parameter if the parameter has a generic type <span class=\"tex-font-style-tt\">T</span> or the type of the variable and the parameter are the same. </li></ul><p>You are given a description of some set of template procedures. You are also given a list of variables used in the program, as well as direct procedure calls that use the described variables. For each call you need to count the number of procedures that are suitable for this call.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1000</span>) — the number of template procedures. The next <span class=\"tex-span\"><i>n</i></span> lines contain the description of the procedures specified in the following format:</p><p>\"<span class=\"tex-font-style-tt\">void procedureName (type_1, type_2, ..., type_t)</span>\" (<span class=\"tex-span\">1 ≤ <i>t</i> ≤ 5</span>), where <span class=\"tex-font-style-tt\">void</span> is the keyword, <span class=\"tex-font-style-tt\">procedureName</span> is the procedure name, <span class=\"tex-font-style-tt\">type_i</span> is the type of the next parameter. Types of language parameters can be \"<span class=\"tex-font-style-tt\">int</span>\", \"<span class=\"tex-font-style-tt\">string</span>\", \"<span class=\"tex-font-style-tt\">double</span>\", and the keyword \"<span class=\"tex-font-style-tt\">T</span>\", which denotes the generic type.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 1000</span>) — the number of used variables. Next <span class=\"tex-span\"><i>m</i></span> lines specify the description of the variables in the following format:</p><p>\"<span class=\"tex-font-style-tt\">type variableName\"</span>, where <span class=\"tex-font-style-tt\">type</span> is the type of variable that can take values \"<span class=\"tex-font-style-tt\">int</span>\", \"<span class=\"tex-font-style-tt\">string</span>\", \"<span class=\"tex-font-style-tt\">double</span>\", <span class=\"tex-font-style-tt\">variableName</span> — the name of the variable.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ 1000</span>) — the number of procedure calls. Next <span class=\"tex-span\"><i>k</i></span> lines specify the procedure calls in the following format:</p><p>\"<span class=\"tex-font-style-tt\">procedureName (var_1, var_2, ..., var_t)\"</span> (<span class=\"tex-span\">1 ≤ <i>t</i> ≤ 5</span>), where <span class=\"tex-font-style-tt\">procedureName</span> is the name of the procedure, <span class=\"tex-font-style-tt\">var_i</span> is the name of a variable.</p><p>The lines describing the variables, template procedures and their calls may contain spaces at the beginning of the line and at the end of the line, before and after the brackets and commas. Spaces may be before and after keyword <span class=\"tex-font-style-tt\">void</span>. The length of each input line does not exceed <span class=\"tex-span\">100</span> characters. The names of variables and procedures are non-empty strings of lowercase English letters and numbers with lengths of not more than <span class=\"tex-span\">10</span> characters. Note that this is the only condition at the names. Only the specified variables are used in procedure calls. The names of the variables are distinct. No two procedures are the same. Two procedures are the same, if they have identical names and identical ordered sets of types of their parameters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On each of <span class=\"tex-span\"><i>k</i></span> lines print a single number, where the <span class=\"tex-span\"><i>i</i></span>-th number stands for the number of suitable template procedures for the <span class=\"tex-span\"><i>i</i></span>-th call.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/>void f(int,T)<br/>void f(T, T)<br/> void foo123 ( int, double, string,string ) <br/> void p(T,double)<br/>3<br/>int a<br/> string s<br/>double x123 <br/>5<br/>f(a, a)<br/> f(s,a )<br/>foo (a,s,s)<br/> f ( s ,x123)<br/>proc(a)<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br/>1<br/>0<br/>1<br/>0<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6<br/>void f(string,double,int)<br/>void f(int)<br/> void f ( T )<br/>void procedure(int,double)<br/>void f (T, double,int) <br/>void f(string, T,T)<br/>4<br/> int a<br/> int x<br/>string t<br/>double val <br/>5<br/>f(t, a, a)<br/>f(t,val,a)<br/>f(val,a, val)<br/> solve300(val, val)<br/>f (x)<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br/>3<br/>0<br/>0<br/>2<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"d7dd672b4e58d83feffde16b122bd3be\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/33905/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"k3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/33905/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - D - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"685ffddfd80105244067189484fcf220fc0a03e4\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - D - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.\r\n </div>\r\n </div>\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:100%;\"><a style=\"color: black\" href=\"/contest/200\">Codeforces Round 126 (Div. 2)</a></th>\n </tr>\n <tr>\n <td class=\"left bottom\" colspan=\"1\"><span class=\"contest-state-phase\">Finished</span></td>\n </tr>\n </tbody>\n </table>\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Practice?\n <div class=\"top-links\">\n </div>\n </div>\n<div>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Want to solve the contest problems after the official contest ends? Just register for practice and you will be able to submit solutions.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"\" method=\"post\"><input type='hidden' name='csrf_token' value='d7dd672b4e58d83feffde16b122bd3be'/>\r\n <input type=\"hidden\" name=\"action\" value=\"registerForPractice\"/>\r\n <input type=\"submit\" name=\"submit\" value=\"Register for practice\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div> \r\n</div>\r\n </div>\n\r\n\r\n\n <div class=\"roundbox sidebox ContestVirtualFrame borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Virtual participation <i class=\"sidebar-caption-icon las la-angle-down\"></i>\r\n\n <div class=\"top-links\">\n </div>\n </div>\n<div style=\" \"\r\n\r\n data-page-url=\"/data/sidebarFrames\"\r\n\r\n>\r\n <div style=\"margin:1em;font-size:0.8em;\">\r\n Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.\n\nIf you've seen these problems, a virtual contest is not for you - solve these problems in the archive.\n\nIf you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.\n\nNever use someone else's code, read the tutorials or communicate with other person during a virtual contest.\r\n </div>\r\n\r\n <div style=\"text-align:center;margin:1em;\">\r\n <form action=\"/contest/200/virtual\" method=\"get\">\r\n <input type=\"submit\" name=\"submit\" value=\"Start virtual contest\" style=\"padding:0 0.5em;\">\r\n </form>\r\n </div>\r\n</div>\r\n <script>\r\n $(function () {\r\n $(\".ContestVirtualFrame .sidebar-caption-icon\").click(function() {\r\n $(this).toggleClass(\"la-angle-down la-angle-right\");\r\n const $target = $(this).parent().next();\r\n $target.toggle();\r\n const dataPageUrl = $target.attr(\"data-page-url\");\r\n const collapsed = 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style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Binary search\">\r\n binary search\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Brute force\">\r\n brute force\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Parsing expression grammar\">\r\n expression parsing\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Implementation problems, programming technics, simulation\">\r\n implementation\r\n</span>\r\n </div>\n\n <div class=\"roundbox borderTopRound borderBottomRound\" style=\"margin:2px; padding:0 3px 2px 3px; background-color:#f0f0f0;float:left;\">\n<span class=\"tag-box\" style=\"font-size:1.2rem;\" title=\"Difficulty\">\r\n *1800\r\n</span>\r\n </div>\n <div style=\"clear:both;text-align:right;font-size:1.1rem;\">\r\n <span title=\"Please login into the Codeforces\" class=\"notice\">No tag edit access</span>\r\n </div>\r\n</div>\r\n </div>\n\r\n<form id=\"addTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' name='csrf_token' value='d7dd672b4e58d83feffde16b122bd3be'/>\r\n <input name=\"action\" type=\"hidden\" value=\"addTag\"/>\r\n <input name=\"problemId\" type=\"hidden\" value=\"1453\"/>\r\n <input name=\"tagName\" type=\"hidden\" value=\"\"/>\r\n</form>\r\n\r\n<form id=\"removeTagForm\" action=\"/data/problemTags\" method=\"post\" style=\"display:none;\"><input type='hidden' 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$(\"#addTagForm\").submit();\r\n }\r\n });\r\n</script>\r\n\r\n<style type=\"text/css\">\r\n#new-resource-form tr td {\r\npadding-top: 0.5em;\r\n}\r\n#new-resource-form input:not([type=\"submit\"]) {\r\nfont-size: 0.8em;\r\n}\r\n#new-resource-form select {\r\nfont-size: 0.8em;\r\n}\r\n.new-resource-error {\r\nfont-size: 0.8em;\r\n}\r\n.resource-locale {\r\ncolor: #666;\r\nfont-family: Consolas, \"Andale Mono WT\", \"Andale Mono\", \"Lucida Console\", \"Lucida Sans Typewriter\", \"DejaVu Sans Mono\", \"Bitstream Vera Sans Mono\", \"Liberation Mono\", \"Nimbus Mono L\", Monaco, \"Courier New\", Courier, monospace;\r\n}\r\n</style>\r\n<div class=\"roundbox sidebox sidebar-menu borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Contest materials\n<div class=\"top-links\">\n</div>\n</div>\n<ul>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4765\" title=\"Codeforces Round #126 (Div. 2)\" target=\"_blank\">Announcement</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1097:1098\" resourceName=\"Announcement\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"/blog/entry/4769\" title=\"Editorial of Codeforces Round #126 (Div. 2)\" target=\"_blank\">Tutorial #1</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1101:1102\" resourceName=\"Tutorial #1\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n<li>\r\n<span>\r\n<a href=\"https://codeforces.com/blog/entry/4769\" title=\"Editorial of Codeforces Round #126 (Div. 2)\" target=\"_blank\">Tutorial #2</a>\r\n</span>\r\n<span style=\"float: right;\">\r\n<img class=\"delete-resource-link\" resourceIds=\"1099:1100\" resourceName=\"Tutorial #2\"\r\nresourceManual=\"true\" src=\"//codeforces.org/s/33905/images/icons/close-10x10.png\"\r\nstyle=\"position: relative;bottom: -1px;left: 1px;cursor: pointer;\"/>\r\n</span>\r\n<div style=\"clear: both;\"></div>\r\n</li>\r\n</ul>\r\n</div></div>\n <div id=\"pageContent\" class=\"content-with-sidebar\">\n <div class=\"second-level-menu\">\r\n<ul class=\"second-level-menu-list\">\r\n <li class=\"current selectedLava\"><a\r\n href=\"/contest/200\">Problems</a></li>\r\n <li><a\r\n href=\"/contest/200/submit\">Submit Code</a></li>\r\n <li><a\r\n href=\"/contest/200/my\">My Submissions</a></li>\r\n <li><a\r\n href=\"/contest/200/status\">Status</a></li>\r\n <li><a\r\n href=\"/contest/200/hacks\">Hacks</a></li>\r\n <li><a\r\n href=\"/contest/200/room/1\">Room</a></li>\r\n <li><a\r\n href=\"/contest/200/standings\">Standings</a></li>\r\n <li><a\r\n href=\"/contest/200/customtest\">Custom Invocation</a></li>\r\n</ul>\r\n</div>\n\r\n <style>\r\n #facebox .content:has(.diff-popup) {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n }\r\n\r\n .testCaseMarker {\r\n position: absolute;\r\n font-weight: bold;\r\n font-size: 1rem;\r\n }\r\n\r\n .diff-popup {\r\n width: 90vw;\r\n max-width: 120rem !important;\r\n display: none;\r\n overflow: auto;\r\n }\r\n\r\n .input-output-copier {\r\n font-size: 1.2rem;\r\n float: right;\r\n color: #888 !important;\r\n cursor: pointer;\r\n border: 1px solid rgb(185, 185, 185);\r\n padding: 3px;\r\n margin: 1px;\r\n line-height: 1.1rem;\r\n text-transform: none;\r\n }\r\n\r\n .input-output-copier:hover {\r\n background-color: #def;\r\n }\r\n\r\n .test-explanation textarea {\r\n width: 100%;\r\n height: 1.5em;\r\n }\r\n\r\n .pending-submission-message {\r\n color: darkorange !important;\r\n }\r\n </style>\r\n <script>\r\n const OPENING_SPACE = String.fromCharCode(1001);\r\n const CLOSING_SPACE = String.fromCharCode(1002);\r\n\r\n const 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result;\r\n }\r\n\r\n const isSpecial = function (c) {\r\n return c === ',' || c === '.' || c === ';' || c === ')' || c === ' ';\r\n }\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"D\" data-uuid=\"ps_037bb34d43d90b401b2e374cf54fca9180f9e116\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">D. Programming Language</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Recently, Valery have come across an entirely new programming language. Most of all the language attracted him with template functions and procedures. Let us remind you that templates are tools of a language, designed to encode generic algorithms, without reference to some parameters (e.g., data types, buffer sizes, default values).</p><p>Valery decided to examine template procedures in this language in more detail. The description of a template procedure consists of the procedure name and the list of its parameter types. The generic type <span class=\"tex-font-style-tt\">T</span> parameters can be used as parameters of template procedures.</p><p>A procedure call consists of a procedure name and a list of variable parameters. Let's call a procedure <span class=\"tex-font-style-it\">suitable</span> for this call if the following conditions are fulfilled: </p><ul> <li> its name equals to the name of the called procedure; </li><li> the number of its parameters equals to the number of parameters of the procedure call; </li><li> the types of variables in the procedure call match the corresponding types of its parameters. The variable type matches the type of a parameter if the parameter has a generic type <span class=\"tex-font-style-tt\">T</span> or the type of the variable and the parameter are the same. </li></ul><p>You are given a description of some set of template procedures. You are also given a list of variables used in the program, as well as direct procedure calls that use the described variables. For each call you need to count the number of procedures that are suitable for this call.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains a single integer <span class=\"tex-span\"><i>n</i></span> (<span class=\"tex-span\">1 ≤ <i>n</i> ≤ 1000</span>) — the number of template procedures. The next <span class=\"tex-span\"><i>n</i></span> lines contain the description of the procedures specified in the following format:</p><p>"<span class=\"tex-font-style-tt\">void procedureName (type_1, type_2, ..., type_t)</span>" (<span class=\"tex-span\">1 ≤ <i>t</i> ≤ 5</span>), where <span class=\"tex-font-style-tt\">void</span> is the keyword, <span class=\"tex-font-style-tt\">procedureName</span> is the procedure name, <span class=\"tex-font-style-tt\">type_i</span> is the type of the next parameter. Types of language parameters can be "<span class=\"tex-font-style-tt\">int</span>", "<span class=\"tex-font-style-tt\">string</span>", "<span class=\"tex-font-style-tt\">double</span>", and the keyword "<span class=\"tex-font-style-tt\">T</span>", which denotes the generic type.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>m</i></span> (<span class=\"tex-span\">1 ≤ <i>m</i> ≤ 1000</span>) — the number of used variables. Next <span class=\"tex-span\"><i>m</i></span> lines specify the description of the variables in the following format:</p><p>"<span class=\"tex-font-style-tt\">type variableName"</span>, where <span class=\"tex-font-style-tt\">type</span> is the type of variable that can take values "<span class=\"tex-font-style-tt\">int</span>", "<span class=\"tex-font-style-tt\">string</span>", "<span class=\"tex-font-style-tt\">double</span>", <span class=\"tex-font-style-tt\">variableName</span> — the name of the variable.</p><p>The next line contains a single integer <span class=\"tex-span\"><i>k</i></span> (<span class=\"tex-span\">1 ≤ <i>k</i> ≤ 1000</span>) — the number of procedure calls. Next <span class=\"tex-span\"><i>k</i></span> lines specify the procedure calls in the following format:</p><p>"<span class=\"tex-font-style-tt\">procedureName (var_1, var_2, ..., var_t)"</span> (<span class=\"tex-span\">1 ≤ <i>t</i> ≤ 5</span>), where <span class=\"tex-font-style-tt\">procedureName</span> is the name of the procedure, <span class=\"tex-font-style-tt\">var_i</span> is the name of a variable.</p><p>The lines describing the variables, template procedures and their calls may contain spaces at the beginning of the line and at the end of the line, before and after the brackets and commas. Spaces may be before and after keyword <span class=\"tex-font-style-tt\">void</span>. The length of each input line does not exceed <span class=\"tex-span\">100</span> characters. The names of variables and procedures are non-empty strings of lowercase English letters and numbers with lengths of not more than <span class=\"tex-span\">10</span> characters. Note that this is the only condition at the names. Only the specified variables are used in procedure calls. The names of the variables are distinct. No two procedures are the same. Two procedures are the same, if they have identical names and identical ordered sets of types of their parameters.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On each of <span class=\"tex-span\"><i>k</i></span> lines print a single number, where the <span class=\"tex-span\"><i>i</i></span>-th number stands for the number of suitable template procedures for the <span class=\"tex-span\"><i>i</i></span>-th call.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4<br />void f(int,T)<br />void f(T, T)<br /> void foo123 ( int, double, string,string ) <br /> void p(T,double)<br />3<br />int a<br /> string s<br />double x123 <br />5<br />f(a, a)<br /> f(s,a )<br />foo (a,s,s)<br /> f ( s ,x123)<br />proc(a)<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>2<br />1<br />0<br />1<br />0<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6<br />void f(string,double,int)<br />void f(int)<br /> void f ( T )<br />void procedure(int,double)<br />void f (T, double,int) <br />void f(string, T,T)<br />4<br /> int a<br /> int x<br />string t<br />double val <br />5<br />f(t, a, a)<br />f(t,val,a)<br />f(val,a, val)<br /> solve300(val, val)<br />f (x)<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1<br />3<br />0<br />0<br />2<br /></pre></div></div></div></div></div>\r\n</div>\r\n\r\n <script>\r\n $(function () {\r\n Codeforces.addMathJaxListener(function () {\r\n let $problem = $(\"div[problemindex=D]\");\r\n let uuid = $problem.attr(\"data-uuid\");\r\n let statementText = convertStatementToText($problem.find(\".ttypography\").get(0));\r\n\r\n let previousStatementText = Codeforces.getFromStorage(uuid);\r\n if (previousStatementText) {\r\n if (previousStatementText !== statementText) {\r\n $problem.find(\".diff-notifier\").show();\r\n\r\n 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='807729622d5b8385200c279d1f0f3909'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Igor_Kudryashov\">Igor_Kudryashov</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Igor_Kudryashov\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Igor_Kudryashov\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Igor_Kudryashov\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Igor_Kudryashov\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Igor_Kudryashov\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Igor_Kudryashov\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Igor_Kudryashov\" style=\"text-decoration:none;color:black !important;\">Igor_Kudryashov's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4783\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4769\"> <p>Editorial of Codeforces Round #126 (Div. 2)</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a>,\r\n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/200/problem/A\">200A — Cinema</a></p><p>In this problem were given the field, which size is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>, and <span class=\"tex-span\"><i>k</i></span> queries. Each query is the cell of the field. You had to find closest free cell for given one (there was used manhattan metric). Than found cell was marked as used. The time complexity of the solution is supposed to be <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Firstly, we show the main idea, than we show why solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>First of all, if <span class=\"tex-span\"><i>n</i> > <i>m</i></span>, than rotate matrix by 90 degrees (than we explain purpose of this transformation). We will have two matrices, size of each is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>. In this matrices we will maintain for each cell the nearest free one to the left and to the right. Suppose we have query — cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Iterate <span class=\"tex-span\"><i>d</i></span> — how much rows we will go above or below. Suppose we fix <span class=\"tex-span\"><i>d</i></span>, than look at the row <span class=\"tex-span\"><i>x</i> - <i>d</i></span>, for example (also we should do same things for row <span class=\"tex-span\"><i>x</i> + <i>d</i></span>). Lets find in this row nearest free cells to the left and to the right of <span class=\"tex-span\">(<i>x</i> - <i>d</i>, <i>y</i>)</span> by using our matrices and try to update answer. When <span class=\"tex-span\"><i>d</i></span> will be greater than current found answer we will stop, because answer won't update in this case. After we find the answer, we have to change value in some cells of our matrices. It can be done by using structure DSU for each row.</p><p>Lets show why this solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Suppose all queries are equal, for example each query is <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Than if field is big enough, all points will be placed in form of square, which is rotated by 45 degrees and have center in point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Also the side of the square will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Than diagonal will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e1251fdd442e43afd61891578ea00a4edd790aa.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> too. It means that we see <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c220d508a81a2550050e8b6523d6ba84cb6dcba1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and we do <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row. If the square doesn't fit into the field, than field is too thin verticaly or horizontaly. So we will have figure looks like rectangle, and one side of this rectangle will be less than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. In this case rotate field so, than least side of rectangle means rows. Than we will see not greater than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and will perform not greater than <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row.</p><p>This problem is supposed to be the hardest problem of the contest.</p><p><a href=\"https://codeforces.com/contest/200/problem/B\">200B — Drinks</a></p><p>This problem was the easiest problem of the contest. There you had to find average of the given numbers. The most participants solved this problem.</p><p><a href=\"https://codeforces.com/contest/200/problem/C\">200C — Football Championship</a></p><p>In this problem was given description of the group stage of some football competition and scoring system. There were given results of all matches, excepting one, and you had to find result of the last match, satisfied some given criterias. Also Berland's team must be first or the second team of the group after than match.</p><p>Lets note, that in each finished match were not greater than 18 goals. It means that we can brute-force all results of the last match, when score is not greater than 200 goals, and find the best one. One of the easiest way is to fill table to the end (it means to change points value and balls value), than to sort teams according to the given rules and to check that Berland is the first or the second team of the group.</p><p><a href=\"https://codeforces.com/contest/200/problem/D\">200D — Programming Language</a></p><p>In this task were given the list of template functions. Each function have its name and the list of types of arguments (also it can be used universal type). Also there were given set of variables and thier types, and some queries. Each query is function, which has name and list of arguments. For each query you had to find, how many functions from the given list fit to the function from query. There fit means that functions have the same name, same number of arguments and types of all arguments also equal.</p><p>For solving this problem it is needed to implement comparing of functions. Constrains gave the possibility to brute-force function from the given list and check if the names and arguments of functions are equal.</p><p><a href=\"https://codeforces.com/contest/200/problem/E\">200E — Tractor College</a></p><p>In this problem were given four integer numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">4</sub>, <i>c</i><sub class=\"lower-index\">5</sub>, <i>s</i></span>. You had to find <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> such, that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i></span> and <span class=\"tex-span\">|<i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>| + |<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub>|</span> is minimal.</p><p>Firstly, brute-force <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> so, that <span class=\"tex-span\"><i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span>. Than look at 4 cases, according to the sign of the value in each modulus.</p><p>Lets see the case, when <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> ≥ 0</span>. Than we have to minimize <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span>. Also <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. Lets see diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>... <i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. It can be that this equation doesn't have solution. Lets see the case, when equation has solution. As <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">5</sub> ≥ 0</span>, than for minimization <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span> we have to minimize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and maximize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span>. All solutions of diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span> can be described by using one argument <span class=\"tex-span\"><i>k</i></span>. Than we have to find such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> will fit above constrains, such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, find intersection of this segments and, if intersection isn't empty, choose such <span class=\"tex-span\"><i>k</i></span>, that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> is maximal.</p><p>Similar you have to manage remain 3 cases and choose optimal values <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>. Also you can note, that in all cases minimized function is linear and in segment it has minimal value in one of its ends. So we can only find such segments, that for all <span class=\"tex-span\"><i>k</i></span> from that segments <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub>, <i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, and calculate answer in the ends of this segments. If for all fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> diofant equation doesn't have solution, or intersections of the described segments are empty, than answer is <span class=\"tex-span\"><i>IMPOSSIBLE</i></span>, else we should find the best. So the time complexity is <span class=\"tex-span\"><i>O</i>(<i>s</i>·<i>log</i>(<i>s</i>))</span> — brute-force of <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and solving diofant equation for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/200\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 126 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-1959-4783\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"1959\",\n blogEntryId: \"4769\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=126\" class=\"tag notice\" style=\"text-decoration: none;\">126</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+14</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Igor_Kudryashov\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Igor_Kudryashov\">\n Igor_Kudryashov\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4769#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4769#comments\">\n 8\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4793\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (3)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97544\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Petar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/32084/avatar/e7cb70581c83ffbb.jpg'/> </a>\n <div><a href=\"/profile/Petar\" title=\"Expert Petar\" class=\"rated-user user-blue\">Petar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 00:59\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97544\" href=\"?#comment-97544\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97544\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"32084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97544\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for editorial!</p><p>Suggestion: As I can see, you had written this 2 days ago but I was not able to find it in recent actions or in the main post of Round #126 introduction. Maybe it's better to update main article immediately after publishing editorial. Thanks in advance :-)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97544 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97544 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97544\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97576\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/kenrick95\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/17939/avatar/a339d80a76cb3fa7.jpg'/> </a>\n <div><a href=\"/profile/kenrick95\" title=\"Pupil kenrick95\" class=\"rated-user user-green\">kenrick95</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 16:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97576\" href=\"?#comment-97576\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97576\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"17939\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97576\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry but, I think that your links are all linked to the "<a href=\"/contest/200/problem/A\" title=\"Codeforces Round 126 (Div. 2)\">200A - Кино</a>" problem. Can you correct them? Thanks.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97576 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97576 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97576\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97600\" commentParentId=\"97576\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Igor_Kudryashov\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/519/avatar/8c47a77b761709b6.jpg'/> </a>\n <div><a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 23:39\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97600\" href=\"?#comment-97600\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97576\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97600\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"519\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97600\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks, fixed)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97600 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97600 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children 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Tractor College"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Tractor College</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>While most students still sit their exams, the tractor college has completed the summer exam session. In fact, students study only one subject at this college — the Art of Operating a Tractor. Therefore, at the end of a term a student gets only one mark, a three (satisfactory), a four (good) or a five (excellent). Those who score lower marks are unfortunately expelled.</p><p>The college has <span class=\"tex-span\"><i>n</i></span> students, and oddly enough, each of them can be on scholarship. The size of the scholarships varies each term. Since the end-of-the-term exam has just ended, it's time to determine the size of the scholarship to the end of next term.</p><p>The monthly budget for the scholarships of the Tractor college is <span class=\"tex-span\"><i>s</i></span> rubles. To distribute the budget optimally, you must follow these rules:</p><ul> <li> The students who received the same mark for the exam, should receive the same scholarship;</li><li> Let us denote the size of the scholarship (in roubles) for students who have received marks <span class=\"tex-span\">3</span>, <span class=\"tex-span\">4</span> and <span class=\"tex-span\">5</span> for the exam, as <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span>, respectively. The values <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> must be integers and satisfy the inequalities <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span>;</li><li> Let's assume that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">4</sub></span>, <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">5</sub></span> show how many students received marks <span class=\"tex-span\">3</span>, <span class=\"tex-span\">4</span> and <span class=\"tex-span\">5</span> for the exam, respectively. The budget of the scholarship should be fully spent on them, that is, <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i></span>;</li><li> Let's introduce function <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e1ef986a685e34e599ab8616f4d55aa9613c5757.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> — the value that shows how well the scholarships are distributed between students. In the optimal distribution function <span class=\"tex-span\"><i>f</i>(<i>k</i><sub class=\"lower-index\">3</sub>, <i>k</i><sub class=\"lower-index\">4</sub>, <i>k</i><sub class=\"lower-index\">5</sub>)</span> takes the <span class=\"tex-font-style-bf\">minimum</span> possible value. </li></ul><p>Given the results of the exam, and the budget size <span class=\"tex-span\"><i>s</i></span>, you have to find the optimal distribution of the scholarship.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line has two integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>s</i></span> (<span class=\"tex-span\">3 ≤ <i>n</i> ≤ 300, 1 ≤ <i>s</i> ≤ 3·10<sup class=\"upper-index\">5</sup></span>) — the number of students and the budget size for the scholarship, respectively. The second line contains <span class=\"tex-span\"><i>n</i></span> integers, where the <span class=\"tex-span\"><i>i</i></span>-th number represents the mark that the <span class=\"tex-span\"><i>i</i></span>-th student got for the exam. It is guaranteed that at each mark was given to at least one student.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On a single line print three integers <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> — the sought values that represent the optimal distribution of the scholarships. If there are multiple optimal answers, print any of them. If there is no answer, print -1.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>5 11<br/>3 4 3 5 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>1 3 3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>6 15<br/>5 3 3 4 4 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>-1<br/></pre></div></div></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"79c5fad6442897259554e9878503b9dc\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/73366/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"j3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/73366/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/73366/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - E - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"685ffddfd80105244067189484fcf220fc0a03e4\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - E - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"E\" data-uuid=\"ps_0c6aa46a52fbf6c0652a436ec61092c9d97ec21f\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">E. Tractor College</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>4 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>While most students still sit their exams, the tractor college has completed the summer exam session. In fact, students study only one subject at this college — the Art of Operating a Tractor. Therefore, at the end of a term a student gets only one mark, a three (satisfactory), a four (good) or a five (excellent). Those who score lower marks are unfortunately expelled.</p><p>The college has <span class=\"tex-span\"><i>n</i></span> students, and oddly enough, each of them can be on scholarship. The size of the scholarships varies each term. Since the end-of-the-term exam has just ended, it's time to determine the size of the scholarship to the end of next term.</p><p>The monthly budget for the scholarships of the Tractor college is <span class=\"tex-span\"><i>s</i></span> rubles. To distribute the budget optimally, you must follow these rules:</p><ul> <li> The students who received the same mark for the exam, should receive the same scholarship;</li><li> Let us denote the size of the scholarship (in roubles) for students who have received marks <span class=\"tex-span\">3</span>, <span class=\"tex-span\">4</span> and <span class=\"tex-span\">5</span> for the exam, as <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span>, respectively. The values <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> must be integers and satisfy the inequalities <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span>;</li><li> Let's assume that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">4</sub></span>, <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">5</sub></span> show how many students received marks <span class=\"tex-span\">3</span>, <span class=\"tex-span\">4</span> and <span class=\"tex-span\">5</span> for the exam, respectively. The budget of the scholarship should be fully spent on them, that is, <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i></span>;</li><li> Let's introduce function <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/e1ef986a685e34e599ab8616f4d55aa9613c5757.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> — the value that shows how well the scholarships are distributed between students. In the optimal distribution function <span class=\"tex-span\"><i>f</i>(<i>k</i><sub class=\"lower-index\">3</sub>, <i>k</i><sub class=\"lower-index\">4</sub>, <i>k</i><sub class=\"lower-index\">5</sub>)</span> takes the <span class=\"tex-font-style-bf\">minimum</span> possible value. </li></ul><p>Given the results of the exam, and the budget size <span class=\"tex-span\"><i>s</i></span>, you have to find the optimal distribution of the scholarship.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line has two integers <span class=\"tex-span\"><i>n</i></span>, <span class=\"tex-span\"><i>s</i></span> (<span class=\"tex-span\">3 ≤ <i>n</i> ≤ 300, 1 ≤ <i>s</i> ≤ 3·10<sup class=\"upper-index\">5</sup></span>) — the number of students and the budget size for the scholarship, respectively. The second line contains <span class=\"tex-span\"><i>n</i></span> integers, where the <span class=\"tex-span\"><i>i</i></span>-th number represents the mark that the <span class=\"tex-span\"><i>i</i></span>-th student got for the exam. It is guaranteed that at each mark was given to at least one student.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>On a single line print three integers <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span>, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> — the sought values that represent the optimal distribution of the scholarships. If there are multiple optimal answers, print any of them. 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='807729622d5b8385200c279d1f0f3909'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> 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href=\"/profile/Igor_Kudryashov\">Igor_Kudryashov</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Igor_Kudryashov\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Igor_Kudryashov\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Igor_Kudryashov\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Igor_Kudryashov\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Igor_Kudryashov\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Igor_Kudryashov\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Igor_Kudryashov\" style=\"text-decoration:none;color:black !important;\">Igor_Kudryashov's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4783\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4769\"> <p>Editorial of Codeforces Round #126 (Div. 2)</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a>,\r\n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><p><a href=\"https://codeforces.com/contest/200/problem/A\">200A — Cinema</a></p><p>In this problem were given the field, which size is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>, and <span class=\"tex-span\"><i>k</i></span> queries. Each query is the cell of the field. You had to find closest free cell for given one (there was used manhattan metric). Than found cell was marked as used. The time complexity of the solution is supposed to be <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Firstly, we show the main idea, than we show why solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>First of all, if <span class=\"tex-span\"><i>n</i> > <i>m</i></span>, than rotate matrix by 90 degrees (than we explain purpose of this transformation). We will have two matrices, size of each is <span class=\"tex-span\"><i>n</i> × <i>m</i></span>. In this matrices we will maintain for each cell the nearest free one to the left and to the right. Suppose we have query — cell <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Iterate <span class=\"tex-span\"><i>d</i></span> — how much rows we will go above or below. Suppose we fix <span class=\"tex-span\"><i>d</i></span>, than look at the row <span class=\"tex-span\"><i>x</i> - <i>d</i></span>, for example (also we should do same things for row <span class=\"tex-span\"><i>x</i> + <i>d</i></span>). Lets find in this row nearest free cells to the left and to the right of <span class=\"tex-span\">(<i>x</i> - <i>d</i>, <i>y</i>)</span> by using our matrices and try to update answer. When <span class=\"tex-span\"><i>d</i></span> will be greater than current found answer we will stop, because answer won't update in this case. After we find the answer, we have to change value in some cells of our matrices. It can be done by using structure DSU for each row.</p><p>Lets show why this solution has time complexity <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1a61675d42920415a81ebf5a81ed0dee2736562a.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Suppose all queries are equal, for example each query is <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Than if field is big enough, all points will be placed in form of square, which is rotated by 45 degrees and have center in point <span class=\"tex-span\">(<i>x</i>, <i>y</i>)</span>. Also the side of the square will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Than diagonal will have length <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e1251fdd442e43afd61891578ea00a4edd790aa.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> too. It means that we see <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/c220d508a81a2550050e8b6523d6ba84cb6dcba1.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and we do <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row. If the square doesn't fit into the field, than field is too thin verticaly or horizontaly. So we will have figure looks like rectangle, and one side of this rectangle will be less than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. In this case rotate field so, than least side of rectangle means rows. Than we will see not greater than <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/67ed7492d1862bd303c4da8ab21d28b87843329f.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> rows in each query and will perform not greater than <span class=\"tex-span\"><i>O</i>(1)</span> operations in each row.</p><p>This problem is supposed to be the hardest problem of the contest.</p><p><a href=\"https://codeforces.com/contest/200/problem/B\">200B — Drinks</a></p><p>This problem was the easiest problem of the contest. There you had to find average of the given numbers. The most participants solved this problem.</p><p><a href=\"https://codeforces.com/contest/200/problem/C\">200C — Football Championship</a></p><p>In this problem was given description of the group stage of some football competition and scoring system. There were given results of all matches, excepting one, and you had to find result of the last match, satisfied some given criterias. Also Berland's team must be first or the second team of the group after than match.</p><p>Lets note, that in each finished match were not greater than 18 goals. It means that we can brute-force all results of the last match, when score is not greater than 200 goals, and find the best one. One of the easiest way is to fill table to the end (it means to change points value and balls value), than to sort teams according to the given rules and to check that Berland is the first or the second team of the group.</p><p><a href=\"https://codeforces.com/contest/200/problem/D\">200D — Programming Language</a></p><p>In this task were given the list of template functions. Each function have its name and the list of types of arguments (also it can be used universal type). Also there were given set of variables and thier types, and some queries. Each query is function, which has name and list of arguments. For each query you had to find, how many functions from the given list fit to the function from query. There fit means that functions have the same name, same number of arguments and types of all arguments also equal.</p><p>For solving this problem it is needed to implement comparing of functions. Constrains gave the possibility to brute-force function from the given list and check if the names and arguments of functions are equal.</p><p><a href=\"https://codeforces.com/contest/200/problem/E\">200E — Tractor College</a></p><p>In this problem were given four integer numbers <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">4</sub>, <i>c</i><sub class=\"lower-index\">5</sub>, <i>s</i></span>. You had to find <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> such, that <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i></span> and <span class=\"tex-span\">|<i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>| + |<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub>|</span> is minimal.</p><p>Firstly, brute-force <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> so, that <span class=\"tex-span\"><i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span>. Than look at 4 cases, according to the sign of the value in each modulus.</p><p>Lets see the case, when <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub> ≥ 0</span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> ≥ 0</span>. Than we have to minimize <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span>. Also <span class=\"tex-span\">0 ≤ <i>k</i><sub class=\"lower-index\">3</sub> ≤ <i>k</i><sub class=\"lower-index\">4</sub> ≤ <i>k</i><sub class=\"lower-index\">5</sub></span> and <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. Lets see diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>... <i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span>. It can be that this equation doesn't have solution. Lets see the case, when equation has solution. As <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>, <i>c</i><sub class=\"lower-index\">5</sub> ≥ 0</span>, than for minimization <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub>–<i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub></span> we have to minimize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and maximize <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span>. All solutions of diofant equation <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\">3</sub>·<i>k</i><sub class=\"lower-index\">3</sub> + <i>c</i><sub class=\"lower-index\">5</sub>·<i>k</i><sub class=\"lower-index\">5</sub> = <i>s</i>–<i>c</i><sub class=\"lower-index\">4</sub>·<i>k</i><sub class=\"lower-index\">4</sub></span> can be described by using one argument <span class=\"tex-span\"><i>k</i></span>. Than we have to find such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> will fit above constrains, such segment, that for all <span class=\"tex-span\"><i>k</i></span> from it, <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, find intersection of this segments and, if intersection isn't empty, choose such <span class=\"tex-span\"><i>k</i></span>, that <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> is maximal.</p><p>Similar you have to manage remain 3 cases and choose optimal values <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub></span> and <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">5</sub></span> for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>. Also you can note, that in all cases minimized function is linear and in segment it has minimal value in one of its ends. So we can only find such segments, that for all <span class=\"tex-span\"><i>k</i></span> from that segments <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">3</sub>, <i>k</i><sub class=\"lower-index\">5</sub></span> will fit above constrains, and calculate answer in the ends of this segments. If for all fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> diofant equation doesn't have solution, or intersections of the described segments are empty, than answer is <span class=\"tex-span\"><i>IMPOSSIBLE</i></span>, else we should find the best. So the time complexity is <span class=\"tex-span\"><i>O</i>(<i>s</i>·<i>log</i>(<i>s</i>))</span> — brute-force of <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span> and solving diofant equation for fixed <span class=\"tex-span\"><i>k</i><sub class=\"lower-index\">4</sub></span>.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/200\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 126 (Div. 2)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-1959-4783\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"1959\",\n blogEntryId: \"4769\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=126\" class=\"tag notice\" style=\"text-decoration: none;\">126</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+14</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4783\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Igor_Kudryashov\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Igor_Kudryashov\">\n Igor_Kudryashov\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jun/24/2012 23:20\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4769#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4769#comments\">\n 8\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4793\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (3)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97544\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Petar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/32084/avatar/e7cb70581c83ffbb.jpg'/> </a>\n <div><a href=\"/profile/Petar\" title=\"Expert Petar\" class=\"rated-user user-blue\">Petar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 00:59\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97544\" href=\"?#comment-97544\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97544\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"1\"\r\n data-commentUserId=\"32084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+1</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97544\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for editorial!</p><p>Suggestion: As I can see, you had written this 2 days ago but I was not able to find it in recent actions or in the main post of Round #126 introduction. Maybe it's better to update main article immediately after publishing editorial. Thanks in advance :-)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97544 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97544 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97544\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97576\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/kenrick95\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/17939/avatar/a339d80a76cb3fa7.jpg'/> </a>\n <div><a href=\"/profile/kenrick95\" title=\"Pupil kenrick95\" class=\"rated-user user-green\">kenrick95</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 16:20\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97576\" href=\"?#comment-97576\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97576\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"3\"\r\n data-commentUserId=\"17939\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+3</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97576\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Sorry but, I think that your links are all linked to the "<a href=\"/contest/200/problem/A\" title=\"Codeforces Round 126 (Div. 2)\">200A - Кино</a>" problem. Can you correct them? Thanks.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97576 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97576 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-97576\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"97600\" commentParentId=\"97576\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Igor_Kudryashov\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/519/avatar/8c47a77b761709b6.jpg'/> </a>\n <div><a href=\"/profile/Igor_Kudryashov\" title=\"International Master Igor_Kudryashov\" class=\"rated-user user-orange\">Igor_Kudryashov</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/27/2012 23:39\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-97600\" href=\"?#comment-97600\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-97576\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"97600\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"519\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-97600\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks, fixed)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-97600 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-97600 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children 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Clear Symmetry"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Clear Symmetry</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Consider some square matrix <span class=\"tex-span\"><i>A</i></span> with side <span class=\"tex-span\"><i>n</i></span> consisting of zeros and ones. There are <span class=\"tex-span\"><i>n</i></span> rows numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from top to bottom and <span class=\"tex-span\"><i>n</i></span> columns numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from left to right in this matrix. We'll denote the element of the matrix which is located at the intersection of the <span class=\"tex-span\"><i>i</i></span>-row and the <span class=\"tex-span\"><i>j</i></span>-th column as <span class=\"tex-span\"><i>A</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub></span>.</p><p>Let's call matrix <span class=\"tex-span\"><i>A</i></span> <span class=\"tex-font-style-underline\">clear</span> if no two cells containing ones have a common side.</p><p>Let's call matrix <span class=\"tex-span\"><i>A</i></span> <span class=\"tex-font-style-underline\">symmetrical</span> if it matches the matrices formed from it by a horizontal and/or a vertical reflection. Formally, for each pair <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> <span class=\"tex-span\">(1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i>)</span> both of the following conditions must be met: <span class=\"tex-span\"><i>A</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub> = <i>A</i><sub class=\"lower-index\"><i>n</i> - <i>i</i> + 1, <i>j</i></sub></span> and <span class=\"tex-span\"><i>A</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub> = <i>A</i><sub class=\"lower-index\"><i>i</i>, <i>n</i> - <i>j</i> + 1</sub></span>.</p><p>Let's define the <span class=\"tex-font-style-underline\">sharpness</span> of matrix <span class=\"tex-span\"><i>A</i></span> as the number of ones in it.</p><p>Given integer <span class=\"tex-span\"><i>x</i></span>, your task is to find the smallest positive integer <span class=\"tex-span\"><i>n</i></span> such that there exists a clear symmetrical matrix <span class=\"tex-span\"><i>A</i></span> with side <span class=\"tex-span\"><i>n</i></span> and sharpness <span class=\"tex-span\"><i>x</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The only line contains a single integer <span class=\"tex-span\"><i>x</i></span> (<span class=\"tex-span\">1 ≤ <i>x</i> ≤ 100</span>) — the required sharpness of the matrix.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the sought value of <span class=\"tex-span\"><i>n</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>9<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The figure below shows the matrices that correspond to the samples:</p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/b645f14acce57b47fb84ad631e38226eee6b0ed4.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"30454e232bba0034c011f405774acc79\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/73366/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"j3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/73366/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/73366/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - A - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"c480cae93911e5cc326e0a6bfdc6ed965aef9be4\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - A - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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}\r\n\r\n const convertStatementToText = function(statmentNode) {\r\n const text = nodeToText(statmentNode, false).join(\"\").replace(/ +/g, \" \").replace(/\\n\\n+/g, \"\\n\\n\");\r\n let result = [];\r\n for (let i = 0; i < text.length; i++) {\r\n const c = text.charAt(i);\r\n if (c === OPENING_SPACE) {\r\n if (!((i > 0 && text.charAt(i - 1) === '(') || (result.length > 0 && result[result.length - 1] === ' '))) {\r\n result.push('+');\r\n }\r\n } else if (c === CLOSING_SPACE) {\r\n if (!(i + 1 < text.length && isSpecial(text.charAt(i + 1)))) {\r\n result.push('-');\r\n }\r\n } else {\r\n result.push(c);\r\n }\r\n }\r\n return result.join(\"\").split(\"\\n\").map(value => value.trim()).join(\"\\n\");\r\n };\r\n </script>\r\n <div class=\"diff-popup\">\r\n </div>\r\n\r\n<div class=\"problemindexholder\" problemindex=\"A\" data-uuid=\"ps_95007adcf8c57b4c5d0dcd46c3a52e526356192c\">\r\n <div style=\"display: none; margin:1em 0;text-align: center; position: relative;\" class=\"alert alert-info diff-notifier\">\r\n <div>The problem statement has recently been changed. <a class=\"view-changes\" href=\"#\">View the changes.</a></div>\r\n <span class=\"diff-notifier-close\" style=\"position: absolute; top: 0.2em; right: 0.3em; cursor: pointer; font-size: 1.4em;\">×</span>\r\n </div>\r\n <div class=\"ttypography\"><div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">A. Clear Symmetry</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Consider some square matrix <span class=\"tex-span\"><i>A</i></span> with side <span class=\"tex-span\"><i>n</i></span> consisting of zeros and ones. There are <span class=\"tex-span\"><i>n</i></span> rows numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from top to bottom and <span class=\"tex-span\"><i>n</i></span> columns numbered from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span> from left to right in this matrix. We'll denote the element of the matrix which is located at the intersection of the <span class=\"tex-span\"><i>i</i></span>-row and the <span class=\"tex-span\"><i>j</i></span>-th column as <span class=\"tex-span\"><i>A</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub></span>.</p><p>Let's call matrix <span class=\"tex-span\"><i>A</i></span> <span class=\"tex-font-style-underline\">clear</span> if no two cells containing ones have a common side.</p><p>Let's call matrix <span class=\"tex-span\"><i>A</i></span> <span class=\"tex-font-style-underline\">symmetrical</span> if it matches the matrices formed from it by a horizontal and/or a vertical reflection. Formally, for each pair <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> <span class=\"tex-span\">(1 ≤ <i>i</i>, <i>j</i> ≤ <i>n</i>)</span> both of the following conditions must be met: <span class=\"tex-span\"><i>A</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub> = <i>A</i><sub class=\"lower-index\"><i>n</i> - <i>i</i> + 1, <i>j</i></sub></span> and <span class=\"tex-span\"><i>A</i><sub class=\"lower-index\"><i>i</i>, <i>j</i></sub> = <i>A</i><sub class=\"lower-index\"><i>i</i>, <i>n</i> - <i>j</i> + 1</sub></span>.</p><p>Let's define the <span class=\"tex-font-style-underline\">sharpness</span> of matrix <span class=\"tex-span\"><i>A</i></span> as the number of ones in it.</p><p>Given integer <span class=\"tex-span\"><i>x</i></span>, your task is to find the smallest positive integer <span class=\"tex-span\"><i>n</i></span> such that there exists a clear symmetrical matrix <span class=\"tex-span\"><i>A</i></span> with side <span class=\"tex-span\"><i>n</i></span> and sharpness <span class=\"tex-span\"><i>x</i></span>.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The only line contains a single integer <span class=\"tex-span\"><i>x</i></span> (<span class=\"tex-span\">1 ≤ <i>x</i> ≤ 100</span>) — the required sharpness of the matrix.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>Print a single number — the sought value of <span class=\"tex-span\"><i>n</i></span>.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>4<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>3<br /></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>9<br /></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>5<br /></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>The figure below 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Extra registration opens 10 minutes after the contest starts and lasts 25 minutes.\"></i></div>\r\n </div>\r\n</div>\r\n </div>\n\n<style data-nocturne=\"true\" type=\"text/css\">\n._StreamsSidebarFrame_frame {\n padding: 0.5em 0.5em 0 0.5em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream {\n text-align: center;\n border-bottom: 1px solid #b9b9b9;\n margin: 0 -0.5em 0.5em -0.5em;\n padding: 0 1em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_user {\n margin: 0 0 0.5em 0;\n font-size: 0.8em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream ._StreamsSidebarFrame_timeMark {\n color: #777;\n font-size: 0.9em;\n}\n._StreamsSidebarFrame_frame ._StreamsSidebarFrame_stream:last-of-type {\n border-bottom: unset;\n margin: unset;\n padding: 0 0.5em 0.5em 1em;\n}\n._StreamsSidebarFrame_frame ._viewAll {\n text-align: right;\n}\n.moreRunningStreamsSidebarNote {\n color: #777 !important;\n text-decoration: none;\n}\n</style>\n\n\n<script data-nocturne=\"true\"> $(function () {\n\n}); </script>\n\n<div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n<div class=\"caption titled\">→ Top rated\n<div class=\"top-links\">\n</div>\n</div>\n<table class=\"rtable \">\n<tbody>\n<tr>\n<th class=\"left\" style=\"width:2.25em;\">#</th>\n<th class=\"\">User</th>\n<th class=\"\" style=\"width:5em;\">Rating</th>\n</tr>\n<tr>\n<td class=\"left dark\">1</td>\n<td class=\" dark\"><a href=\"/profile/tourist\" title=\"Legendary Grandmaster tourist\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">t</span>ourist</a></td>\n<td class=\" dark\">3775</td>\n</tr>\n<tr>\n<td class=\"left \">2</td>\n<td class=\"\"><a href=\"/profile/Benq\" title=\"Legendary Grandmaster Benq\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">B</span>enq</a></td>\n<td class=\"\">3724</td>\n</tr>\n<tr>\n<td class=\"left dark\">3</td>\n<td class=\" dark\"><a href=\"/profile/orzdevinwang\" title=\"Legendary Grandmaster orzdevinwang\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">o</span>rzdevinwang</a></td>\n<td class=\" dark\">3697</td>\n</tr>\n<tr>\n<td class=\"left \">4</td>\n<td class=\"\"><a href=\"/profile/Radewoosh\" title=\"Legendary Grandmaster Radewoosh\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>adewoosh</a></td>\n<td class=\"\">3651</td>\n</tr>\n<tr>\n<td class=\"left dark\">5</td>\n<td class=\" dark\"><a href=\"/profile/jiangly\" title=\"Legendary Grandmaster jiangly\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">j</span>iangly</a></td>\n<td class=\" dark\">3632</td>\n</tr>\n<tr>\n<td class=\"left \">6</td>\n<td class=\"\"><a href=\"/profile/cnnfls_csy\" title=\"Legendary Grandmaster cnnfls_csy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">c</span>nnfls_csy</a></td>\n<td class=\"\">3620</td>\n</tr>\n<tr>\n<td class=\"left dark\">7</td>\n<td class=\" dark\"><a href=\"/profile/-0.5\" title=\"Legendary Grandmaster -0.5\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">-</span>0.5</a></td>\n<td class=\" dark\">3545</td>\n</tr>\n<tr>\n<td class=\"left \">8</td>\n<td class=\"\"><a href=\"/profile/inaFSTream\" title=\"Legendary Grandmaster inaFSTream\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">i</span>naFSTream</a></td>\n<td class=\"\">3478</td>\n</tr>\n<tr>\n<td class=\"left dark\">9</td>\n<td class=\" dark\"><a href=\"/profile/fantasy\" title=\"Legendary Grandmaster fantasy\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">f</span>antasy</a></td>\n<td class=\" dark\">3468</td>\n</tr>\n<tr>\n<td class=\"left bottom\">10</td>\n<td class=\"bottom\"><a href=\"/profile/Rebelz\" title=\"Legendary Grandmaster Rebelz\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">R</span>ebelz</a></td>\n<td class=\"bottom\">3415</td>\n</tr>\n</tbody>\n</table>\n<div class=\"bottom-links\">\n<table style=\"width:100%;\">\n<tbody>\n<tr>\n<td style=\"text-align:left;\">\n<a href=\"/ratings/countries\">Countries</a> |\n<a href=\"/ratings/cities\">Cities</a> |\n<a href=\"/ratings/organizations\">Organizations</a>\n</td>\n<td style=\"text-align:right;\">\n<a href=\"/ratings\">View all →</a>\n</td>\n</tr>\n</tbody>\n</table>\n</div>\n</div><div class=\"roundbox sidebox top-contributed borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Top contributors\n <div class=\"top-links\">\n </div>\n </div>\n <table class=\"rtable \">\n <tbody>\n <tr>\n <th class=\"left\" style=\"width:2.25em;\">#</th>\n <th class=\"\">User</th>\n <th class=\"\" style=\"width:5em;\">Contrib.</th>\n </tr>\n <tr>\n <td class=\"left dark\">1</td>\n <td class=\" dark\"><a href=\"/profile/adamant\" title=\"Grandmaster adamant\" class=\"rated-user user-red\">adamant</a></td>\n <td class=\" dark\">178</td>\n </tr>\n <tr>\n <td class=\"left \">2</td>\n <td class=\"\"><a href=\"/profile/awoo\" title=\"Master awoo\" class=\"rated-user user-orange\">awoo</a></td>\n <td class=\"\">167</td>\n </tr>\n <tr>\n <td class=\"left dark\">3</td>\n <td class=\" dark\"><a href=\"/profile/BledDest\" title=\"International Grandmaster BledDest\" class=\"rated-user user-red\">BledDest</a></td>\n <td class=\" dark\">165</td>\n </tr>\n <tr>\n <td class=\"left \">4</td>\n <td class=\"\"><a href=\"/profile/Um_nik\" title=\"Legendary Grandmaster Um_nik\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">U</span>m_nik</a></td>\n <td class=\"\">163</td>\n </tr>\n <tr>\n <td class=\"left dark\">5</td>\n <td class=\" dark\"><a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a></td>\n <td class=\" dark\">162</td>\n </tr>\n <tr>\n <td class=\"left \">6</td>\n <td class=\"\"><a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a></td>\n <td class=\"\">160</td>\n </tr>\n <tr>\n <td class=\"left dark\">7</td>\n <td class=\" dark\"><a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a></td>\n <td class=\" dark\">158</td>\n </tr>\n <tr>\n <td class=\"left \">8</td>\n <td class=\"\"><a href=\"/profile/-is-this-fft-\" title=\"Grandmaster -is-this-fft-\" class=\"rated-user user-red\">-is-this-fft-</a></td>\n <td class=\"\">152</td>\n </tr>\n <tr>\n <td class=\"left dark\">9</td>\n <td class=\" dark\"><a href=\"/profile/kostka\" title=\"International Grandmaster kostka\" class=\"rated-user user-red\">kostka</a></td>\n <td class=\" dark\">145</td>\n </tr>\n <tr>\n <td class=\"left bottom\">10</td>\n <td class=\"bottom\"><a href=\"/profile/TheScrasse\" title=\"International Grandmaster TheScrasse\" class=\"rated-user user-red\">TheScrasse</a></td>\n <td class=\"bottom\">144</td>\n </tr>\n </tbody>\n </table>\n <div class=\"bottom-links\">\n <table style=\"width:100%;\">\n <tbody>\n <tr>\n <td style=\"text-align:left;\">\n </td>\n <td style=\"text-align:right;\">\n <a href=\"/top-contributed\">View all →</a>\n </td>\n </tr>\n </tbody>\n </table>\n </div>\n </div>\n\r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n });\n </script>\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Find user\n <div class=\"top-links\">\n </div>\n </div>\n <form class=\"handleForm\" method=\"post\"><input type='hidden' name='csrf_token' value='f25d411d766698b2c7014ee8c93854a1'/>\r\n <div style=\"padding:1em;text-align:right;\">\r\n <label style=\"padding-right:1em;\">Handle:\r\n <input style=\"width:12em;\" type=\"text\" class=\"handleBox\"/>\r\n </label>\r\n </div>\r\n <div style=\"padding: 0 1em 1em 1em;text-align:right;\">\r\n <input style=\"height:1.65em;padding:0 0.75em;\" type=\"submit\" value=\"Find\"/>\r\n </div>\r\n </form>\r\n </div>\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".handleBox\").autocomplete(\"/data/handles\", {\r\n delay: 200,\r\n width: 200,\r\n selectFirst: false,\r\n matchContains: true,\r\n minChars: 3\r\n });\r\n $(\".handleForm\").attr(\"autocomplete\", \"off\").submit(function () {\r\n var link = \"/profile/userHandle\".replace(\r\n \"userHandle\", $(this).find(\".handleBox\").val()\r\n );\r\n window.location = link;\r\n return false;\r\n });\r\n });\n </script>\n\r\n\r\n\r\n\r\n\n <div class=\"roundbox sidebox borderTopRound \" style=\"\">\n <div class=\"caption titled\">→ Recent actions\n <div class=\"top-links\">\n </div>\n </div>\n <div class=\"recent-actions\">\r\n <ul>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/.Danet\" title=\"Expert .Danet\" class=\"rated-user user-blue\">.Danet</a> →\r\n <a href=\"/blog/entry/121172\">[TLE on pretest1]</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/121073\">Meta Hacker Cup 2023 Round 1</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pyqe\" title=\"International Grandmaster Pyqe\" class=\"rated-user user-red\">Pyqe</a> →\r\n <a href=\"/blog/entry/121025\">Codeforces Round #902 (Div. 1, Div. 2, based on COMPFEST 15 — Final Round)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Pranshu_Pandya\" title=\"Specialist Pranshu_Pandya\" class=\"rated-user user-cyan\">Pranshu_Pandya</a> →\r\n <a href=\"/blog/entry/121171\">An Interesting Tree Problem</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/sszcdjr\" title=\"Master sszcdjr\" class=\"rated-user user-orange\">sszcdjr</a> →\r\n <a href=\"/blog/entry/119859\">Codeforces Round 896 (Div. 1, Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/SecondThread\" title=\"Master SecondThread\" class=\"rated-user user-orange\">SecondThread</a> →\r\n <a href=\"/blog/entry/119880\">It's Happening! Meta Hacker Cup 2023 Schedule</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/DaviddeGea1\" title=\"Expert DaviddeGea1\" class=\"rated-user user-blue\">DaviddeGea1</a> →\r\n <a href=\"/blog/entry/70917\">Number of ways of dividing an array into 2 parts such that sum of each part is > k</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bekh\" title=\"Master Bekh\" class=\"rated-user user-orange\">Bekh</a> →\r\n <a href=\"/blog/entry/74245\">Questions and doubts regarding Aliens DP trick</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/cgy4ever\" title=\"International Grandmaster cgy4ever\" class=\"rated-user user-red\">cgy4ever</a> →\r\n <a href=\"/blog/entry/8192\">Codeforces Round #190 — Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/hocky\" title=\"Candidate Master hocky\" class=\"rated-user user-violet\">hocky</a> →\r\n <a href=\"/blog/entry/95323\">FBHC wuining uw Day? Incwease uw stacc size! (ㅅ´ ˘ `)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/liouzhou_101\" title=\"International Master liouzhou_101\" class=\"rated-user user-orange\">liouzhou_101</a> →\r\n <a href=\"/blog/entry/87598\">Editorial of Codeforces Round #700</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/yeon_gist\" title=\"Newbie yeon_gist\" class=\"rated-user user-gray\">yeon_gist</a> →\r\n <a href=\"/blog/entry/121170\">plusMinusPermutation computing error</a>\r\n <img alt=\"Text created or updated\" title=\"Text created or updated\" src=\"//codeforces.org/s/81027/images/icons/x-update-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/altforminuscontribution\" title=\"Newbie altforminuscontribution\" class=\"rated-user user-gray\">altforminuscontribution</a> →\r\n <a href=\"/blog/entry/121162\">My screen get unexpectedly big, what should I do</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/atcoder_official\" title=\"Unrated, atcoder_official\" class=\"rated-user user-black\">atcoder_official</a> →\r\n <a href=\"/blog/entry/121120\">We will hold UNIQUE VISION Programming Contest 2023 Autumn(AtCoder Beginner Contest 323)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/YouStill_DontKnowMeYet\" title=\"Candidate Master YouStill_DontKnowMeYet\" class=\"rated-user user-violet\">YouStill_DontKnowMeYet</a> →\r\n <a href=\"/blog/entry/117659\">[GYM] Al-Baath Collegiate Programming Contest 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/ankancool\" title=\"Expert ankancool\" class=\"rated-user user-blue\">ankancool</a> →\r\n <a href=\"/blog/entry/121136\">Invitation to AstroByte 2023</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/GeZhiyuan\" title=\"Grandmaster GeZhiyuan\" class=\"rated-user user-red\">GeZhiyuan</a> →\r\n <a href=\"/blog/entry/120943\">Codeforces Round 901 (Div. 1, Div. 2) Editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/nor\" title=\"Master nor\" class=\"rated-user user-orange\">nor</a> →\r\n <a href=\"/blog/entry/120772\">PSA: Increase your stack size before the Meta Hacker Cup, here's how</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/dino_merlin\" title=\"Expert dino_merlin\" class=\"rated-user user-blue\">dino_merlin</a> →\r\n <a href=\"/blog/entry/121145\">Intuitive approach for CEOI Kangaroo?</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/icecuber\" title=\"Grandmaster icecuber\" class=\"rated-user user-red\">icecuber</a> →\r\n <a href=\"/blog/entry/70018\">CSES DP section editorial</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Bn00b\" title=\"Newbie Bn00b\" class=\"rated-user user-gray\">Bn00b</a> →\r\n <a href=\"/blog/entry/98820\">[FEATURE REQUEST : ATCODER] TOPICS TAGS AND SORTING BY SOLVE COUNT</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n <img alt=\"Necropost\" title=\"Necropost\" src=\"//codeforces.org/s/81027/images/icons/hourglass.png\" style=\"vertical-align:middle; position: relative; top: 1px;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/maroonrk\" title=\"Legendary Grandmaster maroonrk\" class=\"rated-user user-legendary\"><span class=\"legendary-user-first-letter\">m</span>aroonrk</a> →\r\n <a href=\"/blog/entry/121163\">AtCoder Regular Contest 166 Announcement</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/windva\" title=\"Grandmaster windva\" class=\"rated-user user-red\">windva</a> →\r\n <a href=\"/blog/entry/120644\">Codeforces Round 899 (Div. 2)</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" src=\"//codeforces.org/s/81027/images/icons/comment-12x12.png\" style=\"vertical-align:middle;\"/>\r\n</div>\r\n</li>\r\n <li><div style=\"font-size:0.9em;padding:0.5em 0;\">\r\n<a href=\"/profile/Misa-Misa\" title=\"Expert Misa-Misa\" class=\"rated-user user-blue\">Misa-Misa</a> →\r\n <a href=\"/blog/entry/121157\">Someone please help me understand this.</a>\r\n <img alt=\"New comment(s)\" title=\"New comment(s)\" 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href=\"/profile/Romka\">Romka</a></li>\r\n <li class=\"current selectedLava\"><a\r\n href=\"/blog/Romka\">Blog</a></li>\r\n <li><a\r\n href=\"/teams/with/Romka\">Teams</a></li>\r\n <li><a\r\n href=\"/submissions/Romka\">Submissions</a></li>\r\n <li><a\r\n href=\"/groups/with/Romka\">Groups</a></li>\r\n <li><a\r\n href=\"/contests/with/Romka\">Contests</a></li>\r\n <li><a\r\n href=\"/contests/writer/Romka\">Problemsetting</a></li>\r\n</ul>\r\n</div>\n <div style=\"margin-top:0;\">\r\n <div>\r\n <h3><a href=\"/blog/Romka\" style=\"text-decoration:none;color:black !important;\">Romka's blog</a></h3>\r\n </div>\r\n <div style=\"margin-top:2em;\">\r\n\r\n\r\n<div class=\"has-topic-id topic\" topicId=\"4826\">\r\n <div class=\"title\">\r\n <a href=\"/blog/entry/4808\"> <p>Codeforces Round #127 — editorial</p>\r\n</a>\r\n </div>\r\n\r\n <div class=\"info\" style=\"position:relative;\">\r\n By <a href=\"/profile/Romka\" title=\"Grandmaster Romka\" class=\"rated-user user-red\">Romka</a>,\r\n <span class=\"format-humantime\" title=\"Jul/01/2012 11:00\">11 years ago</span>,\r\n translation,\r\n <img style=\"position: relative;top: 5px;\" src=\"//codeforces.org/s/81027/images/flags/24/gb.png\" alt=\"In English\" title=\"In English\"/>\r\n\r\n\r\n\r\n <span style=\"position:absolute;right:0;top:0.05em;margin-right:1em;display:inline;font-size:0.75em;\">\r\n <div style=\"margin-top:0.25em;\">\r\n </div>\r\n </span>\r\n </div>\r\n\r\n <div class=\"content\">\r\n <div class=\"ttypography\"><h4>Problem A(div 2) — LLPS</h4><p>It's assumed that this problem can be solved just looking at the samples and without reading the statement itself :)</p><p>Let's find the letter in the given string which comes last in the alphabet, denote this letter by <span class=\"tex-span\"><i>z</i></span>. If this letter occurs <span class=\"tex-span\"><i>p</i></span> times in the given string, then the answer is string <span class=\"tex-span\"><i>a</i></span> consisting of letter <span class=\"tex-span\"><i>z</i></span> repeated <span class=\"tex-span\"><i>p</i></span> times.</p><p>Why is it so? Using the definition of lexicographical comparison and the fact that <span class=\"tex-span\"><i>z</i></span> is the largest letter in the string it's easy to understand that if some other subsequence <span class=\"tex-span\"><i>b</i></span> of the given string is lexicographically larger than <span class=\"tex-span\"><i>a</i></span>, then string <span class=\"tex-span\"><i>b</i></span> should be longer than <span class=\"tex-span\"><i>a</i></span> and, moreover, <span class=\"tex-span\"><i>a</i></span> should be a prefix of <span class=\"tex-span\"><i>b</i></span> (that is, <span class=\"tex-span\"><i>b</i></span> should start with <span class=\"tex-span\"><i>a</i></span>). But string <span class=\"tex-span\"><i>b</i></span> must be a palindrome, therefore its last letter must be <span class=\"tex-span\"><i>z</i></span>. In this case string <span class=\"tex-span\"><i>b</i></span> must contain more occurrences of letter <span class=\"tex-span\"><i>z</i></span> than the original string <span class=\"tex-span\"><i>s</i></span> does, which is impossible as <span class=\"tex-span\"><i>b</i></span> is a subsequence of <span class=\"tex-span\"><i>s</i></span>.</p><p>Besides that, the constraint on the length of the string was very low, so the problem could be solved using brute force. For every subsequence of the given string it's necessary to check whether it's a palindrome, and from all palindromic subsequences of <span class=\"tex-span\"><i>s</i></span> the lexicographically largest should be chosen as the answer. The complexity of such a solution is <span class=\"tex-span\"><i>O</i>(2<sup class=\"upper-index\"><i>n</i></sup>·<i>n</i>)</span>, where <span class=\"tex-span\"><i>n</i></span> is the length of the string (unlike the solution above with complexity <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>).</p><h4>Problem В(div 2) — Brand New Easy Problem</h4><p>The constraints in this problem were so low that a solution with complexity <span class=\"tex-span\"><i>O</i>(<i>m</i>·<i>k</i><sup class=\"upper-index\"><i>n</i></sup>)</span> was just fine. In each problem's description it's enough to loop over all possible subsequences of words which are permutations of words in Lesha's problem, for each of them calculate the number of inversions and choose a permutation with the smallest number of inversions. This can result in a short solution using recursion or, for example, you can use several nested loops (from <span class=\"tex-span\">1</span> to <span class=\"tex-span\">4</span>).</p><p>Here is an example of pseudocode for <span class=\"tex-span\"><i>n</i> = 4</span>:</p> <pre><code>w - array of words of Lesha''s problem\ns - the description of the current problem\nbest = 100\nfor a = 1 to k do\n for b = 1 to k do\n for c = 1 to k do\n for d = 1 to k do\n if s[a] == w[1] and s[b] == w[2] and s[c] == w[3] and s[d] == w[4] then\n inversions = 0\n if a > b then inversions = inversions + 1\n if a > c then inversions = inversions + 1\n if a > d then inversions = inversions + 1\n if b > c then inversions = inversions + 1\n if b > d then inversions = inversions + 1\n if c > d then inversions = inversions + 1\n if inversions < best then\n best = inversions\n</code></pre><p>At the end you should choose the problem with the smallest value of <span class=\"tex-span\"><i>best</i></span> and print the answer in the corresponding form.</p><h4>Problem A(div 1)/C(div 2) — Clear Symmetry</h4><p>It's interesting that originally the authors had an idea not to include the <span class=\"tex-span\"><i>x</i> = 3</span> case into pretests. Imagine the number of successful hacking attempts in this contest -- considering the fact that none of the first <span class=\"tex-span\">43</span> solutions to this problem passed pretests :)</p><p>Note that the sought <span class=\"tex-span\"><i>n</i></span> is always an odd number. Indeed, if <span class=\"tex-span\"><i>n</i></span> is even, then two central rows of matrix <span class=\"tex-span\"><i>A</i></span> must contain zeroes, otherwise there will exist two neighbouring cells containing ones. Similar restriction applies to two central columns of matrix <span class=\"tex-span\"><i>A</i></span>. Replacing two central rows with just one and two central columns with just one and leaving zeroes in them, we'll obtain a smaller matrix with the same sharpness.</p><p>Note that the sharpness of a matrix with side <span class=\"tex-span\"><i>n</i></span> can't exceed <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/29339c11035e78ed5bb390f53fca8a4e181b9763.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. It's easy to see that it's possible to lay out <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/bc43d746f4c6ffc36753a0a47e2f2ded6b54cfcc.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> "domino pieces" <span class=\"tex-span\">1</span> by <span class=\"tex-span\">2</span> without intersections on a field with side <span class=\"tex-span\"><i>n</i></span> (in other words, all cells except one can be divided into pairs so that each pair contains neighbouring cells). Then there can be at most one one in the cells under each "domino piece" in the corresponding matrix. Therefore, the total number of ones doesn't exceed <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/cded2e926e2c933336187862768cb391b40c5f15.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Note that a matrix with side <span class=\"tex-span\"><i>n</i></span> and sharpness <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/29339c11035e78ed5bb390f53fca8a4e181b9763.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> exists for an odd <span class=\"tex-span\"><i>n</i></span>. Paint all cells of the matrix in chess order and put ones into black cells and zeroes into white cells. It's easy to see that such a matrix is both clear and symmetrical and has sharpenss exactly <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/29339c11035e78ed5bb390f53fca8a4e181b9763.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />.</p><p>Intuitively it seems that if there exists a matrix with sharpness <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/29339c11035e78ed5bb390f53fca8a4e181b9763.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> there should also exist a matrix with every smaller sharpness. That's correct except only one case -- there doesn't exist a matrix with side <span class=\"tex-span\">3</span> and sharpness <span class=\"tex-span\">3</span>, though there exists a matrix with side <span class=\"tex-span\">3</span> and sharpness <span class=\"tex-span\">5</span>.</p><p>Let's show that the claim above is correct for odd <span class=\"tex-span\"><i>n</i> ≥ 5</span>. We'll build a matrix with sharpness <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/29339c11035e78ed5bb390f53fca8a4e181b9763.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> as shown above and gradually turn ones into zeroes reducing the sharpness. Cells containing ones in the matrix can be divided into three types.</p><p>The first type is the central cell. The number in it can be turned into zero and the matrix won't stop satisfying the required conditions.</p><p>The second type is the cells in the central row and the central column (except central cell). Such cells are divided into pairs by the condition of symmetry -- if we turn the number in one of them into zero, we should turn the number in its pair cell into zero as well.</p><p>The third type is all the other cells. Such cells are divided into groups of four by the condition of symmetry -- if we turn the number in one of them into zero, we should turn the number in all cells from this group into zero as well.</p><p>Now for obtaining the required sharpness of <span class=\"tex-span\"><i>x</i></span> we'll act greedily. Let's turn ones into zeroes in third type cells by four until the current shapness exceeds <span class=\"tex-span\"><i>x</i></span> by less than <span class=\"tex-span\">4</span> or there are no third type cells with ones remaining. After that let's turn ones into zeroes in second type cells by pairs while the current sharpness exceeds <span class=\"tex-span\"><i>x</i></span> by at least <span class=\"tex-span\">2</span>. At this moment the sharpness of our matrix is either <span class=\"tex-span\"><i>x</i></span> or <span class=\"tex-span\"><i>x</i> + 1</span>. If it's equal to <span class=\"tex-span\"><i>x</i> + 1</span>, let's put a zero into the central cell and obtain a matrix with sharpness <span class=\"tex-span\"><i>x</i></span>. It's easy to check that we'll be able to obtain a matrix with any sharpness acting this way.</p><p>Why is this reasoning incorrect for <span class=\"tex-span\"><i>n</i> = 3</span>? Because second type cells are absent in the matrix with sharpness <span class=\"tex-span\">5</span> obtained from chess coloring. For <span class=\"tex-span\"><i>n</i> ≥ 5</span> this matrix contains cells of all types, which is important for the algorithm above. It's better to find the answers for <span class=\"tex-span\"><i>x</i> ≤ 5</span> by hand but carefully -- for example, a lot of contestants decided that the answer for <span class=\"tex-span\"><i>x</i> = 2</span> is <span class=\"tex-span\">5</span> instead of <span class=\"tex-span\">3</span>.</p><h4>Problem В(div 1)/D(div 2) — Guess That Car!</h4><p>We need to find such <span class=\"tex-span\"><i>x</i></span> and <span class=\"tex-span\"><i>y</i></span> that the value of <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/12f5e2c2b15380b5464758dd9c8ee104cf388f69.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> is minimum possible. This expression can be rewritten as <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1e4b823733b6d1a3db89b85706493660f92f138c.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Note that the first part doesn't depend on <span class=\"tex-span\"><i>y</i></span> and the second part doesn't depend on <span class=\"tex-span\"><i>x</i></span>, so we can minimize these parts separately. Here is how to minimize <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/2aee18a22eec4ec62732f8060f16e7f01e55a116.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, the second part is minimized similarly. As the expression in the brackets doesn't depend on <span class=\"tex-span\"><i>j</i></span>, this part can be rewritten as <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/cc8b9e3b9923d6db49ad42a39bf4afc277d274f5.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />, where <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/1bf48b459a61e67bd79ad7ffac7105b834eee703.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" />. Now it's enough to calculate the required value for all possible values of <span class=\"tex-span\"><i>x</i></span> and choose <span class=\"tex-span\"><i>x</i></span> for which this value is the smallest. The optimal value of <span class=\"tex-span\"><i>y</i></span> can be found similarly.</p><p>The overall complexity of this solution is <span class=\"tex-span\"><i>O</i>(<i>n</i>·<i>m</i> + <i>n</i><sup class=\"upper-index\">2</sup> + <i>m</i><sup class=\"upper-index\">2</sup>)</span>.</p><p>As the objective function is convex, other approaches to this problem are possible, for example, ternary search, gradient descent or analytical approach (calculation of derivatives).</p><p>The main hero of this problem is <a class=\"rated-user user-orange\" href=\"/profile/Ra16bit\" title=\"Master Ra16bit\">Ra16bit</a>.</p><h4>Problem С(div 1)/E(div 2) — Fragile Bridges</h4><p>There are a few different ways to solve this problem, the editorial contains one of them.</p><p>For any solution the following fact is useful. Suppose the sought path starts on platform <span class=\"tex-span\"><i>i</i></span> and ends on platform <span class=\"tex-span\"><i>j</i></span> (<span class=\"tex-span\"><i>i</i> ≤ <i>j</i></span>, if that's not the case, we can reverse the path). Then all bridges between platforms <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>j</i></span> will be passed through an odd number of times, and all other bridges will be passed through an even number of times.</p><p>Let's find the maximum length of a path with its ends on platforms <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>j</i></span>. To do that, let's find the following auxiliary values for each platform: <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i></sub></span> -- the maximum length of a path starting and ending on platform <span class=\"tex-span\"><i>i</i></span> and passing only through bridges to the left of platform <span class=\"tex-span\"><i>i</i></span>; <span class=\"tex-span\"><i>right</i><sub class=\"lower-index\"><i>j</i></sub></span> -- similarly for bridges to the right of platform <span class=\"tex-span\"><i>j</i></span>. Also for each bridge define <span class=\"tex-span\"><i>odd</i><sub class=\"lower-index\"><i>i</i></sub></span> as the largest odd number not larger than <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i></sub></span>, and for each platform define <span class=\"tex-span\"><i>sumOdd</i><sub class=\"lower-index\"><i>i</i></sub></span> as the sum of <span class=\"tex-span\"><i>odd</i><sub class=\"lower-index\"><i>j</i></sub></span> for all bridges to the left of platform <span class=\"tex-span\"><i>i</i></span>.</p><p>Then the maximum length of a path with its ends on platforms <span class=\"tex-span\"><i>i</i></span> and <span class=\"tex-span\"><i>j</i></span> is equal to <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i></sub> + <i>right</i><sub class=\"lower-index\"><i>j</i></sub> + (<i>sumOdd</i><sub class=\"lower-index\"><i>j</i></sub> - <i>sumOdd</i><sub class=\"lower-index\"><i>i</i></sub>)</span>, or, which is the same, <span class=\"tex-span\">(<i>right</i><sub class=\"lower-index\"><i>j</i></sub> + <i>sumOdd</i><sub class=\"lower-index\"><i>j</i></sub>) + (<i>left</i><sub class=\"lower-index\"><i>i</i></sub> - <i>sumOdd</i><sub class=\"lower-index\"><i>i</i></sub>)</span>.</p><p>Now we can find the pair <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> for which this value is the largest in linear time. Let's loop over <span class=\"tex-span\"><i>j</i></span>. From the formula it's obvious that we should find such <span class=\"tex-span\"><i>i</i> ≤ <i>j</i></span> that <span class=\"tex-span\">(<i>left</i><sub class=\"lower-index\"><i>i</i></sub> - <i>sum</i><sub class=\"lower-index\"><i>Odd</i></sub><sub class=\"lower-index\"><i>i</i></sub>)</span> is the largest. If we loop over <span class=\"tex-span\"><i>j</i></span> from <span class=\"tex-span\">1</span> to <span class=\"tex-span\"><i>n</i></span>, we can maintain the largest value of this expression for all <span class=\"tex-span\"><i>i</i> ≤ <i>j</i></span> and recalculate it when moving to the next <span class=\"tex-span\"><i>j</i></span>, comparing <span class=\"tex-span\">(<i>left</i><sub class=\"lower-index\"><i>j</i></sub> - <i>sumOdd</i><sub class=\"lower-index\"><i>j</i></sub>)</span> with the current maximum and possibly updating this maximum. This way for each <span class=\"tex-span\"><i>j</i></span> we have to check only one value of <span class=\"tex-span\"><i>i</i></span> and not all <span class=\"tex-span\"><i>i</i> ≤ <i>j</i></span>.</p><p>The last thing to show is how to find all <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i></sub></span> quickly (all <span class=\"tex-span\"><i>right</i><sub class=\"lower-index\"><i>j</i></sub></span> can be found similarly). Clearly <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\">1</sub> = 0</span>, then we'll calculate <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i></sub></span> using <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i> - 1</sub></span>. Note that when <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub> = 1</span>, we have <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i></sub> = 0</span> as after passing the bridge to platform <span class=\"tex-span\">(<i>i</i> - 1)</span> this bridge will collapse and it will be impossible to return to platform <span class=\"tex-span\"><i>i</i></span>. If <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub> > 1</span>, then <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i></sub> = <i>left</i><sub class=\"lower-index\"><i>i</i> - 1</sub> + <i>even</i><sub class=\"lower-index\"><i>i</i> - 1</sub></span>, where <span class=\"tex-span\"><i>even</i><sub class=\"lower-index\"><i>i</i> - 1</sub></span> is the largest even number not larger than <span class=\"tex-span\"><i>a</i><sub class=\"lower-index\"><i>i</i> - 1</sub></span>. Indeed, we can move to platform <span class=\"tex-span\">(<i>i</i> - 1)</span>, then move along the path corresponding to <span class=\"tex-span\"><i>left</i><sub class=\"lower-index\"><i>i</i> - 1</sub></span>, and then move along the bridge between platforms <span class=\"tex-span\">(<i>i</i> - 1)</span> and <span class=\"tex-span\"><i>i</i></span> until the limit on the number of transitions is less than <span class=\"tex-span\">2</span> (finishing on platform <span class=\"tex-span\"><i>i</i></span>).</p><p>The overall complexity of this solution is <span class=\"tex-span\"><i>O</i>(<i>n</i>)</span>.</p><h4>Problem D(div 1) — Brand New Problem</h4><p>The first solution coming to mind is dynamic programming <span class=\"tex-span\"><i>f</i>[<i>i</i>][<i>j</i>] = </span> (the smallest possible number of inversions to the moment if among the first <span class=\"tex-span\"><i>j</i></span> words of the archive problem we've found a permutation of words included in bitmask <span class=\"tex-span\"><i>i</i></span>). In this solution parameter <span class=\"tex-span\"><i>j</i></span> varies from <span class=\"tex-span\">0</span> to <span class=\"tex-span\">500000</span>, parameter <span class=\"tex-span\"><i>i</i></span> varies from <span class=\"tex-span\">0</span> to <span class=\"tex-span\">2<sup class=\"upper-index\">15</sup> - 1</span> and calculation of each value is possible in <span class=\"tex-span\"><i>O</i>(1)</span> (we are either using the current word in the subsequence or not). That's too much.</p><p>Let's make use of a standard technique: make the value of DP a new parameter and make one of the existing parameters the value of DP. Not for every DP this is possible, but at least it's possible for this one :)</p><p>It's clear that with a fixed subset of words and a fixed number of inversions it's optimal to choose the first occurrences of these words giving this number of inversions. Let <span class=\"tex-span\"><i>f</i>[<i>i</i>][<i>j</i>] = </span> (the smallest number <span class=\"tex-span\"><i>z</i></span> such that among first <span class=\"tex-span\"><i>z</i></span> words of the archive problem there exists a permutation of words from bitmask <span class=\"tex-span\"><i>i</i></span> containing exactly <span class=\"tex-span\"><i>j</i></span> inversions). The basis of this DP is <span class=\"tex-span\"><i>f</i>[0][0] = 0</span>, <span class=\"tex-span\"><i>f</i>[0][<i>j</i>] = ∞</span> for <span class=\"tex-span\"><i>j</i> > 0</span>. Recalculation of values happens in the following way: loop over a word <span class=\"tex-span\"><i>q</i></span> from the bitmask <span class=\"tex-span\"><i>i</i></span> which was the last in the permutation. With the knowledge of this word and the number of inversions <span class=\"tex-span\"><i>j</i></span> it's easy to find how many inversions <span class=\"tex-span\"><i>j</i>'</span> there were without this word — that's <span class=\"tex-span\"><i>j</i></span> minus the number of words in the mask which appeared later in Lesha's problem than word <span class=\"tex-span\"><i>q</i></span>. Let <span class=\"tex-span\"><i>p</i> = <i>f</i>[<i>i</i>^(1«<i>q</i>)][<i>j</i>']</span>. Then we should consider <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">2</sub></span> equal to the position of the next occurrence of word <span class=\"tex-span\"><i>q</i></span> after position <span class=\"tex-span\"><i>p</i></span> as a possible value for <span class=\"tex-span\"><i>f</i>[<i>i</i>][<i>j</i>]</span>. To find <span class=\"tex-span\"><i>p</i><sub class=\"lower-index\">2</sub></span> quickly we should fill an array <span class=\"tex-span\"><i>next</i>[500010][15]</span> so that <span class=\"tex-span\"><i>next</i>[<i>i</i>][<i>j</i>] = </span> (the smallest position <span class=\"tex-span\"><i>k</i> > <i>i</i></span> such that the <span class=\"tex-span\"><i>k</i></span>-th word in the archive problem equals the <span class=\"tex-span\"><i>j</i></span>-th word in Lesha's problem) for each archive problem in advance. This array can be easily filled passing from right to left once.</p><p>The total number of operations can be calculated as <span class=\"tex-span\"><i>m</i>·(<i>k</i>·<i>n</i> + 2<sup class=\"upper-index\"><i>n</i></sup>·<i>C</i><sub class=\"lower-index\"><i>n</i></sub><sup class=\"upper-index\">2</sup>·<i>n</i>)</span>, where <span class=\"tex-span\"><i>m</i></span> is the number of problems in the archive, <span class=\"tex-span\"><i>k</i></span> is the number of words in one archive problem description and <span class=\"tex-span\"><i>n</i></span> is the number of words in Lesha's problem description. Under the given constraints that is about <span class=\"tex-span\">200</span> million operations, and the author's solutions (including a Java solution) worked for less than <span class=\"tex-span\">2</span> seconds. The time limit was set with a margin -- 5 seconds.</p><p>The main heroes of problems D(div 1) and B(div 2) are <a class=\"rated-user user-red\" href=\"/profile/Chmel_Tolstiy\" title=\"Grandmaster Chmel_Tolstiy\">Chmel_Tolstiy</a> and <a class=\"rated-user user-red\" href=\"/profile/ivan.metelsky\" title=\"Grandmaster ivan.metelsky\">ivan.metelsky</a>.</p><h4>Problem E(div 1) — Thoroughly Bureaucratic Organization</h4><p>Let's imagine that we have a magic function <span class=\"tex-span\"><i>maxN</i>(<i>m</i>, <i>k</i>)</span> that returns, given <span class=\"tex-span\"><i>m</i></span> and <span class=\"tex-span\"><i>k</i></span>, the largest value of <span class=\"tex-span\"><i>n</i></span> such that it's possible to solve the problem for <span class=\"tex-span\"><i>n</i></span> people and <span class=\"tex-span\"><i>m</i></span> empty lines in the form using <span class=\"tex-span\"><i>k</i></span> requests. Then we'll be able to use binary search on the answer -- the number of requests <span class=\"tex-span\"><i>k</i></span>.</p><p>Suppose we've made <span class=\"tex-span\"><i>k</i></span> requests. Let's match a string of length <span class=\"tex-span\"><i>k</i></span> to each person, where the <span class=\"tex-span\"><i>i</i></span>-th character is equal to <span class=\"tex-span\">1</span> if this person is mentioned in the <span class=\"tex-span\"><i>i</i></span>-th request and <span class=\"tex-span\">0</span> otherwise. Note that we'll be able to determine the exact appointment date for each person if and only if all <span class=\"tex-span\"><i>n</i></span> strings of length <span class=\"tex-span\"><i>k</i></span> are pairwise distinct. Indeed, if two persons' strings are the same, their appointment dates could be exchanged and the responses to the requests wouldn't have changed. If all strings are distinct, for each date we may find the person appointed for this date looking at the set of requests with responses containing this date and finding the person mentioned in the same set of requests.</p><p>The constraint on <span class=\"tex-span\"><i>m</i></span> empty lines in the form means that each of <span class=\"tex-span\"><i>k</i></span> positions in the strings should contain no more than <span class=\"tex-span\"><i>m</i></span> ones in all <span class=\"tex-span\"><i>n</i></span> strings overall. Thus function <span class=\"tex-span\"><i>maxN</i>(<i>m</i>, <i>k</i>)</span> should return the maximum size of a set of distinct <span class=\"tex-span\"><i>k</i></span>-bit strings meeting this condition. Let's make this restriction weaker: we'll search for a set such that the total number of ones in all <span class=\"tex-span\"><i>n</i></span> strings doesn't exceed <span class=\"tex-span\"><i>k</i>·<i>m</i></span>. As we'll prove later, the answer won't change.</p><p>With this weaker restriction the problem can be solved using a simple greedy strategy. It's obvious that strings with smaller number of ones are better. Let's loop over the number of ones <span class=\"tex-span\"><i>i</i></span> in the string from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>k</i></span> and also maintain a variable <span class=\"tex-span\"><i>t</i></span> containing the remaining number of ones (initially it's equal to <span class=\"tex-span\"><i>k</i>·<i>m</i></span>). Then at the <span class=\"tex-span\"><i>i</i></span>-th step we can take at most <img align=\"middle\" class=\"tex-formula\" src=\"https://espresso.codeforces.com/820ab484903708c5d1c1ebcef8897e17c8df16af.png\" style=\"max-width: 100.0%;max-height: 100.0%;\" /> strings containing <span class=\"tex-span\"><i>i</i></span> ones. Let's add <span class=\"tex-span\"><i>p</i></span> to the answer and subtract <span class=\"tex-span\"><i>p</i>·<i>i</i></span> from <span class=\"tex-span\"><i>t</i></span>. Note that the values of <span class=\"tex-span\"><i>C</i><sub class=\"lower-index\"><i>k</i></sub><sup class=\"upper-index\"><i>i</i></sup></span> should be calculated with care -- they can turn out to be too large, so it's important not to allow overflows.</p><p>It can be shown that the overall complexity of this algorithm is at most <span class=\"tex-span\"><i>O</i>(<i>log</i><sup class=\"upper-index\">2</sup></span> <span class=\"tex-span\"><i>n</i>)</span>.</p><p>The remaining thing is to prove the claim above. The idea of the proof below belongs to <a class=\"rated-user user-red\" href=\"/profile/rng_58\" title=\"Grandmaster rng_58\">rng_58</a> (the author's proof is notably harder).</p><p>Let's solve the problem with a greedy algorithm with the <span class=\"tex-span\"><i>k</i>·<i>m</i></span> constraint on the total number of ones. The resulting set of strings may not satisfy the restriction of <span class=\"tex-span\"><i>m</i></span> ones for each position. If it doesn't, some of the positions contain more than <span class=\"tex-span\"><i>m</i></span> ones and some contain less than <span class=\"tex-span\"><i>m</i></span> ones. Let's pick any position <span class=\"tex-span\"><i>X</i></span> containing more than <span class=\"tex-span\"><i>m</i></span> ones and any position <span class=\"tex-span\"><i>Y</i></span> containing less than <span class=\"tex-span\"><i>m</i></span> ones. Find all strings containing <span class=\"tex-span\">1</span> at <span class=\"tex-span\"><i>X</i></span> and <span class=\"tex-span\">0</span> at <span class=\"tex-span\"><i>Y</i></span> (suppose there are <span class=\"tex-span\"><i>x</i></span> such strings) and all strings containing <span class=\"tex-span\">0</span> at <span class=\"tex-span\"><i>X</i></span> and <span class=\"tex-span\">1</span> at <span class=\"tex-span\"><i>Y</i></span> (suppose there are <span class=\"tex-span\"><i>y</i></span> such strings). It's clear that <span class=\"tex-span\"><i>x</i> > <i>y</i></span>. In each of <span class=\"tex-span\"><i>x</i></span> strings we can try to put <span class=\"tex-span\">0</span> at <span class=\"tex-span\"><i>X</i></span> and <span class=\"tex-span\">1</span> at <span class=\"tex-span\"><i>Y</i></span> -- then the string we obtain will either remain unique in this set or coincide with one of those <span class=\"tex-span\"><i>y</i></span> strings (but only one). As <span class=\"tex-span\"><i>x</i> > <i>y</i></span>, for at least one of <span class=\"tex-span\"><i>x</i></span> strings the change above leaves this string unique. Let's take this string and put <span class=\"tex-span\">0</span> at <span class=\"tex-span\"><i>X</i></span> and <span class=\"tex-span\">1</span> at <span class=\"tex-span\"><i>Y</i></span>. Now position <span class=\"tex-span\"><i>X</i></span> contains one <span class=\"tex-span\">1</span> less, and position <span class=\"tex-span\"><i>Y</i></span> contains one <span class=\"tex-span\">1</span> more. It means that the total number of "extra" ones in the positions has been decreased (as <span class=\"tex-span\"><i>Y</i></span> still contains no more than <span class=\"tex-span\"><i>m</i></span> ones). Doing this operation for a needed number of times, we'll achieve our goal.</p></div>\r\n\r\n </div>\r\n\r\n\r\n <div style=\"font-size: 1.1rem;line-height: 1.1rem;padding-bottom: 0.5em;\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/paperclip-16x16.png\" style=\"vertical-align: middle;\"/> <span style=\"padding: 0 0.35em;\">Tutorial of <a href=\"/contest/201\" class=\"notice\" style=\"text-decoration: none;\">Codeforces Round 127 (Div. 1)</a> </span>\r\n </div>\r\n \r\n <script type=\"text/javascript\">\n $(document).ready(function () {\n $(\".delete-resource-link-4774-4826\").click(function() {\n var that = this;\n Codeforces.confirm(\"Are you sure you want to detach a contest?\", function () {\n $.post(\"/data/blogAndContest\", {\n action: \"detachBlogFromContest\",\n blogId: \"4774\",\n blogEntryId: \"4808\",\n contestId: $(that).attr(\"data-contestId\"),\n resourceIds: $(that).attr(\"data-resourceIds\")\n }, function(json) { \n Codeforces.reloadAndShowMessageOrShowError(json, \"Contest detached\");\n });\n }, function () {}, \"Yes\", \"No\");\n });\n });\n</script>\r\n \r\n\r\n <div style=\"font-size: 1.1rem;line-height: 11px;\">\r\n <img style=\"vertical-align: middle;\" src=\"//codeforces.org/s/81027/images/blog/tags.png\" title=\"Tags\" alt=\"Tags\"/>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=codeforces+%23127\" class=\"tag notice\" style=\"text-decoration: none;\">codeforces #127</a>,\r\n </span>\r\n <span style=\"padding: 0 0.35em;\">\r\n <a href=\"/search?query=editorial\" class=\"tag notice\" style=\"text-decoration: none;\">editorial</a>\r\n </span>\r\n </div>\r\n\r\n\n <div class=\"roundbox meta borderTopRound borderBottomRound\" style=\"\">\n <div class=\"left-meta\">\r\n <ul>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-up-4826\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/voteup.png\"\n alt=\"Vote: I like it\" title=\"Vote: I like it\"\n /></a>\n\n\n</li>\r\n <li style=\"line-height: 1.6em;\">\n\n \n <span title=\"Topic rating\" style='font-size:larger;position:relative;bottom:1px;font-weight:bold;color:green'>+88</span>\n \n</li>\r\n <li style=\"line-height: 1.6em;\"> <a href=\"#\" class=\"topic-vote-down-4826\"><img style=\"vertical-align:middle;position:relative;top:-0.2em\" src=\"//codeforces.org/s/81027/images/actions/votedown.png\"\n alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"\n /></a>\n\n\n</li>\r\n </ul>\r\n </div>\r\n\r\n\r\n <span style=\"position: relative; line-height: 1.65em; top: 0.75rem; left: 0.8em;\">\r\n </span>\r\n\r\n <div class=\"right-meta\">\r\n <ul>\r\n <li> <a href=\"/profile/Romka\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/user_16x16.png\"\n alt=\"Author\" title=\"Author\"\n /></a>\n\n\n <a href=\"/profile/Romka\">\n Romka\n </a>\n</li>\r\n <li> <img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/date_16x16.png\"\n alt=\"Publication date\" title=\"Publication date\"\n />\n\n\n \n <span class=\"format-humantime\" title=\"Jul/01/2012 11:00\">11 years ago</span>\n \n</li>\r\n <li> <a href=\"/blog/entry/4808#comments\"><img style=\"vertical-align:middle;position:relative;top:-1px\" src=\"//codeforces.org/s/81027/images/blog/comments_16x16.png\"\n alt=\"Comments\" title=\"Comments\"\n /></a>\n\n\n <a href=\"/blog/entry/4808#comments\">\n 14\n </a>\n</li>\r\n </ul>\r\n </div>\r\n\r\n <br style=\"clear:both;\"/>\r\n </div>\n\r\n\r\n<style type=\"text/css\">\r\n .comments .title {\r\n float: left;\r\n }\r\n\r\n .comments .comments-actions-div {\r\n float: right;\r\n margin-top: 3rem;\r\n margin-right: 0.5em;\r\n }\r\n\r\n .comments .comments-actions-div .separator {\r\n margin: 0 1rem;\r\n }\r\n\r\n .comments label.show-archived {\r\n }\r\n\r\n .comments label.show-archived, .comments label.show-archived * {\r\n font-size: 1.4rem !important;\r\n color: black !important;\r\n /*position: relative !important;*/\r\n /*bottom: 0.4rem !important;*/\r\n }\r\n\r\n .comments label.show-archived input {\r\n height: 1.4rem !important;\r\n width: 1.4rem !important;\r\n position: relative;\r\n top: 0.25rem;\r\n }\r\n\r\n .new-root-comment {\r\n font-size: 1.4rem !important;\r\n }\r\n</style>\r\n\r\n <div class=\"comments\" commentableId=\"4836\">\r\n <div style=\"display: flow-root\">\r\n <div class=\"title\">\r\n <img src=\"//codeforces.org/s/81027/images/icons/comments-48x48.png\" alt=\"Comments\" title=\"Comments\"\r\n style=\"position:relative;top:0.6em;\"/>\r\n <a name=\"comments\">Comments (11)</a>\r\n\r\n </div>\r\n <div class=\"comments-actions-div\">\r\n <label class=\"show-archived\">\r\n <input type=\"checkbox\"\r\n class=\"show-archived-checkbox\" \n/>\r\n Show archived\r\n </label>\r\n <span class=\"separator\">|</span>\r\n <a href=\"#\" class=\"new-root-comment\"\r\n >Write comment?</a>\r\n </div>\r\n </div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"98003\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Petar\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/32084/avatar/e7cb70581c83ffbb.jpg'/> </a>\n <div><a href=\"/profile/Petar\" title=\"Expert Petar\" class=\"rated-user user-blue\">Petar</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2012 19:59\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-98003\" href=\"?#comment-98003\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"98003\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"11\"\r\n data-commentUserId=\"32084\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+11</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-98003\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Thanks for publishing editorial! There are some mistakes in text. It seems [user:] function is broken and is not working properly so that links to users are not created. Or is it a problem from my side and other users don't have any problems with it?!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-98003 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-98003 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-98003\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"98008\" commentParentId=\"98003\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/phantom11\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/23523/avatar/db14eeb7ddf66e49.jpg'/> </a>\n <div><a href=\"/profile/phantom11\" title=\"Expert phantom11\" class=\"rated-user user-blue\">phantom11</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2012 21:41\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-98008\" href=\"?#comment-98008\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-98003\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"98008\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"23523\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-98008\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>I think there is problem in ur side because I can see the users in colors with their profile links ..Ofcourse ,Unless I am too late to answer , which I dont assume otherwise the blog author must have replied to u ..</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-98008 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-98008 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-98008\">\r\n </ul>\r\n</div>\r\n</li>\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"98009\" commentParentId=\"98003\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Romka\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/69/avatar/cccd78022d0c3c38.jpg'/> </a>\n <div><a href=\"/profile/Romka\" title=\"Grandmaster Romka\" class=\"rated-user user-red\">Romka</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/01/2012 21:49\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-98009\" href=\"?#comment-98009\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-98003\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"98009\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"14\"\r\n data-commentUserId=\"69\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:green;font-weight:bold;\">+14</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-98009\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>There is a strange bug with Codeforces Markup which has been already reported to <a class=\"rated-user user-admin\" href=\"/profile/MikeMirzayanov\" title=\"Headquarters, MikeMirzayanov\">MikeMirzayanov</a>. Anyway, I've fixed it in this blogpost by adding a couple of linebreaks :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-98009 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-98009 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-98009\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"98087\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/red_coder\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/48093/avatar/3d4e1858413d366e.jpg'/> </a>\n <div><a href=\"/profile/red_coder\" title=\"Expert red_coder\" class=\"rated-user user-blue\">red_coder</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/03/2012 10:02\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-98087\" href=\"?#comment-98087\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"98087\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"48093\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-98087\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>i am still not able to understand the solution of Div 2 problem C. Can anyone please explain me in a more detailed way. Please :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-98087 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-98087 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-98087\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"348805\" commentParentId=\"98087\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/crazy_cow\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/crazy_cow\" title=\"Pupil crazy_cow\" class=\"rated-user user-green\">crazy_cow</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Mar/15/2017 08:48\">7 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-348805\" href=\"?#comment-348805\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-98087\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"348805\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"239756\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-348805\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Can someone explain Div2- C. It is not clear for me too.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-348805 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-348805 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-348805\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"98126\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/Lord_0f_D_C0des\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/Lord_0f_D_C0des\" title=\"Pupil Lord_0f_D_C0des\" class=\"rated-user user-green\">Lord_0f_D_C0des</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/03/2012 16:45\">11 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-98126\" href=\"?#comment-98126\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"98126\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"6049\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-98126\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>anyone please tell me what following line of code is doing</p> <pre>REP(mask,(1<<15)) REP(i,15) for(j=i;j<15;j++) if(mask&(1<<j)) cost[mask][i]++;</pre><p>this line is from rng_58's solution of problem D.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-98126 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-98126 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-98126\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"249929\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/I_love_Hoang_Minh_Trang\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/57652/avatar/a794d94655d7e4bf.jpg'/> </a>\n <div><a href=\"/profile/I_love_Hoang_Minh_Trang\" title=\"Expert I_love_Hoang_Minh_Trang\" class=\"rated-user user-blue\">I_love_Hoang_Minh_Trang</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Sep/09/2015 15:14\">8 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-249929\" href=\"?#comment-249929\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"249929\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"57652\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-249929\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Another solution for E?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-249929 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-249929 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-249929\">\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"636176\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/shriganesh83\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/1442911/avatar/b296614053ce3db6.jpg'/> </a>\n <div><a href=\"/profile/shriganesh83\" title=\"Specialist shriganesh83\" class=\"rated-user user-cyan\">shriganesh83</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/04/2020 22:58\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-636176\" href=\"?#comment-636176\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"636176\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1442911\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-636176\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>If the problem can be solved by brute force why does it appear in tag of binary search and how to solve it using binary search :)</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-636176 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-636176 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-636176\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"636661\" commentParentId=\"636176\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/misaleh\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/415720/avatar/403fd58cd270fbde.jpg'/><img title='Badge of honor for supporting Codeforces on its 10th anniversary' src='//codeforces.org/s/81027/images/if_medal-bronze-blue_46108.png' style='position:absolute;bottom:-4px;right:-6px'/> </a>\n <div><a href=\"/profile/misaleh\" title=\"Expert misaleh\" class=\"rated-user user-blue\">misaleh</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jun/05/2020 17:27\">3 years ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-636661\" href=\"?#comment-636661\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-636176\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"636661\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"415720\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-636661\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>Which problem are you referring to?</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-636661 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-636661 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-636661\">\r\n <li>\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1050428\" commentParentId=\"636661\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/commonsense\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/commonsense\" title=\"Newbie commonsense\" class=\"rated-user user-gray\">commonsense</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/23/2023 14:21\">2 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1050428\" href=\"?#comment-1050428\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\"><a title=\"Parent comment\" href=\"#comment-636661\" style=\"font-size:1.2em;\">^</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1050428\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1239200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1050428\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>For <a href=\"https://codeforces.com/problemset/problem/202/A\">LLPS</a> problem!</p><p><a href=\"https://codeforces.com/blog/entry/4808?#comment-1050420\">My comment</a>!</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1050428 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1050428 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1050428\">\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n</li>\r\n </ul>\r\n</div>\r\n\r\n<div class=\"comment\">\r\n <table class=\"comment-table\"\r\n commentId=\"1050420\" commentParentId=\"-1\">\r\n <tr>\r\n <td class=\"left\">\r\n <div style=\"position: absolute; left: 0;\" class=\"comment-indent-holder\">\r\n <div class=\"comment-no-indent\">\r\n <span>»</span>\r\n </div>\r\n </div>\r\n <div class=\"avatar\">\n <a href=\"/profile/commonsense\" style=\"position: relative;\">\n<img src='https://userpic.codeforces.org/no-avatar.jpg'/> </a>\n <div><a href=\"/profile/commonsense\" title=\"Newbie commonsense\" class=\"rated-user user-gray\">commonsense</a></div>\n </div>\n </td>\r\n <td class=\"right\">\r\n <div class=\"info\">\r\n \r\n <span class=\"item\"><span class=\"format-humantime\" title=\"Jul/23/2023 14:10\">2 months ago</span>,</span>\r\n <span class=\"item\"><a title=\"Link to comment\" name=\"comment-1050420\" href=\"?#comment-1050420\" style=\"font-size:1.2em;\">#</a></span>\r\n <span class=\"item\">|</span>\r\n <span style=\"position: relative; top: 2px;\">\r\n</span>\r\n <div style=\"position:absolute;right:0;top:0;\">\r\n \r\n\r\n<span commentid=\"1050420\" class=\"CommentVoteFrame\"\r\n data-commentRating=\"0\"\r\n data-commentUserId=\"1239200\"\r\n style=\"position:relative;\"\r\n>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"1\" dd=\"x\"><img style=\"position:relative;top:3px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-voteup-blue.png\" alt=\"Vote: I like it\" title=\"Vote: I like it\"/></a>\r\n<span class=\"commentRating\"><span style=\"color:gray;font-weight:bold;\">0</span></span>\r\n<a href=\"#\" class=\"vote-for-comment\" voteDirection=\"-1\" dd=\"y\"><img style=\"position:relative;top:2px;opacity:0.35;\" src=\"//codeforces.org/s/81027/images/actions/comment-votedown-blue.png\" alt=\"Vote: I do not like it\" title=\"Vote: I do not like it\"/></a>\r\n</span>\r\n </div>\r\n </div>\r\n <div class=\"comment-content comment-content-1050420\">\r\n <div class=\"moveup\">\r\n <div class=\"ttypography\"><p>for the first question, <a href=\"https://codeforces.com/problemset/problem/202/A\">LLPS</a>, I solved it in <code>O(n)</code> but one of the tags in the question says <code>binary search</code>, I am not able to understand, how binary search can be applied in this question? Can you help?</p><p>Thanks in advance.</p></div>\r\n </div>\r\n </div>\r\n <div class=\"reply info\">\r\n <a class=\"comment-1050420 en false\" href=\"#\" style=\"text-decoration: none;\"><span class=\"arrow\">→</span></a>\r\n <a class=\"comment-1050420 en false\" href=\"#\">Reply</a>\r\n </div>\r\n </td>\r\n </tr>\r\n </table>\r\n <ul class=\"comment-children comment-1050420\">\r\n </ul>\r\n</div>\r\n <br/>\r\n\r\n<div id=\"editBox-4836\" style=\"width:50em;display:none;\">\r\n <div class=\"previewBody\" style=\"border: 1px solid #d4d4d4; margin-bottom: 0.5em; padding: 0.25em; display:none;\"> </div>\r\n <div style=\"width: 1px\"> </div>\r\n <div class=\"commentLocale\" style=\"position: relative; top: 0.5em;left:4px;display: none;\">\r\n <input type=\"radio\" name=\"locale\" value=\"en\"><span style=\"font-size: 1.2rem;position: relative; bottom: 3px;\">In English</span>\r\n <input style=\"margin-left:1em\" type=\"radio\" name=\"locale\" value=\"ru\"><span style=\"font-size: 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Guess That Car!"},"problem_statement":{"kind":"string","value":"<div class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Guess That Car!</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>A widely known among some people Belarusian sport programmer Yura possesses lots of information about cars. That is why he has been invited to participate in a game show called \"Guess That Car!\".</p><p>The game show takes place on a giant parking lot, which is <span class=\"tex-span\">4<i>n</i></span> meters long from north to south and <span class=\"tex-span\">4<i>m</i></span> meters wide from west to east. The lot has <span class=\"tex-span\"><i>n</i> + 1</span> dividing lines drawn from west to east and <span class=\"tex-span\"><i>m</i> + 1</span> dividing lines drawn from north to south, which divide the parking lot into <span class=\"tex-span\"><i>n</i>·<i>m</i></span> <span class=\"tex-span\">4</span> by <span class=\"tex-span\">4</span> meter squares. There is a car parked strictly inside each square. The dividing lines are numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>n</i></span> from north to south and from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>m</i></span> from west to east. Each square has coordinates <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> so that the square in the north-west corner has coordinates <span class=\"tex-span\">(1, 1)</span> and the square in the south-east corner has coordinates <span class=\"tex-span\">(<i>n</i>, <i>m</i>)</span>. See the picture in the notes for clarifications.</p><p>Before the game show the organizers offer Yura to occupy any of the <span class=\"tex-span\">(<i>n</i> + 1)·(<i>m</i> + 1)</span> intersection points of the dividing lines. After that he can start guessing the cars. After Yura chooses a point, he will be prohibited to move along the parking lot before the end of the game show. As Yura is a car expert, he will always guess all cars he is offered, it's just a matter of time. Yura knows that to guess each car he needs to spend time equal to the square of the euclidean distance between his point and the center of the square with this car, multiplied by some coefficient characterizing the machine's \"rarity\" (the rarer the car is, the harder it is to guess it). More formally, guessing a car with \"rarity\" <span class=\"tex-span\"><i>c</i></span> placed in a square whose center is at distance <span class=\"tex-span\"><i>d</i></span> from Yura takes <span class=\"tex-span\"><i>c</i>·<i>d</i><sup class=\"upper-index\">2</sup></span> seconds. The time Yura spends on turning his head can be neglected.</p><p>It just so happened that Yura knows the \"rarity\" of each car on the parking lot in advance. Help him choose his point so that the total time of guessing all cars is the smallest possible.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i>, <i>m</i> ≤ 1000)</span> — the sizes of the parking lot. Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> integers: the <span class=\"tex-span\"><i>j</i></span>-th number in the <span class=\"tex-span\"><i>i</i></span>-th line describes the \"rarity\" <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>c</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100000</span>) of the car that is located in the square with coordinates <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>In the first line print the minimum total time Yura needs to guess all offered cars. In the second line print two numbers <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>j</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>l</i><sub class=\"lower-index\"><i>i</i></sub> ≤ <i>n</i>, 0 ≤ <i>l</i><sub class=\"lower-index\"><i>j</i></sub> ≤ <i>m</i></span>) — the numbers of dividing lines that form a junction that Yura should choose to stand on at the beginning of the game show. If there are multiple optimal starting points, print the point with smaller <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span>. If there are still multiple such points, print the point with smaller <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>j</i></sub></span>.</p><p>Please do not use the <span class=\"tex-font-style-tt\">%lld</span> specifier to read or write 64-bit integers in С++. It is preferred to use the <span class=\"tex-font-style-tt\">cin</span>, <span class=\"tex-font-style-tt\">cout</span> streams or the <span class=\"tex-font-style-tt\">%I64d</span> specifier.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Examples</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre>2 3<br/>3 4 5<br/>3 9 1<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>392<br/>1 1<br/></pre></div><div class=\"input\"><div class=\"title\">Input</div><pre>3 4<br/>1 0 0 0<br/>0 0 3 0<br/>0 0 5 5<br/></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre>240<br/>2 3<br/></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>In the first test case the total time of guessing all cars is equal to 3·8 + 3·8 + 4·8 + 9·8 + 5·40 + 1·40 = 392.</p><p>The coordinate system of the field: </p><center> <img class=\"tex-graphics\" src=\"https://espresso.codeforces.com/8c19136945e0febce3e1e97e201988608e53a8fd.png\" style=\"max-width: 100.0%;max-height: 100.0%;\"/> </center></div></div>"},"page":{"kind":"string","value":"\r\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\">\n<html lang=\"en\">\n<head>\n <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n <meta name=\"X-Csrf-Token\" content=\"65efcc1d1da1f3070ed4c0533e99e1a4\"/>\n <meta id=\"viewport\" name=\"viewport\" content=\"width=device-width, initial-scale=0.01\"/>\n\n\n <script type=\"text/javascript\" src=\"//codeforces.org/s/73366/js/jquery-1.8.3.js\"></script>\n <script type=\"application/javascript\">\n window.locale = \"en\";\n window.standaloneContest = false;\n function adjustViewport() {\n var screenWidthPx = Math.min($(window).width(), window.screen.width);\n var siteWidthPx = 1100; // min width of site\n var ratio = Math.min(screenWidthPx / siteWidthPx, 1.0);\n var viewport = \"width=device-width, initial-scale=\" + ratio;\n $('#viewport').attr('content', viewport);\n var style = $('<style>html * { max-height: 1000000px; }</style>');\n $('html > head').append(style);\n }\n\n if ( /Android|webOS|iPhone|iPad|iPod|BlackBerry/i.test(navigator.userAgent) ) {\n adjustViewport();\n }\n\n /* Protection against trailing dot in domain. */\n let hostLength = window.location.host.length;\n if (hostLength > 1 && window.location.host[hostLength - 1] === '.') {\n window.location = window.location.protocol + \"//\" + window.location.host.substring(0, hostLength - 1);\n }\n </script>\n <meta http-equiv=\"pragma\" content=\"no-cache\">\n <meta http-equiv=\"expires\" content=\"-1\">\n <meta http-equiv=\"profileName\" content=\"j3\">\n <meta name=\"google-site-verification\" content=\"OTd2dN5x4nS4OPknPI9JFg36fKxjqY0i1PSfFPv_J90\"/>\n <meta property=\"fb:admins\" content=\"100001352546622\" />\n <meta property=\"og:image\" content=\"//codeforces.org/s/73366/images/codeforces-sponsored-by-ton.png\" />\n <link rel=\"image_src\" href=\"//codeforces.org/s/73366/images/codeforces-sponsored-by-ton.png\" />\n <meta property=\"og:title\" content=\"Problem - B - Codeforces\"/>\n <meta property=\"og:description\" content=\"\"/>\n \n <meta property=\"og:site_name\" content=\"Codeforces\"/>\n \n \n \n <meta name=\"cc\" content=\"c480cae93911e5cc326e0a6bfdc6ed965aef9be4\"/>\n \n \n <meta name=\"utc_offset\" content=\"+03:00\"/>\n <meta name=\"verify-reformal\" content=\"f56f99fd7e087fb6ccb48ef2\" />\n <title>Problem - B - Codeforces</title>\n <meta name=\"description\" content=\"Codeforces. 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class=\"problem-statement\"><div class=\"header\"><div class=\"title\">B. Guess That Car!</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>2 seconds</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file\"><div class=\"property-title\">output</div>standard output</div></div><div><p>A widely known among some people Belarusian sport programmer Yura possesses lots of information about cars. That is why he has been invited to participate in a game show called "Guess That Car!".</p><p>The game show takes place on a giant parking lot, which is <span class=\"tex-span\">4<i>n</i></span> meters long from north to south and <span class=\"tex-span\">4<i>m</i></span> meters wide from west to east. The lot has <span class=\"tex-span\"><i>n</i> + 1</span> dividing lines drawn from west to east and <span class=\"tex-span\"><i>m</i> + 1</span> dividing lines drawn from north to south, which divide the parking lot into <span class=\"tex-span\"><i>n</i>·<i>m</i></span> <span class=\"tex-span\">4</span> by <span class=\"tex-span\">4</span> meter squares. There is a car parked strictly inside each square. The dividing lines are numbered from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>n</i></span> from north to south and from <span class=\"tex-span\">0</span> to <span class=\"tex-span\"><i>m</i></span> from west to east. Each square has coordinates <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span> so that the square in the north-west corner has coordinates <span class=\"tex-span\">(1, 1)</span> and the square in the south-east corner has coordinates <span class=\"tex-span\">(<i>n</i>, <i>m</i>)</span>. See the picture in the notes for clarifications.</p><p>Before the game show the organizers offer Yura to occupy any of the <span class=\"tex-span\">(<i>n</i> + 1)·(<i>m</i> + 1)</span> intersection points of the dividing lines. After that he can start guessing the cars. After Yura chooses a point, he will be prohibited to move along the parking lot before the end of the game show. As Yura is a car expert, he will always guess all cars he is offered, it's just a matter of time. Yura knows that to guess each car he needs to spend time equal to the square of the euclidean distance between his point and the center of the square with this car, multiplied by some coefficient characterizing the machine's "rarity" (the rarer the car is, the harder it is to guess it). More formally, guessing a car with "rarity" <span class=\"tex-span\"><i>c</i></span> placed in a square whose center is at distance <span class=\"tex-span\"><i>d</i></span> from Yura takes <span class=\"tex-span\"><i>c</i>·<i>d</i><sup class=\"upper-index\">2</sup></span> seconds. The time Yura spends on turning his head can be neglected.</p><p>It just so happened that Yura knows the "rarity" of each car on the parking lot in advance. Help him choose his point so that the total time of guessing all cars is the smallest possible.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line contains two integers <span class=\"tex-span\"><i>n</i></span> and <span class=\"tex-span\"><i>m</i></span> <span class=\"tex-span\">(1 ≤ <i>n</i>, <i>m</i> ≤ 1000)</span> — the sizes of the parking lot. Each of the next <span class=\"tex-span\"><i>n</i></span> lines contains <span class=\"tex-span\"><i>m</i></span> integers: the <span class=\"tex-span\"><i>j</i></span>-th number in the <span class=\"tex-span\"><i>i</i></span>-th line describes the "rarity" <span class=\"tex-span\"><i>c</i><sub class=\"lower-index\"><i>ij</i></sub></span> (<span class=\"tex-span\">0 ≤ <i>c</i><sub class=\"lower-index\"><i>ij</i></sub> ≤ 100000</span>) of the car that is located in the square with coordinates <span class=\"tex-span\">(<i>i</i>, <i>j</i>)</span>.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>In the first line print the minimum total time Yura needs to guess all offered cars. In the second line print two numbers <span class=\"tex-span\"><i>l</i><sub class=\"lower-index\"><i>i</i></sub></span> and <span class=\"tex-span\"><i>l</i><sub class=\